gtsam/tests/testGncOptimizer.cpp

/* ----------------------------------------------------------------------------

 * GTSAM Copyright 2010, Georgia Tech Research Corporation,
 * Atlanta, Georgia 30332-0415
 * All Rights Reserved
 * Authors: Frank Dellaert, et al. (see THANKS for the full author list)

 * See LICENSE for the license information

 * -------------------------------------------------------------------------- */

/**
 * @file    testGncOptimizer.cpp
 * @brief   Unit tests for GncOptimizer class
 * @author  Jingnan Shi
 * @author  Luca Carlone
 * @author  Frank Dellaert
 *
 * Implementation of the paper: Yang, Antonante, Tzoumas, Carlone, "Graduated Non-Convexity for Robust Spatial Perception:
 * From Non-Minimal Solvers to Global Outlier Rejection", RAL, 2020. (arxiv version: https://arxiv.org/pdf/1909.08605.pdf)
 */

#include <gtsam/nonlinear/LevenbergMarquardtOptimizer.h>
#include <gtsam/nonlinear/GaussNewtonOptimizer.h>
#include <gtsam/nonlinear/NonlinearFactorGraph.h>
#include <tests/smallExample.h>

#include <CppUnitLite/TestHarness.h>

using namespace std;
using namespace gtsam;

using symbol_shorthand::X;
using symbol_shorthand::L;
static double tol = 1e-7;

/* ************************************************************************* */
template<class BaseOptimizerParameters>
class GncParams {
public:
  /** Verbosity levels */
  enum VerbosityGNC {
    SILENT = 0, SUMMARY, VALUES
  };

  /** Choice of robust loss function for GNC */
  enum RobustLossType {
    GM /*Geman McClure*/, TLS /*Truncated least squares*/
  };

  using BaseOptimizer = GaussNewtonOptimizer; // BaseOptimizerParameters::OptimizerType;

  GncParams(const BaseOptimizerParameters& baseOptimizerParams) :
      baseOptimizerParams(baseOptimizerParams) {
  }

  // default constructor
  GncParams() :
      baseOptimizerParams() {
  }

  BaseOptimizerParameters baseOptimizerParams;
  /// any other specific GNC parameters:
  RobustLossType lossType = GM; /* default loss*/
  size_t maxIterations = 100; /* maximum number of iterations*/
  double barcSq = 1.0; /* a factor is considered an inlier if factor.error() < barcSq. Note that factor.error() whitens by the covariance*/
  double muStep = 1.4; /* multiplicative factor to reduce/increase the mu in gnc */
  VerbosityGNC verbosityGNC = SILENT; /* verbosity level */
  std::vector<size_t> knownInliers = std::vector<size_t>(); /* slots in the factor graph corresponding to measurements that we know are inliers */

  void setLossType(const RobustLossType type) {
    lossType = type;
  }
  void setMaxIterations(const size_t maxIter) {
    std::cout
        << "setMaxIterations: changing the max nr of iters might lead to less accurate solutions and is not recommended! "
        << std::endl;
    maxIterations = maxIter;
  }
  void setInlierThreshold(const double inth) {
    barcSq = inth;
  }
  void setMuStep(const double step) {
    muStep = step;
  }
  void setVerbosityGNC(const VerbosityGNC verbosity) {
    verbosityGNC = verbosity;
  }
  void setKnownInliers(const std::vector<size_t> knownIn) {
    for (size_t i = 0; i < knownIn.size(); i++)
      knownInliers.push_back(knownIn[i]);
  }

  /// equals
  bool equals(const GncParams& other, double tol = 1e-9) const {
    return baseOptimizerParams.equals(other.baseOptimizerParams)
        && lossType == other.lossType && maxIterations == other.maxIterations
        && std::fabs(barcSq - other.barcSq) <= tol
        && std::fabs(muStep - other.muStep) <= tol
        && verbosityGNC == other.verbosityGNC
        && knownInliers == other.knownInliers;
  }

