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From "ASF GitHub Bot (JIRA)" <j...@apache.org>
Subject [jira] [Commented] (FLINK-1807) Stochastic gradient descent optimizer for ML library
Date Wed, 29 Apr 2015 15:27:08 GMT

    [ https://issues.apache.org/jira/browse/FLINK-1807?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=14519551#comment-14519551
] 

ASF GitHub Bot commented on FLINK-1807:
---------------------------------------

Github user tillrohrmann commented on a diff in the pull request:

    https://github.com/apache/flink/pull/613#discussion_r29347123
  
    --- Diff: flink-staging/flink-ml/src/main/scala/org/apache/flink/ml/optimization/GradientDescent.scala
---
    @@ -0,0 +1,237 @@
    +/*
    + * Licensed to the Apache Software Foundation (ASF) under one
    + * or more contributor license agreements.  See the NOTICE file
    + * distributed with this work for additional information
    + * regarding copyright ownership.  The ASF licenses this file
    + * to you under the Apache License, Version 2.0 (the
    + * "License"); you may not use this file except in compliance
    + * with the License.  You may obtain a copy of the License at
    + *
    + *     http://www.apache.org/licenses/LICENSE-2.0
    + *
    + * Unless required by applicable law or agreed to in writing, software
    + * distributed under the License is distributed on an "AS IS" BASIS,
    + * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
    + * See the License for the specific language governing permissions and
    + * limitations under the License.
    + */
    +
    +
    +package org.apache.flink.ml.optimization
    +
    +import org.apache.flink.api.common.functions.RichMapFunction
    +import org.apache.flink.api.scala._
    +import org.apache.flink.configuration.Configuration
    +import org.apache.flink.ml.common._
    +import org.apache.flink.ml.math._
    +import org.apache.flink.ml.optimization.IterativeSolver.{Iterations, Stepsize}
    +import org.apache.flink.ml.optimization.Solver._
    +
    +/** This [[Solver]] performs Stochastic Gradient Descent optimization using mini batches
    +  *
    +  * For each labeled vector in a mini batch the gradient is computed and added to a partial
    +  * gradient. The partial gradients are then summed and divided by the size of the batches.
The
    +  * average gradient is then used to updated the weight values, including regularization.
    +  *
    +  * At the moment, the whole partition is used for SGD, making it effectively a batch
gradient
    +  * descent. Once a sampling operator has been introduced, the algorithm can be optimized
    +  *
    +  * @param runParameters The parameters to tune the algorithm. Currently these include:
    +  *                      [[Solver.LossFunction]] for the loss function to be used,
    +  *                      [[Solver.RegularizationType]] for the type of regularization,
    +  *                      [[Solver.RegularizationParameter]] for the regularization parameter,
    +  *                      [[IterativeSolver.Iterations]] for the maximum number of iteration,
    +  *                      [[IterativeSolver.Stepsize]] for the learning rate used.
    +  */
    +class GradientDescent(runParameters: ParameterMap) extends IterativeSolver {
    +
    +  import Solver.WEIGHTVECTOR_BROADCAST
    +
    +  var parameterMap: ParameterMap = parameters ++ runParameters
    +
    +  // TODO(tvas): Use once we have proper sampling in place
    +//  case object MiniBatchFraction extends Parameter[Double] {
    +//    val defaultValue = Some(1.0)
    +//  }
    +//
    +//  def setMiniBatchFraction(fraction: Double): GradientDescent = {
    +//    parameterMap.add(MiniBatchFraction, fraction)
    +//    this
    +//  }
    +
    +  /** Performs one iteration of Stochastic Gradient Descent using mini batches
    +    *
    +    * @param data A Dataset of LabeledVector (label, features) pairs
    +    * @param currentWeights A Dataset with the current weights to be optimized as its
only element
    +    * @return A Dataset containing the weights after one stochastic gradient descent
step
    +    */
    +  private def SGDStep(data: DataSet[(LabeledVector)], currentWeights: DataSet[WeightVector]):
    +    DataSet[WeightVector] = {
    +
    +    // TODO: Sample from input to realize proper SGD
    +    data.map {
    +      new GradientCalculation
    +    }.withBroadcastSet(currentWeights, WEIGHTVECTOR_BROADCAST).reduce {
    +      (left, right) =>
    +        val (leftGradientVector, leftCount) = left
    +        val (rightGradientVector, rightCount) = right
    +
    +        BLAS.axpy(1.0, leftGradientVector.weights, rightGradientVector.weights)
    +        (new WeightVector(
    +          rightGradientVector.weights,
    +          leftGradientVector.intercept + rightGradientVector.intercept),
    +          leftCount + rightCount)
    +    }.map {
    +      new WeightsUpdate
    +    }.withBroadcastSet(currentWeights, WEIGHTVECTOR_BROADCAST)
    +  }
    +
    +  /** Provides a solution for the given optimization problem
    +    *
    +    * @param data A Dataset of LabeledVector (label, features) pairs
    +    * @param initWeights The initial weights that will be optimized
    +    * @return The weights, optimized for the provided data.
    +    */
    +  override def optimize(data: DataSet[LabeledVector], initWeights: Option[DataSet[WeightVector]]):
