A complete refactoring of TrustRegionMinimizer.
1. Break up the monolithic loop in TrustRegionMinimizer::Minimize
into a number of more easily described and analyzed subfunctions.
2. Break out the logic for evaluating the quality of a Trust Region
step into its own object - TrustRegionStepEvaluator.
Change-Id: I08580ecac074cfd74c096cb8e4880cbda3d48296
diff --git a/internal/ceres/CMakeLists.txt b/internal/ceres/CMakeLists.txt
index 3a51309..a9fee1a 100644
--- a/internal/ceres/CMakeLists.txt
+++ b/internal/ceres/CMakeLists.txt
@@ -108,6 +108,7 @@
triplet_sparse_matrix.cc
trust_region_preprocessor.cc
trust_region_minimizer.cc
+ trust_region_step_evaluator.cc
trust_region_strategy.cc
types.cc
visibility.cc
diff --git a/internal/ceres/trust_region_minimizer.cc b/internal/ceres/trust_region_minimizer.cc
index 627430c..7a4a775 100644
--- a/internal/ceres/trust_region_minimizer.cc
+++ b/internal/ceres/trust_region_minimizer.cc
@@ -1,5 +1,5 @@
// Ceres Solver - A fast non-linear least squares minimizer
-// Copyright 2015 Google Inc. All rights reserved.
+// Copyright 2016 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// Redistribution and use in source and binary forms, with or without
@@ -43,681 +43,732 @@
#include "ceres/coordinate_descent_minimizer.h"
#include "ceres/evaluator.h"
#include "ceres/file.h"
-#include "ceres/internal/eigen.h"
-#include "ceres/internal/scoped_ptr.h"
#include "ceres/line_search.h"
-#include "ceres/linear_least_squares_problems.h"
-#include "ceres/sparse_matrix.h"
#include "ceres/stringprintf.h"
-#include "ceres/trust_region_strategy.h"
#include "ceres/types.h"
#include "ceres/wall_time.h"
#include "glog/logging.h"
+// Helper macro to simplify some of the control flow.
+#define RETURN_IF_ERROR_AND_LOG(expr) \
+ do { \
+ if (!(expr)) { \
+ LOG(ERROR) << "Terminating: " << solver_summary_->message; \
+ return; \
+ } \
+ } while (0)
+
namespace ceres {
namespace internal {
-namespace {
-LineSearch::Summary DoLineSearch(const Minimizer::Options& options,
- const Vector& x,
- const Vector& gradient,
- const double cost,
- const Vector& delta,
- Evaluator* evaluator) {
- LineSearchFunction line_search_function(evaluator);
+TrustRegionMinimizer::~TrustRegionMinimizer() {}
+
+void TrustRegionMinimizer::Minimize(const Minimizer::Options& options,
+ double* parameters,
+ Solver::Summary* solver_summary) {
+ start_time_ = WallTimeInSeconds();
+ iteration_start_time_ = start_time_;
+ Init(options, parameters, solver_summary);
+ RETURN_IF_ERROR_AND_LOG(IterationZero());
+
+ // Create the TrustRegionStepEvaluator. The construction needs to be
+ // delayed to this point because we need the cost for the starting
+ // point to initialize the step evaluator.
+ step_evaluator_.reset(new TrustRegionStepEvaluator(
+ x_cost_,
+ options_.use_nonmonotonic_steps
+ ? options_.max_consecutive_nonmonotonic_steps
+ : 0));
+
+ while (FinalizeIterationAndCheckIfMinimizerCanContinue()) {
+ iteration_start_time_ = WallTimeInSeconds();
+ iteration_summary_ = IterationSummary();
+ iteration_summary_.iteration =
+ solver_summary->iterations.back().iteration + 1;
+
+ RETURN_IF_ERROR_AND_LOG(ComputeTrustRegionStep());
+ if (!iteration_summary_.step_is_valid) {
+ RETURN_IF_ERROR_AND_LOG(HandleInvalidStep());
+ continue;
+ }
+
+ if (options_.is_constrained) {
+ // Use a projected line search to enforce the bounds constraints
+ // and improve the quality of the step.
+ DoLineSearch(x_, gradient_, x_cost_, &delta_);
+ }
+
+ ComputeCandidatePointAndEvaluateCost();
+ DoInnerIterationsIfNeeded();
+
+ if (ParameterToleranceReached()) {
+ return;
+ }
+
+ if (FunctionToleranceReached()) {
+ return;
+ }
+
+ if (IsStepSuccessful()) {
+ RETURN_IF_ERROR_AND_LOG(HandleSuccessfulStep());
+ continue;
+ }
+
+ HandleUnsuccessfulStep();
+ }
+}
+
+// Initialize the minimizer, allocate working space and set some of
+// the fields in the solver_summary.
+void TrustRegionMinimizer::Init(const Minimizer::Options& options,
+ double* parameters,
+ Solver::Summary* solver_summary) {
+ options_ = options;
+ sort(options_.trust_region_minimizer_iterations_to_dump.begin(),
+ options_.trust_region_minimizer_iterations_to_dump.end());
+
+ parameters_ = parameters;
+
+ solver_summary_ = solver_summary;
+ solver_summary_->termination_type = NO_CONVERGENCE;
+ solver_summary_->num_successful_steps = 0;
+ solver_summary_->num_unsuccessful_steps = 0;
+ solver_summary_->is_constrained = options.is_constrained;
+
+ evaluator_ = CHECK_NOTNULL(options_.evaluator.get());
+ jacobian_ = CHECK_NOTNULL(options_.jacobian.get());
+ strategy_ = CHECK_NOTNULL(options_.trust_region_strategy.get());
+
+ is_not_silent_ = !options.is_silent;
+ inner_iterations_are_enabled_ =
+ options.inner_iteration_minimizer.get() != NULL;
+ inner_iterations_were_useful_ = false;
+
+ num_parameters_ = evaluator_->NumParameters();
+ num_effective_parameters_ = evaluator_->NumEffectiveParameters();
+ num_residuals_ = evaluator_->NumResiduals();
+ num_consecutive_invalid_steps_ = 0;
+
+ x_ = ConstVectorRef(parameters_, num_parameters_);
+ x_norm_ = x_.norm();
+ residuals_.resize(num_residuals_);
+ trust_region_step_.resize(num_effective_parameters_);
+ delta_.resize(num_effective_parameters_);
+ candidate_x_.resize(num_parameters_);
+ gradient_.resize(num_effective_parameters_);
+ model_residuals_.resize(num_residuals_);
+ negative_gradient_.resize(num_effective_parameters_);
+ projected_gradient_step_.resize(num_parameters_);
+
+ // By default scaling is one, if the user requests Jacobi scaling of
+ // the Jacobian, we will compute and overwrite this vector.
+ jacobian_scaling_ = Vector::Ones(num_effective_parameters_);
+
+ x_norm_ = -1; // Invalid value
+ x_cost_ = std::numeric_limits<double>::max();
+ minimum_cost_ = x_cost_;
+ model_cost_change_ = 0.0;
+}
+
+// 1. Project the initial solution onto the feasible set if needed.
+// 2. Compute the initial cost, jacobian & gradient.
+//
+// Return true if all computations can be performed successfully.
+bool TrustRegionMinimizer::IterationZero() {
+ iteration_summary_ = IterationSummary();
+ iteration_summary_.iteration = 0;
+ iteration_summary_.step_is_valid = false;
+ iteration_summary_.step_is_successful = false;
+ iteration_summary_.cost_change = 0.0;
+ iteration_summary_.gradient_max_norm = 0.0;
+ iteration_summary_.gradient_norm = 0.0;
+ iteration_summary_.step_norm = 0.0;
+ iteration_summary_.relative_decrease = 0.0;
+ iteration_summary_.eta = options_.eta;
+ iteration_summary_.linear_solver_iterations = 0;
+ iteration_summary_.step_solver_time_in_seconds = 0;
+
+ if (options_.is_constrained) {
+ delta_.setZero();
+ if (!evaluator_->Plus(x_.data(), delta_.data(), candidate_x_.data())) {
+ solver_summary_->message =
+ "Unable to project initial point onto the feasible set.";
+ solver_summary_->termination_type = FAILURE;
+ return false;
+ }
+
+ x_ = candidate_x_;
+ x_norm_ = x_.norm();
+ }
+
+ if (!EvaluateGradientAndJacobian()) {
+ return false;
+ }
+
+ solver_summary_->initial_cost = x_cost_ + solver_summary_->fixed_cost;
+ iteration_summary_.step_is_valid = true;
+ iteration_summary_.step_is_successful = true;
+ return true;
+}
+
+// For the current x_, compute
+//
+// 1. Cost
+// 2. Jacobian
+// 3. Gradient
+// 4. Scale the Jacobian if needed (and compute the scaling if we are
+// in iteration zero).