  /// print function
  void print(const std::string& str) const {
    std::cout << str << "\n";
    switch (lossType) {
    case GM:
      std::cout << "lossType: Geman McClure" << "\n";
      break;
    default:
      throw std::runtime_error("GncParams::print: unknown loss type.");
    }
    std::cout << "maxIterations: " << maxIterations << "\n";
    std::cout << "barcSq: " << barcSq << "\n";
    std::cout << "muStep: " << muStep << "\n";
    std::cout << "verbosityGNC: " << verbosityGNC << "\n";
    for (size_t i = 0; i < knownInliers.size(); i++)
      std::cout << "knownInliers: " << knownInliers[i] << "\n";
    baseOptimizerParams.print(str);
  }
};

/* ************************************************************************* */
template<class GncParameters>
class GncOptimizer {
public:
  // types etc

private:
  NonlinearFactorGraph nfg_;
  Values state_;
  GncParameters params_;
  Vector weights_; // this could be a local variable in optimize, but it is useful to make it accessible from outside

public:
  GncOptimizer(const NonlinearFactorGraph& graph, const Values& initialValues,
      const GncParameters& params = GncParameters()) :
      state_(initialValues), params_(params) {

    // make sure all noiseModels are Gaussian or convert to Gaussian
    nfg_.resize(graph.size());
    for (size_t i = 0; i < graph.size(); i++) {
      if (graph[i]) {
        NoiseModelFactor::shared_ptr factor = boost::dynamic_pointer_cast<
            NoiseModelFactor>(graph[i]);
        noiseModel::Robust::shared_ptr robust = boost::dynamic_pointer_cast<
            noiseModel::Robust>(factor->noiseModel());
        if (robust) { // if the factor has a robust loss, we have to change it:
          SharedNoiseModel gaussianNoise = robust->noise();
          NoiseModelFactor::shared_ptr gaussianFactor =
              factor->cloneWithNewNoiseModel(gaussianNoise);
          nfg_[i] = gaussianFactor;
        } else { // else we directly push it back
          nfg_[i] = factor;
        }
      }
    }
  }

  /// getter functions
  NonlinearFactorGraph getFactors() const {
    return NonlinearFactorGraph(nfg_);
  }
  Values getState() const {
    return Values(state_);
  }
  GncParameters getParams() const {
    return GncParameters(params_);
  }
  Vector getWeights() const {
    return weights_;
  }

  /// implement GNC main loop, including graduating nonconvexity with mu
  Values optimize() {
    // start by assuming all measurements are inliers
    weights_ = Vector::Ones(nfg_.size());
    GaussNewtonOptimizer baseOptimizer(nfg_, state_);
    Values result = baseOptimizer.optimize();
    double mu = initializeMu();
    for (size_t iter = 0; iter < params_.maxIterations; iter++) {

      // display info
      if (params_.verbosityGNC >= GncParameters::VerbosityGNC::VALUES) {
        result.print("result\n");
        std::cout << "mu: " << mu << std::endl;
        std::cout << "weights: " << weights_ << std::endl;
      }
      // weights update
      weights_ = calculateWeights(result, mu);

      // variable/values update
      NonlinearFactorGraph graph_iter = this->makeWeightedGraph(weights_);
      GaussNewtonOptimizer baseOptimizer_iter(graph_iter, state_);
      result = baseOptimizer_iter.optimize();

      // stopping condition
      if (checkMuConvergence(mu)) {
        // display info
        if (params_.verbosityGNC >= GncParameters::VerbosityGNC::SUMMARY) {
          std::cout << "final iterations: " << iter << std::endl;
          std::cout << "final mu: " << mu << std::endl;
          std::cout << "final weights: " << weights_ << std::endl;
        }
        break;
      }

