Merge pull request mlpack#1037 from shikharbhardwaj/parallel_sgd

Implementation of parallel SGD

src/mlpack/core/optimizers/lbfgs/test_functions.cpp

@@ -196,6 +196,17 @@ void GeneralizedRosenbrockFunction::Gradient(const arma::mat& coordinates,
   gradient[i + 1] = 200 * (coordinates[i + 1] - std::pow(coordinates[i], 2));
 }
 
+void GeneralizedRosenbrockFunction::Gradient(const arma::mat& coordinates,
+                                             const size_t i,
+                                             arma::sp_mat& gradient) const
+{
+  gradient.set_size(n);
+
+  gradient[i] = 400 * (std::pow(coordinates[i], 3) - coordinates[i] *
+      coordinates[i + 1]) + 2 * (coordinates[i] - 1);
+  gradient[i + 1] = 200 * (coordinates[i + 1] - std::pow(coordinates[i], 2));
+}
+
 const arma::mat& GeneralizedRosenbrockFunction::GetInitialPoint() const
 {
   return initialPoint;

src/mlpack/core/optimizers/lbfgs/test_functions.hpp

@@ -129,6 +129,10 @@ class GeneralizedRosenbrockFunction
                 const size_t i,
                 arma::mat& gradient) const;
 
+  void Gradient(const arma::mat& coordinates,
+                const size_t i,
+                arma::sp_mat& gradient) const;
+
   const arma::mat& GetInitialPoint() const;
 
  private:

src/mlpack/core/optimizers/parallel_sgd/CMakeLists.txt

@@ -0,0 +1,13 @@
+set(SOURCES
+  parallel_sgd.hpp
+  parallel_sgd_impl.hpp
+  sparse_test_function.hpp
+  sparse_test_function_impl.hpp
+)
+
+set(DIR_SRCS)
+foreach(file ${SOURCES})
+  set(DIR_SRCS ${DIR_SRCS} ${CMAKE_CURRENT_SOURCE_DIR}/${file})
+endforeach()
+
+set(MLPACK_SRCS ${MLPACK_SRCS} ${DIR_SRCS} PARENT_SCOPE)

src/mlpack/core/optimizers/parallel_sgd/decay_policies/CMakeLists.txt

@@ -0,0 +1,11 @@
+set(SOURCES
+  constant_step.hpp
+  exponential_backoff.hpp
+)
+
+set(DIR_SRCS)
+foreach(file ${SOURCES})
+  set(DIR_SRCS ${DIR_SRCS} ${CMAKE_CURRENT_SOURCE_DIR}/${file})
+endforeach()
+
+set(MLPACK_SRCS ${MLPACK_SRCS} ${DIR_SRCS} PARENT_SCOPE)

src/mlpack/core/optimizers/parallel_sgd/decay_policies/constant_step.hpp

@@ -0,0 +1,55 @@
+/**
+ * @file constant_step.hpp
+ * @author Shikhar Bhardwaj
+ *
+ * Constant step size policy for parallel Stochastic Gradient Descent.
+ *
+ * mlpack is free software; you may redistribute it and/or modify it under the
+ * terms of the 3-clause BSD license.  You should have received a copy of the
+ * 3-clause BSD license along with mlpack.  If not, see
+ * http://www.opensource.org/licenses/BSD-3-Clause for more information.
+ */
+#ifndef MLPACK_CORE_OPTIMIZERS_PARALLEL_SGD_CONSTANT_STEP_HPP
+#define MLPACK_CORE_OPTIMIZERS_PARALLEL_SGD_CONSTANT_STEP_HPP
+
+#include <mlpack/prereqs.hpp>
+
+namespace mlpack {
+namespace optimization {
+
+/**
+ * Implementation of the ConstantStep stepsize decay policy for parallel SGD.
+ */
+class ConstantStep
+{
+ public:
+  /**
+   * Member initialization constructor.
+   *
+   * The defaults here are not necessarily good for the given problem, so it is
+   * suggested that the values used be tailored to the task at hand.
+   *
+   * @param step The intial stepsize to use.
+   */
+  ConstantStep(const double step = 0.01) : step(step) { /* Nothing to do */ }
+
+  /**
+   * This function is called in each iteration before the gradient update.
+   *
+   * @param numEpoch The iteration number for which the stepsize is to be
+   *    calculated.
+   * @return The step size for the current iteration.
+   */
+  double StepSize(const size_t /* numEpoch */)
+  {
+    return step;
+  }
+ private:
+  //! The initial stepsize, which remains unchanged
+  double step;
+};
+
+} // namespace optimization
+} // namespace mlpack
+
+#endif