+// 5. Compute the 2 and max norm of the gradient.
+//
+// Returns true if all computations could be performed
+// successfully. Any failures are considered fatal and the
+// Solver::Summary is updated to indicate this.
+bool TrustRegionMinimizer::EvaluateGradientAndJacobian() {
+ if (!evaluator_->Evaluate(x_.data(),
+ &x_cost_,
+ residuals_.data(),
+ gradient_.data(),
+ jacobian_)) {
+ solver_summary_->message = "Residual and Jacobian evaluation failed.";
+ solver_summary_->termination_type = FAILURE;
+ return false;
+ }
+
+ iteration_summary_.cost = x_cost_ + solver_summary_->fixed_cost;
+
+ if (options_.jacobi_scaling) {
+ if (iteration_summary_.iteration == 0) {
+ // Compute a scaling vector that is used to improve the
+ // conditioning of the Jacobian.
+ //
+ // jacobian_scaling_ = diag(J'J)^{-1}
+ jacobian_->SquaredColumnNorm(jacobian_scaling_.data());
+ for (int i = 0; i < jacobian_->num_cols(); ++i) {
+ // Add one to the denominator to prevent division by zero.
+ jacobian_scaling_[i] = 1.0 / (1.0 + sqrt(jacobian_scaling_[i]));
+ }
+ }
+
+ // jacobian = jacobian * diag(J'J) ^{-1}
+ jacobian_->ScaleColumns(jacobian_scaling_.data());
+ }
+
+ // The gradient exists in the local tangent space. To account for
+ // the bounds constraints correctly, instead of just computing the
+ // norm of the gradient vector, we compute
+ //
+ // |Plus(x, -gradient) - x|
+ //
+ // Where the Plus operator lifts the negative gradient to the
+ // ambient space, adds it to x and projects it on the hypercube
+ // defined by the bounds.
+ negative_gradient_ = -gradient_;
+ if (!evaluator_->Plus(x_.data(),
+ negative_gradient_.data(),
+ projected_gradient_step_.data())) {
+ solver_summary_->message =
+ "projected_gradient_step = Plus(x, -gradient) failed.";
+ solver_summary_->termination_type = FAILURE;
+ return false;
+ }
+
+ iteration_summary_.gradient_max_norm =
+ (x_ - projected_gradient_step_).lpNorm<Eigen::Infinity>();
+ iteration_summary_.gradient_norm = (x_ - projected_gradient_step_).norm();
+ return true;
+}
+
+// 1. Add the final timing information to the iteration summary.
+// 2. Run the callbacks
+// 3. Check for termination based on
+// a. Run time
+// b. Iteration count
+// c. Max norm of the gradient
+// d. Size of the trust region radius.
+//
+// Returns true if user did not terminate the solver and none of these
+// termination criterion are met.
+bool TrustRegionMinimizer::FinalizeIterationAndCheckIfMinimizerCanContinue() {
+ if (iteration_summary_.step_is_successful) {
+ ++solver_summary_->num_successful_steps;
+ if (x_cost_ < minimum_cost_) {
+ minimum_cost_ = x_cost_;
+ VectorRef(parameters_, num_parameters_) = x_;
+ iteration_summary_.step_is_nonmonotonic = false;
+ } else {
+ iteration_summary_.step_is_nonmonotonic = true;
+ }
+ } else {
+ ++solver_summary_->num_unsuccessful_steps;
+ }
+
+ iteration_summary_.trust_region_radius = strategy_->Radius();
+ iteration_summary_.iteration_time_in_seconds =
+ WallTimeInSeconds() - iteration_start_time_;
+ iteration_summary_.cumulative_time_in_seconds =
+ WallTimeInSeconds() - start_time_ +
+ solver_summary_->preprocessor_time_in_seconds;
+
+ solver_summary_->iterations.push_back(iteration_summary_);
+
+ if (!RunCallbacks(options_, iteration_summary_, solver_summary_)) {
+ return false;
+ }
+
+ if (MaxSolverTimeReached()) {
+ return false;
+ }
+
+ if (MaxSolverIterationsReached()) {
+ return false;
+ }
+
+ if (GradientToleranceReached()) {
+ return false;
+ }
+
+ if (MinTrustRegionRadiusReached()) {
+ return false;
+ }
+
+ return true;
+}
+
+// Compute the trust region step using the TrustRegionStrategy chosen
+// by the user.
+//
+// If the strategy returns with LINEAR_SOLVER_FATAL_ERROR, which
+// indicates an unrecoverable error, return false. This is the only
+// condition that returns false.
+//
+// If the strategy returns with LINEAR_SOLVER_FAILURE, which indicates
+// a numerical failure that could be recovered from by retrying
+// (e.g. by increasing the strength of the regularization), we set
+// iteration_summary_.step_is_valid to false and return true.
+//
+// In all other cases, we compute the decrease in the trust region
+// model problem. In exact arithmetic, this should always be
+// positive, but due to numerical problems in the TrustRegionStrategy
+// or round off error when computing the decrease it may be
+// negative. In which case again, we set
+// iteration_summary_.step_is_valid to false.
+bool TrustRegionMinimizer::ComputeTrustRegionStep() {
+ const double strategy_start_time = WallTimeInSeconds();
+ iteration_summary_.step_is_valid = false;
+ TrustRegionStrategy::PerSolveOptions per_solve_options;
+ per_solve_options.eta = options_.eta;
+ if (find(options_.trust_region_minimizer_iterations_to_dump.begin(),
+ options_.trust_region_minimizer_iterations_to_dump.end(),
+ iteration_summary_.iteration) !=
+ options_.trust_region_minimizer_iterations_to_dump.end()) {
+ per_solve_options.dump_format_type =
+ options_.trust_region_problem_dump_format_type;
+ per_solve_options.dump_filename_base =
+ JoinPath(options_.trust_region_problem_dump_directory,
+ StringPrintf("ceres_solver_iteration_%03d",
+ iteration_summary_.iteration));
+ }
+
+ TrustRegionStrategy::Summary strategy_summary =
+ strategy_->ComputeStep(per_solve_options,
+ jacobian_,
+ residuals_.data(),
+ trust_region_step_.data());
+
+ if (strategy_summary.termination_type == LINEAR_SOLVER_FATAL_ERROR) {
+ solver_summary_->message =
+ "Linear solver failed due to unrecoverable "
+ "non-numeric causes. Please see the error log for clues. ";
+ solver_summary_->termination_type = FAILURE;
+ return false;
+ }
+
+ iteration_summary_.step_solver_time_in_seconds =
+ WallTimeInSeconds() - strategy_start_time;
+ iteration_summary_.linear_solver_iterations = strategy_summary.num_iterations;
+
+ if (strategy_summary.termination_type == LINEAR_SOLVER_FAILURE) {
+ return true;
+ }
+
+ // new_model_cost
+ // = 1/2 [f + J * step]^2
+ // = 1/2 [ f'f + 2f'J * step + step' * J' * J * step ]
+ // model_cost_change
+ // = cost - new_model_cost
+ // = f'f/2 - 1/2 [ f'f + 2f'J * step + step' * J' * J * step]
+ // = -f'J * step - step' * J' * J * step / 2
+ // = -(J * step)'(f + J * step / 2)
+ model_residuals_.setZero();
+ jacobian_->RightMultiply(trust_region_step_.data(), model_residuals_.data());
+ model_cost_change_ =
+ -model_residuals_.dot(residuals_ + model_residuals_ / 2.0);
+
+ // TODO(sameeragarwal)
+ //
+ // 1. What happens if model_cost_change_ = 0
+ // 2. What happens if -epsilon <= model_cost_change_ < 0 for some
+ // small epsilon due to round off error.
+ iteration_summary_.step_is_valid = (model_cost_change_ > 0.0);
+ if (iteration_summary_.step_is_valid) {
+ // Undo the Jacobian column scaling.
+ delta_ = (trust_region_step_.array() * jacobian_scaling_.array()).matrix();
+ num_consecutive_invalid_steps_ = 0;
+ }
+
+ VLOG_IF(1, is_not_silent_ && !iteration_summary_.step_is_valid)
+ << "Invalid step: current_cost: " << x_cost_
+ << " absolute model cost change: " << model_cost_change_
+ << " relative model cost change: " << (model_cost_change_ / x_cost_);
+ return true;
+}
+
+// Invalid steps can happen due to a number of reasons, and we allow a
+// limited number of consecutive failures, and return false if this
+// limit is exceeded.