      // otherwise update mu
      mu = updateMu(mu);
    }
    return result;
  }

  /// initialize the gnc parameter mu such that loss is approximately convex (remark 5 in GNC paper)
  double initializeMu() const {
    // compute largest error across all factors
    double rmax_sq = 0.0;
    for (size_t i = 0; i < nfg_.size(); i++) {
      if (nfg_[i]) {
        rmax_sq = std::max(rmax_sq, nfg_[i]->error(state_));
      }
    }
    // set initial mu
    switch (params_.lossType) {
    case GncParameters::GM:
      return 2 * rmax_sq / params_.barcSq; // initial mu
    default:
      throw std::runtime_error(
          "GncOptimizer::initializeMu: called with unknown loss type.");
    }
  }

  /// update the gnc parameter mu to gradually increase nonconvexity
  double updateMu(const double mu) const {
    switch (params_.lossType) {
    case GncParameters::GM:
      return std::max(1.0, mu / params_.muStep); // reduce mu, but saturate at 1
    default:
      throw std::runtime_error(
          "GncOptimizer::updateMu: called with unknown loss type.");
    }
  }

  /// check if we have reached the value of mu for which the surrogate loss matches the original loss
  bool checkMuConvergence(const double mu) const {
    switch (params_.lossType) {
    case GncParameters::GM:
      return std::fabs(mu - 1.0) < 1e-9; // mu=1 recovers the original GM function
    default:
      throw std::runtime_error(
          "GncOptimizer::checkMuConvergence: called with unknown loss type.");
    }
  }

  /// create a graph where each factor is weighted by the gnc weights
  NonlinearFactorGraph makeWeightedGraph(const Vector& weights) const {
    // make sure all noiseModels are Gaussian or convert to Gaussian
    NonlinearFactorGraph newGraph;
    newGraph.resize(nfg_.size());
    for (size_t i = 0; i < nfg_.size(); i++) {
      if (nfg_[i]) {
        NoiseModelFactor::shared_ptr factor = boost::dynamic_pointer_cast<
            NoiseModelFactor>(nfg_[i]);
        noiseModel::Gaussian::shared_ptr noiseModel =
            boost::dynamic_pointer_cast<noiseModel::Gaussian>(
                factor->noiseModel());
        if (noiseModel) {
          Matrix newInfo = weights[i] * noiseModel->information();
          SharedNoiseModel newNoiseModel = noiseModel::Gaussian::Information(
              newInfo);
          newGraph[i] = factor->cloneWithNewNoiseModel(newNoiseModel);
        } else {
          throw std::runtime_error(
              "GncOptimizer::makeWeightedGraph: unexpected non-Gaussian noise model.");
        }
      }
    }
    return newGraph;
  }

  /// calculate gnc weights
  Vector calculateWeights(const Values currentEstimate, const double mu) {
    Vector weights = Vector::Ones(nfg_.size());

    // do not update the weights that the user has decided are known inliers
    std::vector<size_t> allWeights;
    for (size_t k = 0; k < nfg_.size(); k++) {
      allWeights.push_back(k);
    }
    std::vector<size_t> unknownWeights;
    std::set_difference(allWeights.begin(), allWeights.end(),
        params_.knownInliers.begin(), params_.knownInliers.end(),
        std::inserter(unknownWeights, unknownWeights.begin()));

    // update weights of known inlier/outlier measurements
    switch (params_.lossType) {
    case GncParameters::GM: // use eq (12) in GNC paper
      for (size_t k : unknownWeights) {
        if (nfg_[k]) {
          double u2_k = nfg_[k]->error(currentEstimate); // squared (and whitened) residual
          weights[k] = std::pow(
              (mu * params_.barcSq) / (u2_k + mu * params_.barcSq), 2);
        }
      }
      return weights;
    default:
      throw std::runtime_error(
          "GncOptimizer::calculateWeights: called with unknown loss type.");
    }
  }
};