src/mlpack/core/optimizers/parallel_sgd/decay_policies/exponential_backoff.hpp

@@ -0,0 +1,92 @@
+/**
+ * @file exponential_backoff.hpp
+ * @author Shikhar Bhardwaj
+ *
+ * Exponential backoff step size decay policy for parallel Stochastic Gradient
+ * Descent.
+ *
+ * mlpack is free software; you may redistribute it and/or modify it under the
+ * terms of the 3-clause BSD license.  You should have received a copy of the
+ * 3-clause BSD license along with mlpack.  If not, see
+ * http://www.opensource.org/licenses/BSD-3-Clause for more information.
+ */
+#ifndef MLPACK_CORE_OPTIMIZERS_PARALLEL_SGD_EXP_BACKOFF_HPP
+#define MLPACK_CORE_OPTIMIZERS_PARALLEL_SGD_EXP_BACKOFF_HPP
+
+#include <mlpack/prereqs.hpp>
+
+namespace mlpack {
+namespace optimization {
+
+/**
+ * Exponential backoff stepsize reduction policy for parallel SGD.
+ *
+ * For more information, see the following.
+ *
+ * @misc{1106.5730,
+ *   Author = {Feng Niu and Benjamin Recht and Christopher Re and Stephen J.
+ *             Wright},
+ *   Title = {HOGWILD!: A Lock-Free Approach to Parallelizing Stochastic
+ *            Gradient Descent},
+ *   Year = {2011},
+ *   Eprint = {arXiv:1106.5730},
+ * }
+ *
+ * This stepsize update scheme gives robust 1/k convergence rates to the
+ * implementation of parallel SGD.
+ */
+class ExponentialBackoff
+{
+ public:
+  /**
+   * Member initializer constructor to construct the exponential backoff policy
+   * with the required parameters.
+   *
+   * @param firstBackoffEpoch The number of updates to run before the first
+   * stepsize backoff.
+   * @param step The initial stepsize(gamma).
+   * @param beta The reduction factor. This should be a value in range (0, 1).
+   */
+  ExponentialBackoff(const size_t firstBackoffEpoch,
+                     const double step,
+                     const double beta) :
+    firstBackoffEpoch(firstBackoffEpoch),
+    cutoffEpoch(firstBackoffEpoch),
+    step(step),
+    beta(beta)
+  { /* Nothing to do. */ }
+
+  /**
+   * Get the step size for the current gradient update.
+   *
+   * @param numEpoch The iteration number of the current update.
+   * @return The stepsize for the current iteration.
+   */
+  double StepSize(const size_t numEpoch)
+  {
+    if (numEpoch >= cutoffEpoch)
+    {
+      step *= beta;
+      cutoffEpoch += firstBackoffEpoch / beta;
+    }
+    return step;
+  }
+
+ private:
+  //! The first iteration at which the stepsize should be reduced.
+  size_t firstBackoffEpoch;
+
+  //! The iteration at which the next decay will be performed.
+  size_t cutoffEpoch;
+
+  //! The initial stepsize.
+  double step;
+
+  //! The reduction factor, should be in range (0, 1).
+  double beta;
+};
+
+} // namespace optimization
+} // namespace mlpack
+
+#endif