+bool TrustRegionMinimizer::HandleInvalidStep() {
+ // TODO(sameeragarwal): Should we be returning FAILURE or
+ // NO_CONVERGENCE? The solution value is still usable in many cases,
+ // it is not clear if we should declare the solver a failure
+ // entirely. For example the case where model_cost_change ~ 0.0, but
+ // just slightly negative.
+ if (++num_consecutive_invalid_steps_ >=
+ options_.max_num_consecutive_invalid_steps) {
+ solver_summary_->message = StringPrintf(
+ "Number of consecutive invalid steps more "
+ "than Solver::Options::max_num_consecutive_invalid_steps: %d",
+ options_.max_num_consecutive_invalid_steps);
+ solver_summary_->termination_type = FAILURE;
+ return false;
+ }
+
+ strategy_->StepIsInvalid();
+
+ // We are going to try and reduce the trust region radius and
+ // solve again. To do this, we are going to treat this iteration
+ // as an unsuccessful iteration. Since the various callbacks are
+ // still executed, we are going to fill the iteration summary
+ // with data that assumes a step of length zero and no progress.
+ iteration_summary_.cost = x_cost_ + solver_summary_->fixed_cost;
+ iteration_summary_.cost_change = 0.0;
+ iteration_summary_.gradient_max_norm =
+ solver_summary_->iterations.back().gradient_max_norm;
+ iteration_summary_.gradient_norm =
+ solver_summary_->iterations.back().gradient_norm;
+ iteration_summary_.step_norm = 0.0;
+ iteration_summary_.relative_decrease = 0.0;
+ iteration_summary_.eta = options_.eta;
+ return true;
+}
+
+// Use the supplied coordinate descent minimizer to perform inner
+// iterations and compute the improvement due to it. Returns the cost
+// after performing the inner iterations.
+//
+// The optimization is performed with candidate_x_ as the starting
+// point, and if the optimization is successful, candidate_x_ will be
+// updated with the optimized parameters.
+void TrustRegionMinimizer::DoInnerIterationsIfNeeded() {
+ if (!inner_iterations_are_enabled_ ||
+ candidate_cost_ >= std::numeric_limits<double>::max()) {
+ return;
+ }
+
+ double inner_iteration_start_time = WallTimeInSeconds();
+ ++solver_summary_->num_inner_iteration_steps;
+ inner_iteration_x_ = candidate_x_;
+ Solver::Summary inner_iteration_summary;
+ options_.inner_iteration_minimizer->Minimize(
+ options_, inner_iteration_x_.data(), &inner_iteration_summary);
+ double inner_iteration_cost;
+ if (!evaluator_->Evaluate(
+ inner_iteration_x_.data(), &inner_iteration_cost, NULL, NULL, NULL)) {
+ VLOG_IF(2, is_not_silent_) << "Inner iteration failed.";
+ return;
+ }
+
+ VLOG_IF(2, is_not_silent_)
+ << "Inner iteration succeeded; Current cost: " << x_cost_
+ << " Trust region step cost: " << candidate_cost_
+ << " Inner iteration cost: " << inner_iteration_cost;
+
+ candidate_x_ = inner_iteration_x_;
+
+ // Normally, the quality of a trust region step is measured by
+ // the ratio
+ //
+ // cost_change
+ // r = -----------------
+ // model_cost_change
+ //
+ // All the change in the nonlinear objective is due to the trust
+ // region step so this ratio is a good measure of the quality of
+ // the trust region radius. However, when inner iterations are
+ // being used, cost_change includes the contribution of the
+ // inner iterations and its not fair to credit it all to the
+ // trust region algorithm. So we change the ratio to be
+ //
+ // cost_change
+ // r = ------------------------------------------------
+ // (model_cost_change + inner_iteration_cost_change)
+ //
+ // Practically we do this by increasing model_cost_change by
+ // inner_iteration_cost_change.
+
+ const double inner_iteration_cost_change =
+ candidate_cost_ - inner_iteration_cost;
+ model_cost_change_ += inner_iteration_cost_change;
+ inner_iterations_were_useful_ = inner_iteration_cost < x_cost_;
+ const double inner_iteration_relative_progress =
+ 1.0 - inner_iteration_cost / candidate_cost_;
+
+ // Disable inner iterations once the relative improvement
+ // drops below tolerance.
+ inner_iterations_are_enabled_ =
+ (inner_iteration_relative_progress > options_.inner_iteration_tolerance);
+ VLOG_IF(2, is_not_silent_ && !inner_iterations_are_enabled_)
+ << "Disabling inner iterations. Progress : "
+ << inner_iteration_relative_progress;
+ candidate_cost_ = inner_iteration_cost;
+
+ solver_summary_->inner_iteration_time_in_seconds +=
+ WallTimeInSeconds() - inner_iteration_start_time;
+}
+
+// Perform a projected line search to improve the objective function
+// value along delta.
+//
+// TODO(sameeragarwal): The current implementation does not do
+// anything illegal but is incorrect and not terribly effective.
+//
+// https://github.com/ceres-solver/ceres-solver/issues/187
+void TrustRegionMinimizer::DoLineSearch(const Vector& x,
+ const Vector& gradient,
+ const double cost,
+ Vector* delta) {
+ LineSearchFunction line_search_function(evaluator_);
LineSearch::Options line_search_options;
line_search_options.is_silent = true;
line_search_options.interpolation_type =
- options.line_search_interpolation_type;
- line_search_options.min_step_size = options.min_line_search_step_size;
+ options_.line_search_interpolation_type;
+ line_search_options.min_step_size = options_.min_line_search_step_size;
line_search_options.sufficient_decrease =
- options.line_search_sufficient_function_decrease;
+ options_.line_search_sufficient_function_decrease;
line_search_options.max_step_contraction =
- options.max_line_search_step_contraction;
+ options_.max_line_search_step_contraction;
line_search_options.min_step_contraction =
- options.min_line_search_step_contraction;
+ options_.min_line_search_step_contraction;
line_search_options.max_num_iterations =
- options.max_num_line_search_step_size_iterations;
+ options_.max_num_line_search_step_size_iterations;
line_search_options.sufficient_curvature_decrease =
- options.line_search_sufficient_curvature_decrease;
+ options_.line_search_sufficient_curvature_decrease;
line_search_options.max_step_expansion =
- options.max_line_search_step_expansion;
+ options_.max_line_search_step_expansion;
line_search_options.function = &line_search_function;
std::string message;
- scoped_ptr<LineSearch> line_search(
- CHECK_NOTNULL(LineSearch::Create(ceres::ARMIJO,
- line_search_options,
- &message)));
- LineSearch::Summary summary;
- line_search_function.Init(x, delta);
- line_search->Search(1.0, cost, gradient.dot(delta), &summary);
- return summary;
-}
+ scoped_ptr<LineSearch> line_search(CHECK_NOTNULL(
+ LineSearch::Create(ceres::ARMIJO, line_search_options, &message)));
+ LineSearch::Summary line_search_summary;
+ line_search_function.Init(x, *delta);
+ line_search->Search(1.0, cost, gradient.dot(*delta), &line_search_summary);
-} // namespace
+ solver_summary_->num_line_search_steps += line_search_summary.num_iterations;
+ solver_summary_->line_search_cost_evaluation_time_in_seconds +=
+ line_search_summary.cost_evaluation_time_in_seconds;
+ solver_summary_->line_search_gradient_evaluation_time_in_seconds +=
+ line_search_summary.gradient_evaluation_time_in_seconds;
+ solver_summary_->line_search_polynomial_minimization_time_in_seconds +=
+ line_search_summary.polynomial_minimization_time_in_seconds;
+ solver_summary_->line_search_total_time_in_seconds +=
+ line_search_summary.total_time_in_seconds;
-// Compute a scaling vector that is used to improve the conditioning
-// of the Jacobian.
