improved efficiency of diagonal damping (avoiding multiple traversal of binary tree)
Luca
parent
afb5bac2f7
commit
a6d73e8884
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@ -31,37 +31,61 @@
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using namespace std;
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namespace gtsam {
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using boost::adaptors::map_values;
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/* ************************************************************************* */
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LevenbergMarquardtParams::VerbosityLM LevenbergMarquardtParams::verbosityLMTranslator(const std::string &src) const {
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std::string s = src; boost::algorithm::to_upper(s);
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if (s == "SILENT") return LevenbergMarquardtParams::SILENT;
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if (s == "LAMBDA") return LevenbergMarquardtParams::LAMBDA;
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if (s == "TRYLAMBDA") return LevenbergMarquardtParams::TRYLAMBDA;
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if (s == "TRYCONFIG") return LevenbergMarquardtParams::TRYCONFIG;
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if (s == "TRYDELTA") return LevenbergMarquardtParams::TRYDELTA;
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if (s == "DAMPED") return LevenbergMarquardtParams::DAMPED;
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LevenbergMarquardtParams::VerbosityLM LevenbergMarquardtParams::verbosityLMTranslator(
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const std::string &src) const {
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std::string s = src;
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boost::algorithm::to_upper(s);
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if (s == "SILENT")
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return LevenbergMarquardtParams::SILENT;
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if (s == "LAMBDA")
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return LevenbergMarquardtParams::LAMBDA;
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if (s == "TRYLAMBDA")
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return LevenbergMarquardtParams::TRYLAMBDA;
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if (s == "TRYCONFIG")
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return LevenbergMarquardtParams::TRYCONFIG;
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if (s == "TRYDELTA")
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return LevenbergMarquardtParams::TRYDELTA;
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if (s == "DAMPED")
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return LevenbergMarquardtParams::DAMPED;
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/* default is silent */
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return LevenbergMarquardtParams::SILENT;
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}
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/* ************************************************************************* */
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std::string LevenbergMarquardtParams::verbosityLMTranslator(VerbosityLM value) const {
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std::string LevenbergMarquardtParams::verbosityLMTranslator(
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VerbosityLM value) const {
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std::string s;
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switch (value) {
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case LevenbergMarquardtParams::SILENT: s = "SILENT" ; break;
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case LevenbergMarquardtParams::TERMINATION: s = "TERMINATION" ; break;
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case LevenbergMarquardtParams::LAMBDA: s = "LAMBDA" ; break;
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case LevenbergMarquardtParams::TRYLAMBDA: s = "TRYLAMBDA" ; break;
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case LevenbergMarquardtParams::TRYCONFIG: s = "TRYCONFIG" ; break;
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case LevenbergMarquardtParams::TRYDELTA: s = "TRYDELTA" ; break;
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case LevenbergMarquardtParams::DAMPED: s = "DAMPED" ; break;
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default: s = "UNDEFINED" ; break;
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case LevenbergMarquardtParams::SILENT:
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s = "SILENT";
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break;
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case LevenbergMarquardtParams::TERMINATION:
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s = "TERMINATION";
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break;
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case LevenbergMarquardtParams::LAMBDA:
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s = "LAMBDA";
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break;
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case LevenbergMarquardtParams::TRYLAMBDA:
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s = "TRYLAMBDA";
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break;
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case LevenbergMarquardtParams::TRYCONFIG:
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s = "TRYCONFIG";
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break;
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case LevenbergMarquardtParams::TRYDELTA:
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s = "TRYDELTA";
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break;
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case LevenbergMarquardtParams::DAMPED:
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s = "DAMPED";
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break;
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default:
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s = "UNDEFINED";
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break;
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}
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return s;
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}
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@ -73,10 +97,12 @@ void LevenbergMarquardtParams::print(const std::string& str) const {
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std::cout << " lambdaFactor: " << lambdaFactor << "\n";
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std::cout << " lambdaUpperBound: " << lambdaUpperBound << "\n";
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std::cout << " lambdaLowerBound: " << lambdaLowerBound << "\n";
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std::cout << " disableInnerIterations: " << disableInnerIterations << "\n";
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std::cout << " disableInnerIterations: " << disableInnerIterations
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<< "\n";
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std::cout << " minModelFidelity: " << minModelFidelity << "\n";
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std::cout << " diagonalDamping: " << diagonalDamping << "\n";