    +  DataSet[WeightVector] = {
    +    // TODO: Faster way to do this?
    +    val dimensionsDS = data.map(_.vector.size).reduce((a, b) => b)
    +
    +    val numberOfIterations: Int = parameterMap(Iterations)
    +
    +
    +    val initialWeightsDS: DataSet[WeightVector] = initWeights match {
    +      //TODO(tvas): Need to figure out if and where we want to pass initial weights
    +      case Some(x) => x
    +      case None => createInitialWeightVector(dimensionsDS)
    +    }
    +
    +    // We need the weights vector to initialize the regularization value.
    +    val initWeightsVector = initialWeightsDS.collect()(0).weights
    +
    +    val initRegVal = parameterMap(RegularizationType)
    +      .applyRegularization(initWeightsVector, 0.0, parameterMap(RegularizationParameter))._2
    +
    +    // TODO: Is there a way to initialize the regularization parameter without collect()?
    +    // The following code should give us a dataset with the initial reg. parameter, but
we still
    +    // need to call collect to retrieve it. Question is: call collect here, or on the
weights as we
    +    // currently do?
    +    //val initRegValue: DataSet[Double] = initialWeights.map {x => parameterMap(RegularizationType)
    +    //  .applyRegularization(x.weights, 0.0, parameterMap(RegularizationParameter))._2}
    +    //  .reduce(_ + _)
    +
    +    // Perform the iterations
    +    // TODO: Enable convergence stopping criterion, as in Multiple Linear regression
    +    initialWeightsDS.iterate(numberOfIterations) {
    +      weightVector => {
    +        SGDStep(data, weightVector)
    +      }
    +    }
    +  }
    +
    +  /** Mapping function that calculates the weight gradients from the data.
    +    *
    +    */
    +  private class GradientCalculation extends
    +  RichMapFunction[LabeledVector, (WeightVector, Int)] {
    +
    +    var weightVector: WeightVector = null
    +
    +    @throws(classOf[Exception])
    +    override def open(configuration: Configuration): Unit = {
    +      val list = this.getRuntimeContext.
    +        getBroadcastVariable[WeightVector](WEIGHTVECTOR_BROADCAST)
    +
    +      weightVector = list.get(0)
    +    }
    +
    +    override def map(example: LabeledVector): (WeightVector, Int) = {
    +
    +      val lossFunction = parameterMap(LossFunction)
    +      //TODO(tvas): Should throw an error if Dimensions has not been defined
    +      val dimensions = example.vector.size
    +      // TODO(tvas): Any point in carrying the weightGradient vector for in-place replacement?
    +      // The idea in spark is to avoid object creation, but here we have to do it anyway
    +      val weightGradient = new DenseVector(new Array[Double](dimensions))
    +
    +      val (loss, lossDeriv) = lossFunction.lossAndGradient(example, weightVector, weightGradient)
    +
    +      // Restrict the value of the loss derivative to avoid numerical instabilities
    +      val restrictedLossDeriv: Double = {
    +        if (lossDeriv < -IterativeSolver.MAX_DLOSS) {
    +          -IterativeSolver.MAX_DLOSS
    +        }
    +        else if (lossDeriv > IterativeSolver.MAX_DLOSS) {
    +          IterativeSolver.MAX_DLOSS
    +        }
    +        else {
    +          lossDeriv
    +        }
    +      }
    +
    +      (new WeightVector(weightGradient, restrictedLossDeriv), 1)
    +    }
    +  }
    +
    +  /** Performs the update of the weights, according to the given gradients and regularization
type.
    +    *
    +    */
    +  private class WeightsUpdate() extends
    +  RichMapFunction[(WeightVector, Int), WeightVector] {
    +
    +
    +    var weightVector: WeightVector = null
    +
    +    @throws(classOf[Exception])
    +    override def open(configuration: Configuration): Unit = {
    +      val list = this.getRuntimeContext.
    +        getBroadcastVariable[WeightVector](WEIGHTVECTOR_BROADCAST)
    +
    +      weightVector = list.get(0)
    +    }
    +
    +    override def map(gradientsAndCount: (WeightVector, Int)): WeightVector = {
    +      val regularizationType = parameterMap(RegularizationType)
    +      val regularizationParameter = parameterMap(RegularizationParameter)
    +      val stepsize = parameterMap(Stepsize)
    +      val weightGradients = gradientsAndCount._1
    +      val count = gradientsAndCount._2
    +
    +      // Scale the gradients according to batch size
    +      BLAS.scal(1.0/count, weightGradients.weights)
    +
    +      val weight0Gradient = weightGradients.intercept / count
    +
    +      val iteration = getIterationRuntimeContext.getSuperstepNumber
    +
    +      // Scale initial stepsize by the inverse square root of the iteration number
    +      // TODO(tvas): There are more ways to determine the stepsize, possible low-effort
extensions
    +      // here
    +      val effectiveStepsize = stepsize/math.sqrt(iteration)
    +
    +      val newWeights = weightVector.weights.copy
    +      // Take the gradient step
    +      BLAS.axpy(-effectiveStepsize, weightGradients.weights, newWeights)
    +      val newWeight0 = weightVector.intercept - effectiveStepsize * weight0Gradient
    +
    +      // Apply the regularization
    +      val (updatedWeights, regVal) = regularizationType.applyRegularization(
    --- End diff --
    