-void TrustRegionMinimizer::EstimateScale(const SparseMatrix& jacobian,
- double* scale) const {
- jacobian.SquaredColumnNorm(scale);
- for (int i = 0; i < jacobian.num_cols(); ++i) {
- scale[i] = 1.0 / (1.0 + sqrt(scale[i]));
+ if (line_search_summary.success) {
+ *delta *= line_search_summary.optimal_step_size;
}
}
-void TrustRegionMinimizer::Init(const Minimizer::Options& options) {
- options_ = options;
- sort(options_.trust_region_minimizer_iterations_to_dump.begin(),
- options_.trust_region_minimizer_iterations_to_dump.end());
+bool TrustRegionMinimizer::MaxSolverTimeReached() {
+ const double total_solver_time =
+ WallTimeInSeconds() - start_time_ +
+ solver_summary_->preprocessor_time_in_seconds;
+ if (total_solver_time < options_.max_solver_time_in_seconds) {
+ return false;
+ }
+
+ solver_summary_->message = StringPrintf("Maximum solver time reached. "
+ "Total solver time: %e >= %e.",
+ total_solver_time,
+ options_.max_solver_time_in_seconds);
+ solver_summary_->termination_type = NO_CONVERGENCE;
+ VLOG_IF(1, is_not_silent_) << "Terminating: " << solver_summary_->message;
+ return true;
}
-void TrustRegionMinimizer::Minimize(const Minimizer::Options& options,
- double* parameters,
- Solver::Summary* summary) {
- double start_time = WallTimeInSeconds();
- double iteration_start_time = start_time;
- Init(options);
+bool TrustRegionMinimizer::MaxSolverIterationsReached() {
+ if (iteration_summary_.iteration < options_.max_num_iterations) {
+ return false;
+ }
- Evaluator* evaluator = CHECK_NOTNULL(options_.evaluator.get());
- SparseMatrix* jacobian = CHECK_NOTNULL(options_.jacobian.get());
- TrustRegionStrategy* strategy =
- CHECK_NOTNULL(options_.trust_region_strategy.get());
+ solver_summary_->message =
+ StringPrintf("Maximum number of iterations reached. "
+ "Number of iterations: %d.",
+ iteration_summary_.iteration);
- const bool is_not_silent = !options.is_silent;
+ solver_summary_->termination_type = NO_CONVERGENCE;
+ VLOG_IF(1, is_not_silent_) << "Terminating: " << solver_summary_->message;
+ return true;
+}
- // If the problem is bounds constrained, then enable the use of a
- // line search after the trust region step has been computed. This
- // line search will automatically use a projected test point onto
- // the feasible set, there by guaranteeing the feasibility of the
- // final output.
+bool TrustRegionMinimizer::GradientToleranceReached() {
+ if (!iteration_summary_.step_is_successful ||
+ iteration_summary_.gradient_max_norm > options_.gradient_tolerance) {
+ return false;
+ }
+
+ solver_summary_->message = StringPrintf(
+ "Gradient tolerance reached. "
+ "Gradient max norm: %e <= %e",
+ iteration_summary_.gradient_max_norm,
+ options_.gradient_tolerance);
+ solver_summary_->termination_type = CONVERGENCE;
+ VLOG_IF(1, is_not_silent_) << "Terminating: " << solver_summary_->message;
+ return true;
+}
+
+bool TrustRegionMinimizer::MinTrustRegionRadiusReached() {
+ if (iteration_summary_.trust_region_radius >
+ options_.min_trust_region_radius) {
+ return false;
+ }
+
+ solver_summary_->message =
+ StringPrintf("Minimum trust region radius reached. "
+ "Trust region radius: %e <= %e",
+ iteration_summary_.trust_region_radius,
+ options_.min_trust_region_radius);
+ solver_summary_->termination_type = CONVERGENCE;
+ VLOG_IF(1, is_not_silent_) << "Terminating: " << solver_summary_->message;
+ return true;
+}
+
+// Solver::Options::parameter_tolerance based convergence check.
+bool TrustRegionMinimizer::ParameterToleranceReached() {
+ iteration_summary_.step_norm = (x_ - candidate_x_).norm();
+ const double step_size_tolerance =
+ options_.parameter_tolerance * (x_norm_ + options_.parameter_tolerance);
+
+ if (iteration_summary_.step_norm > step_size_tolerance) {
+ return false;
+ }
+
+ solver_summary_->message = StringPrintf(
+ "Parameter tolerance reached. "
+ "Relative step_norm: %e <= %e.",
+ (iteration_summary_.step_norm / (x_norm_ + options_.parameter_tolerance)),
+ options_.parameter_tolerance);
+ solver_summary_->termination_type = CONVERGENCE;
+ VLOG_IF(1, is_not_silent_) << "Terminating: " << solver_summary_->message;
+ return true;
+}
+
+// Solver::Options::function_tolerance based convergence check.
+bool TrustRegionMinimizer::FunctionToleranceReached() {
+ iteration_summary_.cost_change = x_cost_ - candidate_cost_;
+ const double absolute_function_tolerance =
+ options_.function_tolerance * x_cost_;
+
+ if (fabs(iteration_summary_.cost_change) > absolute_function_tolerance) {
+ return false;
+ }
+
+ solver_summary_->message = StringPrintf(
+ "Function tolerance reached. "
+ "|cost_change|/cost: %e <= %e",
+ fabs(iteration_summary_.cost_change) / x_cost_,
+ options_.function_tolerance);
+ solver_summary_->termination_type = CONVERGENCE;
+ VLOG_IF(1, is_not_silent_) << "Terminating: " << solver_summary_->message;
+ return true;
+}
+
+// Compute candidate_x_ = Plus(x_, delta_)
+// Evaluate the cost of candidate_x_ as candidate_cost_.
+//
+// Failure to compute the step or the cost mean that candidate_cost_
+// is set to std::numeric_limits<double>::max(). Unlike
+// EvaluateGradientAndJacobian, failure in this function is not fatal
+// as we are only computing and evaluating a candidate point, and if
+// for some reason we are unable to evaluate it, we consider it to be
+// a point with very high cost. This allows the user to deal with edge
+// cases/constraints as part of the LocalParameterization and
+// CostFunction objects.
+void TrustRegionMinimizer::ComputeCandidatePointAndEvaluateCost() {
+ if (!evaluator_->Plus(x_.data(), delta_.data(), candidate_x_.data())) {
+ LOG_IF(WARNING, is_not_silent_)
+ << "x_plus_delta = Plus(x, delta) failed. "
+ << "Treating it as a step with infinite cost";
+ candidate_cost_ = std::numeric_limits<double>::max();
+ return;
+ }
+
+ if (!evaluator_->Evaluate(
+ candidate_x_.data(), &candidate_cost_, NULL, NULL, NULL)) {
+ LOG_IF(WARNING, is_not_silent_)
+ << "Step failed to evaluate. "
+ << "Treating it as a step with infinite cost";
+ candidate_cost_ = std::numeric_limits<double>::max();
+ }
+}
+
+bool TrustRegionMinimizer::IsStepSuccessful() {
+ iteration_summary_.relative_decrease =
+ step_evaluator_->StepQuality(candidate_cost_, model_cost_change_);
+
+ // In most cases, boosting the model_cost_change by the
+ // improvement caused by the inner iterations is fine, but it can
+ // be the case that the original trust region step was so bad that
+ // the resulting improvement in the cost was negative, and the
+ // change caused by the inner iterations was large enough to
+ // improve the step, but also to make relative decrease quite
+ // small.
//
- // TODO(sameeragarwal): Make line search available more generally.
- const bool use_line_search = options.is_constrained;
-
- summary->termination_type = NO_CONVERGENCE;
- summary->num_successful_steps = 0;
- summary->num_unsuccessful_steps = 0;
- summary->is_constrained = options.is_constrained;
-
- const int num_parameters = evaluator->NumParameters();
- const int num_effective_parameters = evaluator->NumEffectiveParameters();
- const int num_residuals = evaluator->NumResiduals();
-
- Vector residuals(num_residuals);
- Vector trust_region_step(num_effective_parameters);
- Vector delta(num_effective_parameters);
- Vector x_plus_delta(num_parameters);
- Vector gradient(num_effective_parameters);
- Vector model_residuals(num_residuals);
- Vector scale(num_effective_parameters);
- Vector negative_gradient(num_effective_parameters);
- Vector projected_gradient_step(num_parameters);
-
- IterationSummary iteration_summary;
- iteration_summary.iteration = 0;
- iteration_summary.step_is_valid = false;
- iteration_summary.step_is_successful = false;
- iteration_summary.cost_change = 0.0;
- iteration_summary.gradient_max_norm = 0.0;
- iteration_summary.gradient_norm = 0.0;
- iteration_summary.step_norm = 0.0;
- iteration_summary.relative_decrease = 0.0;
- iteration_summary.trust_region_radius = strategy->Radius();
- iteration_summary.eta = options_.eta;
- iteration_summary.linear_solver_iterations = 0;
- iteration_summary.step_solver_time_in_seconds = 0;
-
- VectorRef x_min(parameters, num_parameters);
- Vector x = x_min;
- // Project onto the feasible set.