/* ************************************************************************* */
TEST(GncOptimizer, gncParamsConstructor) {
  //check params are correctly parsed
  LevenbergMarquardtParams lmParams;
  GncParams<LevenbergMarquardtParams> gncParams1(lmParams);
  CHECK(lmParams.equals(gncParams1.baseOptimizerParams));

  // check also default constructor
  GncParams<LevenbergMarquardtParams> gncParams1b;
  CHECK(lmParams.equals(gncParams1b.baseOptimizerParams));

  // and check params become different if we change lmParams
  lmParams.setVerbosity("DELTA");
  CHECK(!lmParams.equals(gncParams1.baseOptimizerParams));

  // and same for GN
  GaussNewtonParams gnParams;
  GncParams<GaussNewtonParams> gncParams2(gnParams);
  CHECK(gnParams.equals(gncParams2.baseOptimizerParams));

  // check default constructor
  GncParams<GaussNewtonParams> gncParams2b;
  CHECK(gnParams.equals(gncParams2b.baseOptimizerParams));

  // change something at the gncParams level
  GncParams<GaussNewtonParams> gncParams2c(gncParams2b);
  gncParams2c.setLossType(GncParams<GaussNewtonParams>::RobustLossType::TLS);
  CHECK(!gncParams2c.equals(gncParams2b.baseOptimizerParams));
}

/* ************************************************************************* */
TEST(GncOptimizer, gncConstructor) {
  // has to have Gaussian noise models !
  auto fg = example::createReallyNonlinearFactorGraph(); // just a unary factor on a 2D point

  Point2 p0(3, 3);
  Values initial;
  initial.insert(X(1), p0);

  LevenbergMarquardtParams lmParams;
  GncParams<LevenbergMarquardtParams> gncParams(lmParams);
  auto gnc = GncOptimizer<GncParams<LevenbergMarquardtParams>>(fg, initial,
      gncParams);

  CHECK(gnc.getFactors().equals(fg));
  CHECK(gnc.getState().equals(initial));
  CHECK(gnc.getParams().equals(gncParams));
}

/* ************************************************************************* */
TEST(GncOptimizer, gncConstructorWithRobustGraphAsInput) {
  auto fg = example::sharedNonRobustFactorGraphWithOutliers();
  // same graph with robust noise model
  auto fg_robust = example::sharedRobustFactorGraphWithOutliers();

  Point2 p0(3, 3);
  Values initial;
  initial.insert(X(1), p0);

  LevenbergMarquardtParams lmParams;
  GncParams<LevenbergMarquardtParams> gncParams(lmParams);
  auto gnc = GncOptimizer<GncParams<LevenbergMarquardtParams>>(fg_robust,
      initial, gncParams);

  // make sure that when parsing the graph is transformed into one without robust loss
  CHECK(fg.equals(gnc.getFactors()));
}

/* ************************************************************************* */
TEST(GncOptimizer, initializeMu) {
  auto fg = example::createReallyNonlinearFactorGraph();

  Point2 p0(3, 3);
  Values initial;
  initial.insert(X(1), p0);

  LevenbergMarquardtParams lmParams;
  GncParams<LevenbergMarquardtParams> gncParams(lmParams);
  gncParams.setLossType(
      GncParams<LevenbergMarquardtParams>::RobustLossType::GM);
  auto gnc = GncOptimizer<GncParams<LevenbergMarquardtParams>>(fg, initial,
      gncParams);
  EXPECT_DOUBLES_EQUAL(gnc.initializeMu(), 2 * 198.999, 1e-3); // according to rmk 5 in the gnc paper: m0 = 2 rmax^2 / barcSq (barcSq=1 in this example)
}

/* ************************************************************************* */
TEST(GncOptimizer, updateMu) {
  // has to have Gaussian noise models !
  auto fg = example::createReallyNonlinearFactorGraph();

  Point2 p0(3, 3);
  Values initial;
  initial.insert(X(1), p0);