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std::cout << " verbosityLM: " << verbosityLMTranslator(verbosityLM) << "\n";
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std::cout << " verbosityLM: "
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<< verbosityLMTranslator(verbosityLM) << "\n";
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std::cout.flush();
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}
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@ -86,10 +112,10 @@ GaussianFactorGraph::shared_ptr LevenbergMarquardtOptimizer::linearize() const {
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}
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/* ************************************************************************* */
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void LevenbergMarquardtOptimizer::increaseLambda(){
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if(params_.useFixedLambdaFactor_){
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void LevenbergMarquardtOptimizer::increaseLambda() {
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if (params_.useFixedLambdaFactor_) {
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state_.lambda *= params_.lambdaFactor;
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}else{
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} else {
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state_.lambda *= params_.lambdaFactor;
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params_.lambdaFactor *= 2.0;
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}
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@ -97,11 +123,11 @@ void LevenbergMarquardtOptimizer::increaseLambda(){
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}
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/* ************************************************************************* */
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void LevenbergMarquardtOptimizer::decreaseLambda(double stepQuality){
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void LevenbergMarquardtOptimizer::decreaseLambda(double stepQuality) {
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if(params_.useFixedLambdaFactor_){
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if (params_.useFixedLambdaFactor_) {
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state_.lambda /= params_.lambdaFactor;
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}else{
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} else {
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// CHECK_GT(step_quality, 0.0);
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state_.lambda *= std::max(1.0 / 3.0, 1.0 - pow(2.0 * stepQuality - 1.0, 3));
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params_.lambdaFactor = 2.0;
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@ -138,21 +164,29 @@ GaussianFactorGraph LevenbergMarquardtOptimizer::buildDampedSystem(
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double sigma = 1.0 / std::sqrt(state_.lambda);
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GaussianFactorGraph damped = linear;
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damped.reserve(damped.size() + state_.values.size());
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BOOST_FOREACH(const Values::KeyValuePair& key_value, state_.values) {
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size_t dim = key_value.value.dim();
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Matrix A = Matrix::Identity(dim, dim);
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//Replace the identity matrix with diagonal of Hessian
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if (params_.diagonalDamping){
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if (params_.diagonalDamping) {
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BOOST_FOREACH(const VectorValues::KeyValuePair& key_vector, state_.hessianDiagonal) {
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// Fill in the diagonal of A with diag(hessian)
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try {
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A.diagonal() = state_.hessianDiagonal.at(key_value.key);
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Matrix A = Eigen::DiagonalMatrix<double, Eigen::Dynamic>(state_.hessianDiagonal.at(key_vector.first));
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size_t dim = key_vector.second.size();
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Vector b = Vector::Zero(dim);
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SharedDiagonal model = noiseModel::Isotropic::Sigma(dim, sigma);
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damped += boost::make_shared<JacobianFactor>(key_vector.first, A, b, model);
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} catch (std::exception e) {
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// Don't attempt any damping if no key found in diagonal
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continue;
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}
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}
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Vector b = Vector::Zero(dim);
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SharedDiagonal model = noiseModel::Isotropic::Sigma(dim, sigma);
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damped += boost::make_shared<JacobianFactor>(key_value.key, A, b, model);
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} else {
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// Straightforward damping:
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BOOST_FOREACH(const Values::KeyValuePair& key_value, state_.values) {
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size_t dim = key_value.value.dim();
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Matrix A = Matrix::Identity(dim, dim);
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Vector b = Vector::Zero(dim);
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SharedDiagonal model = noiseModel::Isotropic::Sigma(dim, sigma);
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damped += boost::make_shared<JacobianFactor>(key_value.key, A, b, model);
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}
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}
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gttoc(damp);
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return damped;
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@ -161,20 +195,22 @@ GaussianFactorGraph LevenbergMarquardtOptimizer::buildDampedSystem(
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/* ************************************************************************* */
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void LevenbergMarquardtOptimizer::iterate() {
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gttic (LM_iterate);
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gttic(LM_iterate);
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// Pull out parameters we'll use
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const NonlinearOptimizerParams::Verbosity nloVerbosity = params_.verbosity;
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const LevenbergMarquardtParams::VerbosityLM lmVerbosity = params_.verbosityLM;
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// Linearize graph
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if(lmVerbosity >= LevenbergMarquardtParams::DAMPED) cout << "linearizing = " << endl;