    I don't think that is the correct way to calculate the updated weights with regularization.
Regularization is part of the cost function we want to minimize and thus it influences our
gradient. We have to incorporate the gradient of the regularization term into the overall
gradient before calculating the new weights.
    
    As far as I can tell, the L2 regularizer only need the old weight vector to calculate
the regularizer gradient. The L1 regularizer using a proximal operator however operates on
the new weight vector which it shrinks towards 0. Thus, in order to make the data treatment
consistent, we could let the regularizer do the calculation of the updated weight vector.
As input it gets the old weight vector, the gradient of the loss function, the stepsize and
the regularization value. 
    
    That way, it gives us enough flexibility to implement the L2 regularizer as well as the
L1 regularizer.


> Stochastic gradient descent optimizer for ML library
> ----------------------------------------------------
>
>                 Key: FLINK-1807
>                 URL: https://issues.apache.org/jira/browse/FLINK-1807
>             Project: Flink
>          Issue Type: Improvement
>          Components: Machine Learning Library
>            Reporter: Till Rohrmann
>            Assignee: Theodore Vasiloudis
>              Labels: ML
>
> Stochastic gradient descent (SGD) is a widely used optimization technique in different
ML algorithms. Thus, it would be helpful to provide a generalized SGD implementation which
can be instantiated with the respective gradient computation. Such a building block would
make the development of future algorithms easier.



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