src/mlpack/core/optimizers/parallel_sgd/parallel_sgd.hpp

@@ -0,0 +1,151 @@
+/**
+ * @file parallel_sgd.hpp
+ * @author Shikhar Bhardwaj
+ *
+ * Parallel Stochastic Gradient Descent.
+ *
+ * mlpack is free software; you may redistribute it and/or modify it under the
+ * terms of the 3-clause BSD license.  You should have received a copy of the
+ * 3-clause BSD license along with mlpack.  If not, see
+ * http://www.opensource.org/licenses/BSD-3-Clause for more information.
+ */
+#ifndef MLPACK_CORE_OPTIMIZERS_PARALLEL_SGD_HPP
+#define MLPACK_CORE_OPTIMIZERS_PARALLEL_SGD_HPP
+
+#include <mlpack/prereqs.hpp>
+#include <mlpack/core/math/random.hpp>
+#include "decay_policies/constant_step.hpp"
+
+namespace mlpack {
+namespace optimization {
+
+/**
+ * An implementation of parallel stochastic gradient descent using the lock-free
+ * HOGWILD! approach.
+ *
+ * For more information, see the following.
+ * @misc{1106.5730,
+ *   Author = {Feng Niu and Benjamin Recht and Christopher Re and Stephen J.
+ *             Wright},
+ *   Title = {HOGWILD!: A Lock-Free Approach to Parallelizing Stochastic
+ *            Gradient Descent},
+ *   Year = {2011},
+ *   Eprint = {arXiv:1106.5730},
+ * }
+ *
+ * For Parallel SGD to work, a SparseFunctionType template parameter is
+ * required. This class must implement the following functions:
+ *
+ *   size_t NumFunctions();
+ *   double Evaluate(const arma::mat& coordinates, const size_t i);
+ *   void Gradient(const arma::mat& coordinates,
+ *                 const size_t i,
+ *                 arma::sp_mat& gradient);
+ *
+ * In these functions the parameter id refers to which individual function (or
+ * gradient) is being evaluated. In case of a data-dependent function, the id
+ * would refer to the index of the datapoint(or training example).
+ * The data is distributed uniformly among the threads made available to the
+ * program by the OpenMP runtime.
+ *
+ * The Gradient function interface is slightly changed from the
+ * DecomposableFunctionType interface, it takes in a sparse matrix as the
+ * out-param for the gradient, as ParallelSGD is only expected to be relevant in
+ * situations where the computed gradient is sparse.
+ *
+ * @tparam DecayPolicyType Step size update policy used by parallel SGD
+ *     to update the stepsize after each iteration.
+ */
+template <typename DecayPolicyType = ConstantStep>
+class ParallelSGD
+{
+ public:
+  /**
+   * Construct the parallel SGD optimizer to optimize the given function with
+   * the given parameters. One iteration means one batch of datapoints processed
+   * by each thread.
+   *
+   * The defaults here are not necessarily good for the given problem, so it is
+   * suggested that the values used be tailored to the task at hand.
+   *
+   * @param maxIterations Maximum number of iterations allowed (0 means no
+   *     limit).
+   * @param threadShareSize Number of datapoints to be processed in one
+   *     iteration by each thread.
+   * @param tolerance Maximum absolute tolerance to terminate the algorithm.
+   * @param shuffle If true, the function order is shuffled; otherwise, each
+   *     function is visited in linear order.
+   * @param decayPolicy The step size update policy to use.
+  */
+  ParallelSGD(const size_t maxIterations,
+              const size_t threadShareSize,
+              const double tolerance = 1e-5,
+              const bool shuffle = true,
+              const DecayPolicyType& decayPolicy = DecayPolicyType());
+
+  /**
+   * Optimize the given function using the parallel SGD algorithm. The given
+   * starting point will be modified to store the finishing point of the
+   * algorithm, and the value of the loss function at the final point is
+   * returned.
+   *
+   * @tparam SparseFunctionType Type of function to be optimized.
+   * @param function Function to be optimized(minimized).
+   * @param iterate Starting point(will be modified).
+   * @return Objective value at the final point.
+   */
+  template <typename SparseFunctionType>
+  double Optimize(SparseFunctionType& function, arma::mat& iterate);
+
+  //! Get the maximum number of iterations (0 indicates no limits).
+  size_t MaxIterations() const { return maxIterations; }
+  //! Modify the maximum number of iterations (0 indicates no limits).
+  size_t& MaxIterations() { return maxIterations; }
+
+  //! Get the number of datapoints to be processed in one iteration by each
+  //! thread.
+  size_t ThreadShareSize() const { return threadShareSize; }
+  //! Modify the number of datapoints to be processed in one iteration by each
+  //! thread.
+  size_t& ThreadShareSize() { return threadShareSize; }
+
+  //! Get the tolerance for termination.
+  double Tolerance() const { return tolerance; }
+  //! Modify the tolerance for termination.
+  double& Tolerance() { return tolerance; }
+
+  //! Get whether or not the individual functions are shuffled.
+  bool Shuffle() const { return shuffle; }
+  //! Modify whether or not the individual functions are shuffled.
+  bool& Shuffle() { return shuffle; }
+
+  //! Get the step size decay policy.
+  DecayPolicyType& DecayPolicy() const { return decayPolicy; }
+  //! Modify the step size decay policy.
+  DecayPolicyType& DecayPolicy() { return decayPolicy; }
+
+ private:
+  //! The maximum number of allowed iterations.
+  size_t maxIterations;
+
+  //! The number of datapoints to be processed in one iteration by each thread.
+  size_t threadShareSize;
+
+  //! The tolerance for termination.
+  double tolerance;
+
+  //! Controls whether or not the individual functions are shuffled when
+  //! iterating.
+  bool shuffle;
+
+  //! The step size decay policy.
+  DecayPolicyType decayPolicy;
+};
+
+} // namespace optimization
+} // namespace mlpack
+
+// Include implementation.
+#include "parallel_sgd_impl.hpp"
+
+#endif