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if (lmVerbosity >= LevenbergMarquardtParams::DAMPED)
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cout << "linearizing = " << endl;
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GaussianFactorGraph::shared_ptr linear = linearize();
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// Keep increasing lambda until we make make progress
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while (true) {
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if (lmVerbosity >= LevenbergMarquardtParams::TRYLAMBDA) cout << "trying lambda = " << state_.lambda << endl;
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if (lmVerbosity >= LevenbergMarquardtParams::TRYLAMBDA)
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cout << "trying lambda = " << state_.lambda << endl;
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// Build damped system for this lambda (adds prior factors that make it like gradient descent)
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GaussianFactorGraph dampedSystem = buildDampedSystem(*linear);
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@ -183,9 +219,11 @@ void LevenbergMarquardtOptimizer::iterate() {
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if (!params_.logFile.empty()) {
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ofstream os(params_.logFile.c_str(), ios::app);
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boost::posix_time::ptime currentTime = boost::posix_time::microsec_clock::universal_time();
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boost::posix_time::ptime currentTime =
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boost::posix_time::microsec_clock::universal_time();
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os << state_.totalNumberInnerIterations << "," << 1e-6 * (currentTime - state_.startTime).total_microseconds() << ","
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os << state_.totalNumberInnerIterations << ","
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<< 1e-6 * (currentTime - state_.startTime).total_microseconds() << ","
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<< state_.error << "," << state_.lambda << endl;
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}
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@ -203,44 +241,48 @@ void LevenbergMarquardtOptimizer::iterate() {
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try {
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delta = solve(dampedSystem, state_.values, params_);
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systemSolvedSuccessfully = true;
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} catch(IndeterminantLinearSystemException& e) {
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} catch (IndeterminantLinearSystemException& e) {
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systemSolvedSuccessfully = false;
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}
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if(systemSolvedSuccessfully) {
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if (systemSolvedSuccessfully) {
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params_.reuse_diagonal_ = true;
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if (lmVerbosity >= LevenbergMarquardtParams::TRYLAMBDA) cout << "linear delta norm = " << delta.norm() << endl;
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if (lmVerbosity >= LevenbergMarquardtParams::TRYDELTA) delta.print("delta");
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if (lmVerbosity >= LevenbergMarquardtParams::TRYLAMBDA)
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cout << "linear delta norm = " << delta.norm() << endl;
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if (lmVerbosity >= LevenbergMarquardtParams::TRYDELTA)
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delta.print("delta");
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// cost change in the linearized system (old - new)
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double newlinearizedError = linear->error(delta);
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double linearizedCostChange = state_.error - newlinearizedError;
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if(linearizedCostChange >= 0){ // step is valid
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if (linearizedCostChange >= 0) { // step is valid
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// update values
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gttic (retract);
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gttic(retract);
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newValues = state_.values.retract(delta);
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gttoc(retract);
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// compute new error
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gttic (compute_error);
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if(lmVerbosity >= LevenbergMarquardtParams::TRYLAMBDA) cout << "calculating error" << endl;
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gttic(compute_error);
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if (lmVerbosity >= LevenbergMarquardtParams::TRYLAMBDA)
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cout << "calculating error" << endl;
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newError = graph_.error(newValues);
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gttoc(compute_error);
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// cost change in the original, nonlinear system (old - new)
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double costChange = state_.error - newError;
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double absolute_function_tolerance = params_.relativeErrorTol * state_.error;
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double absolute_function_tolerance = params_.relativeErrorTol
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* state_.error;
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if (fabs(costChange) >= absolute_function_tolerance) {
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// fidelity of linearized model VS original system between
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if(linearizedCostChange > 1e-15){
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if (linearizedCostChange > 1e-15) {
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modelFidelity = costChange / linearizedCostChange;
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// if we decrease the error in the nonlinear system and modelFidelity is above threshold
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step_is_successful = modelFidelity > params_.minModelFidelity;
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}else{
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} else {
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step_is_successful = true; // linearizedCostChange close to zero
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}
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} else {
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@ -249,20 +291,23 @@ void LevenbergMarquardtOptimizer::iterate() {
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}
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}
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if(step_is_successful){ // we have successfully decreased the cost and we have good modelFidelity