- if (options.is_constrained) {
- delta.setZero();
- if (!evaluator->Plus(x.data(), delta.data(), x_plus_delta.data())) {
- summary->message =
- "Unable to project initial point onto the feasible set.";
- summary->termination_type = FAILURE;
- LOG_IF(WARNING, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
- x_min = x_plus_delta;
- x = x_plus_delta;
- }
-
- double x_norm = x.norm();
-
- // Do initial cost and Jacobian evaluation.
- double cost = 0.0;
- if (!evaluator->Evaluate(x.data(),
- &cost,
- residuals.data(),
- gradient.data(),
- jacobian)) {
- summary->message = "Residual and Jacobian evaluation failed.";
- summary->termination_type = FAILURE;
- LOG_IF(WARNING, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
-
- negative_gradient = -gradient;
- if (!evaluator->Plus(x.data(),
- negative_gradient.data(),
- projected_gradient_step.data())) {
- summary->message = "Unable to compute gradient step.";
- summary->termination_type = FAILURE;
- LOG(ERROR) << "Terminating: " << summary->message;
- return;
- }
-
- summary->initial_cost = cost + summary->fixed_cost;
- iteration_summary.cost = cost + summary->fixed_cost;
- iteration_summary.gradient_max_norm =
- (x - projected_gradient_step).lpNorm<Eigen::Infinity>();
- iteration_summary.gradient_norm = (x - projected_gradient_step).norm();
-
- if (iteration_summary.gradient_max_norm <= options.gradient_tolerance) {
- summary->message = StringPrintf("Gradient tolerance reached. "
- "Gradient max norm: %e <= %e",
- iteration_summary.gradient_max_norm,
- options_.gradient_tolerance);
- summary->termination_type = CONVERGENCE;
- VLOG_IF(1, is_not_silent) << "Terminating: " << summary->message;
-
- // Ensure that there is an iteration summary object for iteration
- // 0 in Summary::iterations.
- iteration_summary.iteration_time_in_seconds =
- WallTimeInSeconds() - iteration_start_time;
- iteration_summary.cumulative_time_in_seconds =
- WallTimeInSeconds() - start_time +
- summary->preprocessor_time_in_seconds;
- summary->iterations.push_back(iteration_summary);
- return;
- }
-
- if (options_.jacobi_scaling) {
- EstimateScale(*jacobian, scale.data());
- jacobian->ScaleColumns(scale.data());
- } else {
- scale.setOnes();
- }
-
- iteration_summary.iteration_time_in_seconds =
- WallTimeInSeconds() - iteration_start_time;
- iteration_summary.cumulative_time_in_seconds =
- WallTimeInSeconds() - start_time
- + summary->preprocessor_time_in_seconds;
- summary->iterations.push_back(iteration_summary);
-
- int num_consecutive_nonmonotonic_steps = 0;
- double minimum_cost = cost;
- double reference_cost = cost;
- double accumulated_reference_model_cost_change = 0.0;
- double candidate_cost = cost;
- double accumulated_candidate_model_cost_change = 0.0;
- int num_consecutive_invalid_steps = 0;
- bool inner_iterations_are_enabled =
- options.inner_iteration_minimizer.get() != NULL;
- while (true) {
- bool inner_iterations_were_useful = false;
- if (!RunCallbacks(options, iteration_summary, summary)) {
- return;
- }
-
- iteration_start_time = WallTimeInSeconds();
- if (iteration_summary.iteration >= options_.max_num_iterations) {
- summary->message = "Maximum number of iterations reached.";
- summary->termination_type = NO_CONVERGENCE;
- VLOG_IF(1, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
-
- const double total_solver_time = iteration_start_time - start_time +
- summary->preprocessor_time_in_seconds;
- if (total_solver_time >= options_.max_solver_time_in_seconds) {
- summary->message = "Maximum solver time reached.";
- summary->termination_type = NO_CONVERGENCE;
- VLOG_IF(1, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
-
- const double strategy_start_time = WallTimeInSeconds();
- TrustRegionStrategy::PerSolveOptions per_solve_options;
- per_solve_options.eta = options_.eta;
- if (find(options_.trust_region_minimizer_iterations_to_dump.begin(),
- options_.trust_region_minimizer_iterations_to_dump.end(),
- iteration_summary.iteration) !=
- options_.trust_region_minimizer_iterations_to_dump.end()) {
- per_solve_options.dump_format_type =
- options_.trust_region_problem_dump_format_type;
- per_solve_options.dump_filename_base =
- JoinPath(options_.trust_region_problem_dump_directory,
- StringPrintf("ceres_solver_iteration_%03d",
- iteration_summary.iteration));
- } else {
- per_solve_options.dump_format_type = TEXTFILE;
- per_solve_options.dump_filename_base.clear();
- }
-
- TrustRegionStrategy::Summary strategy_summary =
- strategy->ComputeStep(per_solve_options,
- jacobian,
- residuals.data(),
- trust_region_step.data());
-
- if (strategy_summary.termination_type == LINEAR_SOLVER_FATAL_ERROR) {
- summary->message =
- "Linear solver failed due to unrecoverable "
- "non-numeric causes. Please see the error log for clues. ";
- summary->termination_type = FAILURE;
- LOG_IF(WARNING, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
-
- iteration_summary = IterationSummary();
- iteration_summary.iteration = summary->iterations.back().iteration + 1;
- iteration_summary.step_solver_time_in_seconds =
- WallTimeInSeconds() - strategy_start_time;
- iteration_summary.linear_solver_iterations =
- strategy_summary.num_iterations;
- iteration_summary.step_is_valid = false;
- iteration_summary.step_is_successful = false;
-
- double model_cost_change = 0.0;
- if (strategy_summary.termination_type != LINEAR_SOLVER_FAILURE) {
- // new_model_cost
- // = 1/2 [f + J * step]^2
- // = 1/2 [ f'f + 2f'J * step + step' * J' * J * step ]
- // model_cost_change
- // = cost - new_model_cost
- // = f'f/2 - 1/2 [ f'f + 2f'J * step + step' * J' * J * step]
- // = -f'J * step - step' * J' * J * step / 2
- model_residuals.setZero();
- jacobian->RightMultiply(trust_region_step.data(), model_residuals.data());
- model_cost_change =
- - model_residuals.dot(residuals + model_residuals / 2.0);
-
- if (model_cost_change < 0.0) {
- VLOG_IF(1, is_not_silent)
- << "Invalid step: current_cost: " << cost
- << " absolute difference " << model_cost_change
- << " relative difference " << (model_cost_change / cost);
- } else {
- iteration_summary.step_is_valid = true;
- }
- }
-
- if (!iteration_summary.step_is_valid) {
- // Invalid steps can happen due to a number of reasons, and we
- // allow a limited number of successive failures, and return with
- // FAILURE if this limit is exceeded.
- if (++num_consecutive_invalid_steps >=
- options_.max_num_consecutive_invalid_steps) {
- summary->message = StringPrintf(
- "Number of successive invalid steps more "
- "than Solver::Options::max_num_consecutive_invalid_steps: %d",
- options_.max_num_consecutive_invalid_steps);
- summary->termination_type = FAILURE;
- LOG_IF(WARNING, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
-
- // We are going to try and reduce the trust region radius and
- // solve again. To do this, we are going to treat this iteration
- // as an unsuccessful iteration. Since the various callbacks are
- // still executed, we are going to fill the iteration summary
- // with data that assumes a step of length zero and no progress.
- iteration_summary.cost = cost + summary->fixed_cost;
- iteration_summary.cost_change = 0.0;
- iteration_summary.gradient_max_norm =
- summary->iterations.back().gradient_max_norm;
- iteration_summary.gradient_norm =
- summary->iterations.back().gradient_norm;
- iteration_summary.step_norm = 0.0;
- iteration_summary.relative_decrease = 0.0;
- iteration_summary.eta = options_.eta;
- } else {
- // The step is numerically valid, so now we can judge its quality.
- num_consecutive_invalid_steps = 0;
-
- // Undo the Jacobian column scaling.
- delta = (trust_region_step.array() * scale.array()).matrix();
-
- // Try improving the step further by using an ARMIJO line
- // search.
- //
- // TODO(sameeragarwal): What happens to trust region sizing as
- // it interacts with the line search ?
- if (use_line_search) {
- const LineSearch::Summary line_search_summary =
- DoLineSearch(options, x, gradient, cost, delta, evaluator);
-
- // Iterations inside the line search algorithm are considered
- // 'steps' in the broader context, to distinguish these inner
- // iterations from from the outer iterations of the trust
- // region minimizer The number of line search steps is the
- // total number of inner line search iterations (or steps)
- // across the entire minimization.