  LevenbergMarquardtParams lmParams;
  GncParams<LevenbergMarquardtParams> gncParams(lmParams);
  gncParams.setLossType(
      GncParams<LevenbergMarquardtParams>::RobustLossType::GM);
  auto gnc = GncOptimizer<GncParams<LevenbergMarquardtParams>>(fg, initial,
      gncParams);

  double mu = 5.0;
  EXPECT_DOUBLES_EQUAL(gnc.updateMu(mu), mu / 1.4, tol);

  // check it correctly saturates to 1 for GM
  mu = 1.2;
  EXPECT_DOUBLES_EQUAL(gnc.updateMu(mu), 1.0, tol);
}

/* ************************************************************************* */
TEST(GncOptimizer, checkMuConvergence) {
  // has to have Gaussian noise models !
  auto fg = example::createReallyNonlinearFactorGraph();

  Point2 p0(3, 3);
  Values initial;
  initial.insert(X(1), p0);

  LevenbergMarquardtParams lmParams;
  GncParams<LevenbergMarquardtParams> gncParams(lmParams);
  gncParams.setLossType(
      GncParams<LevenbergMarquardtParams>::RobustLossType::GM);
  auto gnc = GncOptimizer<GncParams<LevenbergMarquardtParams>>(fg, initial,
      gncParams);

  double mu = 1.0;
  CHECK(gnc.checkMuConvergence(mu));
}

/* ************************************************************************* */
TEST(GncOptimizer, calculateWeights) {
  auto fg = example::sharedNonRobustFactorGraphWithOutliers();

  Point2 p0(0, 0);
  Values initial;
  initial.insert(X(1), p0);

  // we have 4 factors, 3 with zero errors (inliers), 1 with error 50 = 0.5 * 1/sigma^2 || [1;0] - [0;0] ||^2 (outlier)
  Vector weights_expected = Vector::Zero(4);
  weights_expected[0] = 1.0; // zero error
  weights_expected[1] = 1.0; // zero error
  weights_expected[2] = 1.0; // zero error
  weights_expected[3] = std::pow(1.0 / (50.0 + 1.0), 2); // outlier, error = 50

  GaussNewtonParams gnParams;
  GncParams<GaussNewtonParams> gncParams(gnParams);
  auto gnc = GncOptimizer<GncParams<GaussNewtonParams>>(fg, initial, gncParams);
  double mu = 1.0;
  Vector weights_actual = gnc.calculateWeights(initial, mu);
  CHECK(assert_equal(weights_expected, weights_actual, tol));

  mu = 2.0;
  double barcSq = 5.0;
  weights_expected[3] = std::pow(mu * barcSq / (50.0 + mu * barcSq), 2); // outlier, error = 50
  gncParams.setInlierThreshold(barcSq);
  auto gnc2 = GncOptimizer<GncParams<GaussNewtonParams>>(fg, initial,
      gncParams);
  weights_actual = gnc2.calculateWeights(initial, mu);
  CHECK(assert_equal(weights_expected, weights_actual, tol));
}

/* ************************************************************************* */
TEST(GncOptimizer, makeWeightedGraph) {
  // create original factor
  double sigma1 = 0.1;
  NonlinearFactorGraph nfg = example::nonlinearFactorGraphWithGivenSigma(
      sigma1);

  // create expected
  double sigma2 = 10;
  NonlinearFactorGraph expected = example::nonlinearFactorGraphWithGivenSigma(
      sigma2);

  // create weights
  Vector weights = Vector::Ones(1); // original info:1/0.1^2 = 100. New info: 1/10^2 = 0.01. Ratio is 10-4
  weights[0] = 1e-4;

  // create actual
  Point2 p0(3, 3);
  Values initial;
  initial.insert(X(1), p0);

  LevenbergMarquardtParams lmParams;
  GncParams<LevenbergMarquardtParams> gncParams(lmParams);
  auto gnc = GncOptimizer<GncParams<LevenbergMarquardtParams>>(nfg, initial,
      gncParams);
  NonlinearFactorGraph actual = gnc.makeWeightedGraph(weights);