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if (step_is_successful) { // we have successfully decreased the cost and we have good modelFidelity
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state_.values.swap(newValues);
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state_.error = newError;
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decreaseLambda(modelFidelity);
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break;
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}else if (!stopSearchingLambda){ // we failed to solved the system or we had no decrease in cost
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} else if (!stopSearchingLambda) { // we failed to solved the system or we had no decrease in cost
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if (lmVerbosity >= LevenbergMarquardtParams::TRYLAMBDA)
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cout << "increasing lambda: old error (" << state_.error << ") new error (" << newError << ")" << endl;
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cout << "increasing lambda: old error (" << state_.error
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<< ") new error (" << newError << ")" << endl;
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increaseLambda();
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// check if lambda is too big
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if(state_.lambda >= params_.lambdaUpperBound) {
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if(nloVerbosity >= NonlinearOptimizerParams::TERMINATION)
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cout << "Warning: Levenberg-Marquardt giving up because cannot decrease error with maximum lambda" << endl;
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if (state_.lambda >= params_.lambdaUpperBound) {
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if (nloVerbosity >= NonlinearOptimizerParams::TERMINATION)
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cout
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<< "Warning: Levenberg-Marquardt giving up because cannot decrease error with maximum lambda"
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<< endl;
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break;
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}
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} else { // the change in the cost is very small and it is not worth trying bigger lambdas
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@ -276,9 +321,8 @@ void LevenbergMarquardtOptimizer::iterate() {
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/* ************************************************************************* */
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LevenbergMarquardtParams LevenbergMarquardtOptimizer::ensureHasOrdering(
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LevenbergMarquardtParams params, const NonlinearFactorGraph& graph) const
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{
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if(!params.ordering)
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LevenbergMarquardtParams params, const NonlinearFactorGraph& graph) const {
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if (!params.ordering)
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params.ordering = Ordering::COLAMD(graph);
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return params;
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}
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@ -234,7 +234,7 @@ TEST(NonlinearOptimizer, NullFactor) {
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}
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/* ************************************************************************* */
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TEST(NonlinearOptimizer, MoreOptimization) {
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TEST_UNSAFE(NonlinearOptimizer, MoreOptimization) {
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NonlinearFactorGraph fg;
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fg += PriorFactor<Pose2>(0, Pose2(0, 0, 0),
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@ -284,57 +284,59 @@ TEST(NonlinearOptimizer, MoreOptimization) {
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// cout << "===================================================================================" << endl;
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// Try LM with diagonal damping
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Values initBetter = init;
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// initBetter.insert(0, Pose2(3,4,0));
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// initBetter.insert(1, Pose2(10,2,M_PI/3));
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// initBetter.insert(2, Pose2(11,7,M_PI/2));
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Values initBetter;
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initBetter.insert(0, Pose2(3,4,0));
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initBetter.insert(1, Pose2(10,2,M_PI/3));
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initBetter.insert(2, Pose2(11,7,M_PI/2));
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{
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// params.setDiagonalDamping(true);
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// LevenbergMarquardtOptimizer optimizer(fg, initBetter, params);
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//
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// // test the diagonal
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// GaussianFactorGraph::shared_ptr linear = optimizer.linearize();
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// GaussianFactorGraph damped = optimizer.buildDampedSystem(*linear);
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// VectorValues d = linear->hessianDiagonal(), //
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// expectedDiagonal = d + params.lambdaInitial * d;
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// EXPECT(assert_equal(expectedDiagonal, damped.hessianDiagonal()));
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//
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// // test convergence (does not!)
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// Values actual = optimizer.optimize();
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// EXPECT(assert_equal(expected, actual));
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//
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// // Check that the gradient is zero (it is not!)
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// linear = optimizer.linearize();
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// EXPECT(assert_equal(expectedGradient,linear->gradientAtZero()));
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//
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// // Check that the gradient is zero for damped system (it is not!)
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// damped = optimizer.buildDampedSystem(*linear);
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// VectorValues actualGradient = damped.gradientAtZero();
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// EXPECT(assert_equal(expectedGradient,actualGradient));
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//
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// // Check errors at convergence and errors in direction of gradient (decreases!)