- summary->num_line_search_steps += line_search_summary.num_iterations;
- summary->line_search_cost_evaluation_time_in_seconds +=
- line_search_summary.cost_evaluation_time_in_seconds;
- summary->line_search_gradient_evaluation_time_in_seconds +=
- line_search_summary.gradient_evaluation_time_in_seconds;
- summary->line_search_polynomial_minimization_time_in_seconds +=
- line_search_summary.polynomial_minimization_time_in_seconds;
- summary->line_search_total_time_in_seconds +=
- line_search_summary.total_time_in_seconds;
-
- if (line_search_summary.success) {
- delta *= line_search_summary.optimal_step_size;
- }
- }
-
- double new_cost = std::numeric_limits<double>::max();
- if (evaluator->Plus(x.data(), delta.data(), x_plus_delta.data())) {
- if (!evaluator->Evaluate(x_plus_delta.data(),
- &new_cost,
- NULL,
- NULL,
- NULL)) {
- LOG_IF(WARNING, is_not_silent)
- << "Step failed to evaluate. "
- << "Treating it as a step with infinite cost";
- new_cost = std::numeric_limits<double>::max();
- }
- } else {
- LOG_IF(WARNING, is_not_silent)
- << "x_plus_delta = Plus(x, delta) failed. "
- << "Treating it as a step with infinite cost";
- }
-
- if (new_cost < std::numeric_limits<double>::max()) {
- // Check if performing an inner iteration will make it better.
- if (inner_iterations_are_enabled) {
- ++summary->num_inner_iteration_steps;
- double inner_iteration_start_time = WallTimeInSeconds();
- const double x_plus_delta_cost = new_cost;
- Vector inner_iteration_x = x_plus_delta;
- Solver::Summary inner_iteration_summary;
- options.inner_iteration_minimizer->Minimize(options,
- inner_iteration_x.data(),
- &inner_iteration_summary);
- if (!evaluator->Evaluate(inner_iteration_x.data(),
- &new_cost,
- NULL, NULL, NULL)) {
- VLOG_IF(2, is_not_silent) << "Inner iteration failed.";
- new_cost = x_plus_delta_cost;
- } else {
- x_plus_delta = inner_iteration_x;
- // Boost the model_cost_change, since the inner iteration
- // improvements are not accounted for by the trust region.
- model_cost_change += x_plus_delta_cost - new_cost;
- VLOG_IF(2, is_not_silent)
- << "Inner iteration succeeded; Current cost: " << cost
- << " Trust region step cost: " << x_plus_delta_cost
- << " Inner iteration cost: " << new_cost;
-
- inner_iterations_were_useful = new_cost < cost;
-
- const double inner_iteration_relative_progress =
- 1.0 - new_cost / x_plus_delta_cost;
- // Disable inner iterations once the relative improvement
- // drops below tolerance.
- inner_iterations_are_enabled =
- (inner_iteration_relative_progress >
- options.inner_iteration_tolerance);
- VLOG_IF(2, is_not_silent && !inner_iterations_are_enabled)
- << "Disabling inner iterations. Progress : "
- << inner_iteration_relative_progress;
- }
- summary->inner_iteration_time_in_seconds +=
- WallTimeInSeconds() - inner_iteration_start_time;
- }
- }
-
- iteration_summary.step_norm = (x - x_plus_delta).norm();
-
- // Convergence based on parameter_tolerance.
- const double step_size_tolerance = options_.parameter_tolerance *
- (x_norm + options_.parameter_tolerance);
- if (iteration_summary.step_norm <= step_size_tolerance) {
- summary->message =
- StringPrintf("Parameter tolerance reached. "
- "Relative step_norm: %e <= %e.",
- (iteration_summary.step_norm /
- (x_norm + options_.parameter_tolerance)),
- options_.parameter_tolerance);
- summary->termination_type = CONVERGENCE;
- VLOG_IF(1, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
-
- iteration_summary.cost_change = cost - new_cost;
- const double absolute_function_tolerance =
- options_.function_tolerance * cost;
- if (fabs(iteration_summary.cost_change) <= absolute_function_tolerance) {
- summary->message =
- StringPrintf("Function tolerance reached. "
- "|cost_change|/cost: %e <= %e",
- fabs(iteration_summary.cost_change) / cost,
- options_.function_tolerance);
- summary->termination_type = CONVERGENCE;
- VLOG_IF(1, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
-
- const double relative_decrease =
- iteration_summary.cost_change / model_cost_change;
-
- const double historical_relative_decrease =
- (reference_cost - new_cost) /
- (accumulated_reference_model_cost_change + model_cost_change);
-
- // If monotonic steps are being used, then the relative_decrease
- // is the usual ratio of the change in objective function value
- // divided by the change in model cost.
- //
- // If non-monotonic steps are allowed, then we take the maximum
- // of the relative_decrease and the
- // historical_relative_decrease, which measures the increase
- // from a reference iteration. The model cost change is
- // estimated by accumulating the model cost changes since the
- // reference iteration. The historical relative_decrease offers
- // a boost to a step which is not too bad compared to the
- // reference iteration, allowing for non-monotonic steps.
- iteration_summary.relative_decrease =
- options.use_nonmonotonic_steps
- ? std::max(relative_decrease, historical_relative_decrease)
- : relative_decrease;
-
- // Normally, the quality of a trust region step is measured by
- // the ratio
- //
- // cost_change
- // r = -----------------
- // model_cost_change
- //
- // All the change in the nonlinear objective is due to the trust
- // region step so this ratio is a good measure of the quality of
- // the trust region radius. However, when inner iterations are
- // being used, cost_change includes the contribution of the
- // inner iterations and its not fair to credit it all to the
- // trust region algorithm. So we change the ratio to be
- //
- // cost_change
- // r = ------------------------------------------------
- // (model_cost_change + inner_iteration_cost_change)
- //
- // In most cases this is fine, but it can be the case that the
- // change in solution quality due to inner iterations is so large
- // and the trust region step is so bad, that this ratio can become
- // quite small.
- //
- // This can cause the trust region loop to reject this step. To
- // get around this, we expicitly check if the inner iterations
- // led to a net decrease in the objective function value. If
- // they did, we accept the step even if the trust region ratio
- // is small.
- //
- // Notice that we do not just check that cost_change is positive
- // which is a weaker condition and would render the
- // min_relative_decrease threshold useless. Instead, we keep
- // track of inner_iterations_were_useful, which is true only
- // when inner iterations lead to a net decrease in the cost.
- iteration_summary.step_is_successful =
- (inner_iterations_were_useful ||
- iteration_summary.relative_decrease >
- options_.min_relative_decrease);
-
- if (iteration_summary.step_is_successful) {
- accumulated_candidate_model_cost_change += model_cost_change;
- accumulated_reference_model_cost_change += model_cost_change;
-
- if (!inner_iterations_were_useful &&
- relative_decrease <= options_.min_relative_decrease) {
- iteration_summary.step_is_nonmonotonic = true;
- VLOG_IF(2, is_not_silent)
- << "Non-monotonic step! "
- << " relative_decrease: "
- << relative_decrease
- << " historical_relative_decrease: "
- << historical_relative_decrease;
- }
- }
- }
-
- if (iteration_summary.step_is_successful) {
- ++summary->num_successful_steps;
- strategy->StepAccepted(iteration_summary.relative_decrease);
-
- x = x_plus_delta;
- x_norm = x.norm();
-
- // Step looks good, evaluate the residuals and Jacobian at this
- // point.
- if (!evaluator->Evaluate(x.data(),
- &cost,
- residuals.data(),
- gradient.data(),
- jacobian)) {
- summary->message = "Residual and Jacobian evaluation failed.";
- summary->termination_type = FAILURE;
- LOG_IF(WARNING, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
-
- negative_gradient = -gradient;
- if (!evaluator->Plus(x.data(),
- negative_gradient.data(),
- projected_gradient_step.data())) {
- summary->message =
- "projected_gradient_step = Plus(x, -gradient) failed.";
- summary->termination_type = FAILURE;
- LOG(ERROR) << "Terminating: " << summary->message;
- return;
- }
-
- iteration_summary.gradient_max_norm =
- (x - projected_gradient_step).lpNorm<Eigen::Infinity>();
- iteration_summary.gradient_norm = (x - projected_gradient_step).norm();
-
- if (options_.jacobi_scaling) {
- jacobian->ScaleColumns(scale.data());
- }
-
- // Update the best, reference and candidate iterates.
- //
- // Based on algorithm 10.1.2 (page 357) of "Trust Region
- // Methods" by Conn Gould & Toint, or equations 33-40 of
- // "Non-monotone trust-region algorithms for nonlinear
- // optimization subject to convex constraints" by Phil Toint,
- // Mathematical Programming, 77, 1997.