  // check it's all good
  CHECK(assert_equal(expected, actual));
}

/* ************************************************************************* */
TEST(GncOptimizer, optimizeSimple) {
  auto fg = example::createReallyNonlinearFactorGraph();

  Point2 p0(3, 3);
  Values initial;
  initial.insert(X(1), p0);

  LevenbergMarquardtParams lmParams;
  GncParams<LevenbergMarquardtParams> gncParams(lmParams);
  auto gnc = GncOptimizer<GncParams<LevenbergMarquardtParams>>(fg, initial,
      gncParams);

  Values actual = gnc.optimize();
  DOUBLES_EQUAL(0, fg.error(actual), tol);
}

/* ************************************************************************* */
TEST(GncOptimizer, optimize) {
  auto fg = example::sharedNonRobustFactorGraphWithOutliers();

  Point2 p0(1, 0);
  Values initial;
  initial.insert(X(1), p0);

  // try with nonrobust cost function and standard GN
  GaussNewtonParams gnParams;
  GaussNewtonOptimizer gn(fg, initial, gnParams);
  Values gn_results = gn.optimize();
  // converges to incorrect point due to lack of robustness to an outlier, ideal solution is Point2(0,0)
  CHECK(assert_equal(Point2(0.25, 0.0), gn_results.at<Point2>(X(1)), 1e-3));

  // try with robust loss function and standard GN
  auto fg_robust = example::sharedRobustFactorGraphWithOutliers(); // same as fg, but with factors wrapped in Geman McClure losses
  GaussNewtonOptimizer gn2(fg_robust, initial, gnParams);
  Values gn2_results = gn2.optimize();
  // converges to incorrect point, this time due to the nonconvexity of the loss
  CHECK(assert_equal(Point2(0.999706, 0.0), gn2_results.at<Point2>(X(1)), 1e-3));

  // .. but graduated nonconvexity ensures both robustness and convergence in the face of nonconvexity
  GncParams<GaussNewtonParams> gncParams(gnParams);
  // gncParams.setVerbosityGNC(GncParams<GaussNewtonParams>::VerbosityGNC::SUMMARY);
  auto gnc = GncOptimizer<GncParams<GaussNewtonParams>>(fg, initial, gncParams);
  Values gnc_result = gnc.optimize();
  CHECK(assert_equal(Point2(0.0, 0.0), gnc_result.at<Point2>(X(1)), 1e-3));
}

/* ************************************************************************* */
TEST(GncOptimizer, optimizeWithKnownInliers) {
  auto fg = example::sharedNonRobustFactorGraphWithOutliers();

  Point2 p0(1, 0);
  Values initial;
  initial.insert(X(1), p0);

  std::vector<size_t> knownInliers;
  knownInliers.push_back(0);
  knownInliers.push_back(1);
  knownInliers.push_back(2);

  // nonconvexity with known inliers
  GncParams<GaussNewtonParams> gncParams = GncParams<GaussNewtonParams>();
  gncParams.setKnownInliers(knownInliers);
  // gncParams.setVerbosityGNC(GncParams<GaussNewtonParams>::VerbosityGNC::VALUES);
  auto gnc = GncOptimizer<GncParams<GaussNewtonParams>>(fg, initial, gncParams);

  Values gnc_result = gnc.optimize();
  CHECK(assert_equal(Point2(0.0, 0.0), gnc_result.at<Point2>(X(1)), 1e-3));

  // check weights were actually fixed:
  Vector finalWeights = gnc.getWeights();
  DOUBLES_EQUAL(1.0, finalWeights[0], tol);
  DOUBLES_EQUAL(1.0, finalWeights[1], tol);
  DOUBLES_EQUAL(1.0, finalWeights[2], tol);
}

/* ************************************************************************* */
int main() {
  TestResult tr;
  return TestRegistry::runAllTests(tr);
}
/* ************************************************************************* */