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// EXPECT_DOUBLES_EQUAL(46.02558,fg.error(actual),1e-5);
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// EXPECT_DOUBLES_EQUAL(44.742237,fg.error(actual.retract(-0.01*actualGradient)),1e-5);
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//
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// // Check that solve yields gradient (it's not equal to gradient, as predicted)
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// VectorValues delta = damped.optimize();
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// double factor = actualGradient[0][0]/delta[0][0];
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// EXPECT(assert_equal(actualGradient,factor*delta));
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//
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// // Still pointing downhill wrt actual gradient !
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// EXPECT_DOUBLES_EQUAL( 0.1056157,dot(-1*actualGradient,delta),1e-3);
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//
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// // delta.print("This is the delta value computed by LM with diagonal damping");
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//
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// // Still pointing downhill wrt expected gradient (IT DOES NOT! actually they are perpendicular)
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// EXPECT_DOUBLES_EQUAL( 0.0,dot(-1*expectedGradient,delta),1e-5);
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//
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// // Check errors at convergence and errors in direction of solution (does not decrease!)
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// EXPECT_DOUBLES_EQUAL(46.0254859,fg.error(actual.retract(delta)),1e-5);
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//
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// // Check errors at convergence and errors at a small step in direction of solution (does not decrease!)
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// EXPECT_DOUBLES_EQUAL(46.0255,fg.error(actual.retract(0.01*delta)),1e-3);
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params.setDiagonalDamping(true);
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LevenbergMarquardtOptimizer optimizer(fg, initBetter, params);
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// test the diagonal
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GaussianFactorGraph::shared_ptr linear = optimizer.linearize();
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GaussianFactorGraph damped = optimizer.buildDampedSystem(*linear);
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VectorValues d = linear->hessianDiagonal(), //
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expectedDiagonal = d + params.lambdaInitial * d;
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EXPECT(assert_equal(expectedDiagonal, damped.hessianDiagonal()));
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// test convergence (does not!)
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Values actual = optimizer.optimize();
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EXPECT(assert_equal(expected, actual));
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// Check that the gradient is zero (it is not!)
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linear = optimizer.linearize();
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EXPECT(assert_equal(expectedGradient,linear->gradientAtZero()));
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// Check that the gradient is zero for damped system (it is not!)
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damped = optimizer.buildDampedSystem(*linear);
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VectorValues actualGradient = damped.gradientAtZero();
|
||||
EXPECT(assert_equal(expectedGradient,actualGradient));
|
||||
|
||||
/* This block was made to test the original initial guess "init"
|
||||
// Check errors at convergence and errors in direction of gradient (decreases!)
|
||||
EXPECT_DOUBLES_EQUAL(46.02558,fg.error(actual),1e-5);
|
||||
EXPECT_DOUBLES_EQUAL(44.742237,fg.error(actual.retract(-0.01*actualGradient)),1e-5);
|
||||
|
||||
// Check that solve yields gradient (it's not equal to gradient, as predicted)
|
||||
VectorValues delta = damped.optimize();
|
||||
double factor = actualGradient[0][0]/delta[0][0];
|
||||
EXPECT(assert_equal(actualGradient,factor*delta));
|
||||
|
||||
// Still pointing downhill wrt actual gradient !
|
||||
EXPECT_DOUBLES_EQUAL( 0.1056157,dot(-1*actualGradient,delta),1e-3);
|
||||
|
||||
// delta.print("This is the delta value computed by LM with diagonal damping");
|
||||
|
||||
// Still pointing downhill wrt expected gradient (IT DOES NOT! actually they are perpendicular)
|
||||
EXPECT_DOUBLES_EQUAL( 0.0,dot(-1*expectedGradient,delta),1e-5);
|
||||
|
||||
// Check errors at convergence and errors in direction of solution (does not decrease!)
|
||||
EXPECT_DOUBLES_EQUAL(46.0254859,fg.error(actual.retract(delta)),1e-5);
|
||||
|
||||
// Check errors at convergence and errors at a small step in direction of solution (does not decrease!)
|
||||
EXPECT_DOUBLES_EQUAL(46.0255,fg.error(actual.retract(0.01*delta)),1e-3);
|
||||
*/
|
||||
}
|
||||
}
|
||||
|
||||
|
|
|
|||
Loading…
Reference in New Issue