- if (cost < minimum_cost) {
- // A step that improves solution quality was found.
- x_min = x;
- minimum_cost = cost;
- // Set the candidate iterate to the current point.
- candidate_cost = cost;
- num_consecutive_nonmonotonic_steps = 0;
- accumulated_candidate_model_cost_change = 0.0;
- } else {
- ++num_consecutive_nonmonotonic_steps;
- if (cost > candidate_cost) {
- // The current iterate is has a higher cost than the
- // candidate iterate. Set the candidate to this point.
- VLOG_IF(2, is_not_silent)
- << "Updating the candidate iterate to the current point.";
- candidate_cost = cost;
- accumulated_candidate_model_cost_change = 0.0;
- }
-
- // At this point we have made too many non-monotonic steps and
- // we are going to reset the value of the reference iterate so
- // as to force the algorithm to descend.
- //
- // This is the case because the candidate iterate has a value
- // greater than minimum_cost but smaller than the reference
- // iterate.
- if (num_consecutive_nonmonotonic_steps ==
- options.max_consecutive_nonmonotonic_steps) {
- VLOG_IF(2, is_not_silent)
- << "Resetting the reference point to the candidate point";
- reference_cost = candidate_cost;
- accumulated_reference_model_cost_change =
- accumulated_candidate_model_cost_change;
- }
- }
- } else {
- ++summary->num_unsuccessful_steps;
- if (iteration_summary.step_is_valid) {
- strategy->StepRejected(iteration_summary.relative_decrease);
- } else {
- strategy->StepIsInvalid();
- }
- }
-
- iteration_summary.cost = cost + summary->fixed_cost;
- iteration_summary.trust_region_radius = strategy->Radius();
- iteration_summary.iteration_time_in_seconds =
- WallTimeInSeconds() - iteration_start_time;
- iteration_summary.cumulative_time_in_seconds =
- WallTimeInSeconds() - start_time
- + summary->preprocessor_time_in_seconds;
- summary->iterations.push_back(iteration_summary);
-
- // If the step was successful, check for the gradient norm
- // collapsing to zero, and if the step is unsuccessful then check
- // if the trust region radius has collapsed to zero.
- //
- // For correctness (Number of IterationSummary objects, correct
- // final cost, and state update) these convergence tests need to
- // be performed at the end of the iteration.
- if (iteration_summary.step_is_successful) {
- // Gradient norm can only go down in successful steps.
- if (iteration_summary.gradient_max_norm <= options.gradient_tolerance) {
- summary->message = StringPrintf("Gradient tolerance reached. "
- "Gradient max norm: %e <= %e",
- iteration_summary.gradient_max_norm,
- options_.gradient_tolerance);
- summary->termination_type = CONVERGENCE;
- VLOG_IF(1, is_not_silent) << "Terminating: " << summary->message;
- return;
- }
- } else {
- // Trust region radius can only go down if the step if
- // unsuccessful.
- if (iteration_summary.trust_region_radius <
- options_.min_trust_region_radius) {
- summary->message = "Termination. Minimum trust region radius reached.";
- summary->termination_type = CONVERGENCE;
- VLOG_IF(1, is_not_silent) << summary->message;
- return;
- }
- }
- }
+ // This can cause the trust region loop to reject this step. To
+ // get around this, we expicitly check if the inner iterations
+ // led to a net decrease in the objective function value. If
+ // they did, we accept the step even if the trust region ratio
+ // is small.
+ //
+ // Notice that we do not just check that cost_change is positive
+ // which is a weaker condition and would render the
+ // min_relative_decrease threshold useless. Instead, we keep
+ // track of inner_iterations_were_useful, which is true only
+ // when inner iterations lead to a net decrease in the cost.
+ return (inner_iterations_were_useful_ ||
+ iteration_summary_.relative_decrease >
+ options_.min_relative_decrease);
}
+bool TrustRegionMinimizer::HandleSuccessfulStep() {
+ x_ = candidate_x_;
+ x_norm_ = x_.norm();
+
+ if (!EvaluateGradientAndJacobian()) {
+ return false;
+ }
+
+ iteration_summary_.step_is_successful = true;
+ strategy_->StepAccepted(iteration_summary_.relative_decrease);
+ step_evaluator_->StepAccepted(candidate_cost_, model_cost_change_);
+ return true;
+}
+
+void TrustRegionMinimizer::HandleUnsuccessfulStep() {
+ iteration_summary_.step_is_successful = false;
+ strategy_->StepRejected(iteration_summary_.relative_decrease);
+ iteration_summary_.cost = candidate_cost_ + solver_summary_->fixed_cost;
+}
} // namespace internal
} // namespace ceres
diff --git a/internal/ceres/trust_region_minimizer.h b/internal/ceres/trust_region_minimizer.h
index ed52c26..ac4a6ed 100644
--- a/internal/ceres/trust_region_minimizer.h
+++ b/internal/ceres/trust_region_minimizer.h
@@ -1,5 +1,5 @@
// Ceres Solver - A fast non-linear least squares minimizer
-// Copyright 2015 Google Inc. All rights reserved.
+// Copyright 2016 Google Inc. All rights reserved.
// http://ceres-solver.org/
//
// Redistribution and use in source and binary forms, with or without
@@ -31,35 +31,106 @@
#ifndef CERES_INTERNAL_TRUST_REGION_MINIMIZER_H_
#define CERES_INTERNAL_TRUST_REGION_MINIMIZER_H_
+#include "ceres/internal/eigen.h"
+#include "ceres/internal/scoped_ptr.h"
#include "ceres/minimizer.h"
#include "ceres/solver.h"
+#include "ceres/sparse_matrix.h"
+#include "ceres/trust_region_step_evaluator.h"
+#include "ceres/trust_region_strategy.h"
#include "ceres/types.h"
namespace ceres {
namespace internal {
-// Generic trust region minimization algorithm. The heavy lifting is
-// done by a TrustRegionStrategy object passed in as part of options.
+// Generic trust region minimization algorithm.
//
// For example usage, see SolverImpl::Minimize.
class TrustRegionMinimizer : public Minimizer {
public:
- ~TrustRegionMinimizer() {}
+ ~TrustRegionMinimizer();
+
+ // This method is not thread safe.
virtual void Minimize(const Minimizer::Options& options,
double* parameters,
- Solver::Summary* summary);
+ Solver::Summary* solver_summary);
private:
- void Init(const Minimizer::Options& options);
- void EstimateScale(const SparseMatrix& jacobian, double* scale) const;
- bool MaybeDumpLinearLeastSquaresProblem(const int iteration,
- const SparseMatrix* jacobian,
- const double* residuals,
- const double* step) const;
+ void Init(const Minimizer::Options& options,
+ double* parameters,
+ Solver::Summary* solver_summary);
+ bool IterationZero();
+ bool FinalizeIterationAndCheckIfMinimizerCanContinue();
+ bool ComputeTrustRegionStep();
+
+ bool EvaluateGradientAndJacobian();
+ void ComputeCandidatePointAndEvaluateCost();
+
+ void DoLineSearch(const Vector& x,
+ const Vector& gradient,
+ const double cost,
+ Vector* delta);
+ void DoInnerIterationsIfNeeded();
+
+ bool ParameterToleranceReached();
+ bool FunctionToleranceReached();
+ bool GradientToleranceReached();
+ bool MaxSolverTimeReached();
+ bool MaxSolverIterationsReached();
+ bool MinTrustRegionRadiusReached();
+
+ bool IsStepSuccessful();
+ void HandleUnsuccessfulStep();
+ bool HandleSuccessfulStep();
+ bool HandleInvalidStep();
Minimizer::Options options_;
+
+ // These pointers are shortcuts to objects passed to the
+ // TrustRegionMinimizer. The TrustRegionMinimizer does not own them.
+ double* parameters_;
+ Solver::Summary* solver_summary_;
+ Evaluator* evaluator_;
+ SparseMatrix* jacobian_;
+ TrustRegionStrategy* strategy_;
+
+ scoped_ptr<TrustRegionStepEvaluator> step_evaluator_;
+
+ bool is_not_silent_;
+ bool inner_iterations_are_enabled_;
+ bool inner_iterations_were_useful_;
+
+ // Summary of the current iteration.
+ IterationSummary iteration_summary_;
+
+ int num_parameters_;
+ int num_effective_parameters_;
+ int num_residuals_;
+
+ Vector delta_;
+ Vector gradient_;
+ Vector inner_iteration_x_;
+ Vector model_residuals_;
+ Vector negative_gradient_;
+ Vector projected_gradient_step_;
+ Vector residuals_;
+ Vector trust_region_step_;
+ Vector x_;
+ Vector candidate_x_;
+ Vector jacobian_scaling_;
+
+ double x_norm_;
+ double x_cost_;
+ double minimum_cost_;
+ double model_cost_change_;
+ double candidate_cost_;
+
+ double start_time_;
+ double iteration_start_time_;
+ int num_consecutive_invalid_steps_;
};
} // namespace internal
} // namespace ceres
+
#endif // CERES_INTERNAL_TRUST_REGION_MINIMIZER_H_
diff --git a/internal/ceres/trust_region_step_evaluator.cc b/internal/ceres/trust_region_step_evaluator.cc
new file mode 100644
index 0000000..c9167e6
--- /dev/null
+++ b/internal/ceres/trust_region_step_evaluator.cc
@@ -0,0 +1,107 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2016 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+// used to endorse or promote products derived from this software without
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#include <algorithm>
+#include "ceres/trust_region_step_evaluator.h"
+#include "glog/logging.h"
+
+namespace ceres {
+namespace internal {
+
+TrustRegionStepEvaluator::TrustRegionStepEvaluator(
+ const double initial_cost,
+ const int max_consecutive_nonmonotonic_steps)
+ : max_consecutive_nonmonotonic_steps_(max_consecutive_nonmonotonic_steps),
+ minimum_cost_(initial_cost),
+ current_cost_(initial_cost),
+ reference_cost_(initial_cost),
+ candidate_cost_(initial_cost),
+ accumulated_reference_model_cost_change_(0.0),
+ accumulated_candidate_model_cost_change_(0.0),
+ num_consecutive_nonmonotonic_steps_(0){
+}
+
+double TrustRegionStepEvaluator::StepQuality(
+ const double cost,
+ const double model_cost_change) const {
+ const double relative_decrease = (current_cost_ - cost) / model_cost_change;
+ const double historical_relative_decrease =
+ (reference_cost_ - cost) /
+ (accumulated_reference_model_cost_change_ + model_cost_change);
+ return std::max(relative_decrease, historical_relative_decrease);
+}
+
+void TrustRegionStepEvaluator::StepAccepted(
+ const double cost,
+ const double model_cost_change) {
+ // Algorithm 10.1.2 from Trust Region Methods by Conn, Gould &
+ // Toint.
+ //
+ // Step 3a
+ current_cost_ = cost;
+ accumulated_candidate_model_cost_change_ += model_cost_change;
+ accumulated_reference_model_cost_change_ += model_cost_change;
+
+ // Step 3b.
+ if (current_cost_ < minimum_cost_) {
+ minimum_cost_ = current_cost_;
+ num_consecutive_nonmonotonic_steps_ = 0;
+ candidate_cost_ = current_cost_;
+ accumulated_candidate_model_cost_change_ = 0.0;
+ } else {
+ // Step 3c.
+ ++num_consecutive_nonmonotonic_steps_;
+ if (current_cost_ > candidate_cost_) {
+ candidate_cost_ = current_cost_;
+ accumulated_candidate_model_cost_change_ = 0.0;
+ }
+ }
+
+ // Step 3d.
+ //
+ // At this point we have made too many non-monotonic steps and
+ // we are going to reset the value of the reference iterate so
+ // as to force the algorithm to descend.
+ //
+ // Note: In the original algorithm by Toint, this step was only
+ // executed if the step was non-monotonic, but that would not handle
+ // the case of max_consecutive_nonmonotonic_steps = 0. The small
+ // modification of doing this always handles that corner case
+ // correctly.
+ if (num_consecutive_nonmonotonic_steps_ ==
+ max_consecutive_nonmonotonic_steps_) {
+ reference_cost_ = candidate_cost_;
+ accumulated_reference_model_cost_change_ =
+ accumulated_candidate_model_cost_change_;
+ }
+}
+
+} // namespace internal
+} // namespace ceres
diff --git a/internal/ceres/trust_region_step_evaluator.h b/internal/ceres/trust_region_step_evaluator.h
new file mode 100644
index 0000000..1f14954
--- /dev/null
+++ b/internal/ceres/trust_region_step_evaluator.h
@@ -0,0 +1,98 @@
+// Ceres Solver - A fast non-linear least squares minimizer
+// Copyright 2016 Google Inc. All rights reserved.
+// http://ceres-solver.org/
+//
+// Redistribution and use in source and binary forms, with or without
+// modification, are permitted provided that the following conditions are met:
+//
+// * Redistributions of source code must retain the above copyright notice,
+// this list of conditions and the following disclaimer.
+// * Redistributions in binary form must reproduce the above copyright notice,
+// this list of conditions and the following disclaimer in the documentation
+// and/or other materials provided with the distribution.
+// * Neither the name of Google Inc. nor the names of its contributors may be
+// used to endorse or promote products derived from this software without
+// specific prior written permission.
+//
+// THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
+// AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
+// IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
+// ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
+// LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
+// CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
+// SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
+// INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
+// CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
+// ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
+// POSSIBILITY OF SUCH DAMAGE.
+//
+// Author: sameeragarwal@google.com (Sameer Agarwal)
+
+#ifndef CERES_INTERNAL_TRUST_REGION_STEP_EVALUATOR_H_
+#define CERES_INTERNAL_TRUST_REGION_STEP_EVALUATOR_H_
+
+namespace ceres {
+namespace internal {
+
+// The job of the TrustRegionStepEvaluator is to evaluate the quality
+// of a step, i.e., how the cost of a step compares with the reduction
+// in the objective of the trust region problem.
+//
+// Classic trust region methods are descent methods, in that they only
+// accept a point if it strictly reduces the value of the objective
+// function. They do this by measuring the quality of a step as
+//
+// cost_change / model_cost_change.
+//
+// Relaxing the monotonic descent requirement allows the algorithm to
+// be more efficient in the long term at the cost of some local
+// increase in the value of the objective function.
+//
+// This is because allowing for non-decreasing objective function
+// values in a principaled manner allows the algorithm to "jump over
+// boulders" as the method is not restricted to move into narrow
+// valleys while preserving its convergence properties.
+//
+// The parameter max_consecutive_nonmonotonic_steps controls the
+// window size used by the step selection algorithm to accept
+// non-monotonic steps. Setting this parameter to zero, recovers the
+// classic montonic descent algorithm.
+//
+// Based on algorithm 10.1.2 (page 357) of "Trust Region
+// Methods" by Conn Gould & Toint, or equations 33-40 of
+// "Non-monotone trust-region algorithms for nonlinear
+// optimization subject to convex constraints" by Phil Toint,
+// Mathematical Programming, 77, 1997.
+//
+// Example usage:
+//
+// TrustRegionStepEvaluator* step_evaluator = ...
+//
+// cost = ... // Compute the non-linear objective function value.
+// model_cost_change = ... // Change in the value of the trust region objective.
+// if (step_evaluator->StepQuality(cost, model_cost_change) > threshold) {
+// x = x + delta;
+// step_evaluator->StepAccepted(cost, model_cost_change);
+// }
+class TrustRegionStepEvaluator {
+ public:
+ TrustRegionStepEvaluator(double initial_cost,
+ int max_consecutive_nonmonotonic_steps);
+ double StepQuality(double cost, double model_cost_change) const;
+ void StepAccepted(double cost, double model_cost_change);
+
+ private:
+ const int max_consecutive_nonmonotonic_steps_;
+ double minimum_cost_;
+ double current_cost_;
+ double reference_cost_;
+ double candidate_cost_;
+ double accumulated_reference_model_cost_change_;
+ double accumulated_candidate_model_cost_change_;
+ int num_consecutive_nonmonotonic_steps_;
+};
+
+} // namespace internal
+} // namespace ceres
+
+#endif // CERES_INTERNAL_TRUST_REGION_STEP_EVALUATOR_H_
diff --git a/internal/ceres/trust_region_strategy.h b/internal/ceres/trust_region_strategy.h
index 9560e67..36e8e98 100644
--- a/internal/ceres/trust_region_strategy.h
+++ b/internal/ceres/trust_region_strategy.h
@@ -86,20 +86,20 @@
struct PerSolveOptions {
PerSolveOptions()
: eta(0),
- dump_filename_base(""),
dump_format_type(TEXTFILE) {
}
// Forcing sequence for inexact solves.
double eta;
+ DumpFormatType dump_format_type;
+
// If non-empty and dump_format_type is not CONSOLE, the trust
// regions strategy will write the linear system to file(s) with
// name starting with dump_filename_base. If dump_format_type is
// CONSOLE then dump_filename_base will be ignored and the linear
// system will be written to the standard error.
std::string dump_filename_base;
- DumpFormatType dump_format_type;
};
struct Summary {
