Github user staple commented on a diff in the pull request:
https://github.com/apache/spark/pull/4934#discussion_r26186113
--- Diff:
mllib/src/main/scala/org/apache/spark/mllib/optimization/AcceleratedGradientDescent.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.spark.mllib.optimization
+
+import scala.collection.mutable.ArrayBuffer
+
+import breeze.linalg.{DenseVector => BDV, norm}
+
+import org.apache.spark.Logging
+import org.apache.spark.annotation.DeveloperApi
+import org.apache.spark.mllib.linalg.{Vector, Vectors}
+import org.apache.spark.rdd.RDD
+
+/**
+ * :: DeveloperApi ::
+ * This class optimizes a vector of weights via accelerated (proximal)
gradient descent.
+ * The implementation is based on TFOCS [[http://cvxr.com/tfocs]],
described in Becker, Candes, and
+ * Grant 2010.
+ * @param gradient Delegate that computes the loss function value and
gradient for a vector of
+ * weights.
+ * @param updater Delegate that updates weights in the direction of a
gradient.
+ */
+@DeveloperApi
+class AcceleratedGradientDescent (private var gradient: Gradient, private
var updater: Updater)
+ extends Optimizer {
+
+ private var stepSize: Double = 1.0
+ private var convergenceTol: Double = 1e-4
+ private var numIterations: Int = 100
+ private var regParam: Double = 0.0
+
+ /**
+ * Set the initial step size, used for the first step. Default 1.0.
+ * On subsequent steps, the step size will be adjusted by the
acceleration algorithm.
+ */
+ def setStepSize(step: Double): this.type = {
+ this.stepSize = step
+ this
+ }
+
+ /**
+ * Set the optimization convergence tolerance. Default 1e-4.
+ * Smaller values will increase accuracy but require additional
iterations.
+ */
+ def setConvergenceTol(tol: Double): this.type = {
+ this.convergenceTol = tol
+ this
+ }
+
+ /**
+ * Set the maximum number of iterations. Default 100.
+ */
+ def setNumIterations(iters: Int): this.type = {
+ this.numIterations = iters
+ this
+ }
+
+ /**
+ * Set the regularization parameter. Default 0.0.
+ */
+ def setRegParam(regParam: Double): this.type = {
+ this.regParam = regParam
+ this
+ }
+
+ /**
+ * Set a Gradient delegate for computing the loss function value and
gradient.
+ */
+ def setGradient(gradient: Gradient): this.type = {
+ this.gradient = gradient
+ this
+ }
+
+ /**
+ * Set an Updater delegate for updating weights in the direction of a
gradient.
+ * If regularization is used, the Updater will implement the
regularization term's proximity
+ * operator. Thus the type of regularization penalty is configured by
providing a corresponding
+ * Updater implementation.
+ */
+ def setUpdater(updater: Updater): this.type = {
+ this.updater = updater
+ this
+ }
+
+ /**
+ * Run accelerated gradient descent on the provided training data.
+ * @param data training data
+ * @param initialWeights initial weights
+ * @return solution vector
+ */
+ def optimize(data: RDD[(Double, Vector)], initialWeights: Vector):
Vector = {
+ val (weights, _) = AcceleratedGradientDescent.run(
+ data,
+ gradient,
+ updater,
+ stepSize,
+ convergenceTol,
+ numIterations,
+ regParam,
+ initialWeights)
+ weights
+ }
+}
+
+/**
+ * :: DeveloperApi ::
+ * Top-level method to run accelerated (proximal) gradient descent.
+ */
+@DeveloperApi
+object AcceleratedGradientDescent extends Logging {
+ /**
+ * Run accelerated proximal gradient descent.
+ * The implementation is based on TFOCS [[http://cvxr.com/tfocs]],
described in Becker, Candes,
+ * and Grant 2010. A limited but useful subset of the TFOCS feature set
is implemented, including
+ * support for composite loss functions, the Auslender and Teboulle
acceleration method, and
+ * automatic restart using the gradient test. A global Lipschitz bound
is supported in preference
+ * to local Lipschitz estimation via backtracking. On each iteration,
the loss function and
+ * gradient are caclculated from the full training dataset, requiring
one Spark map reduce.
+ *
+ * @param data Input data. RDD containing data examples of the form
(label, [feature values]).
+ * @param gradient Delegate that computes the loss function value and
gradient for a vector of
+ weights (for one single data example).
+ * @param updater Delegate that updates weights in the direction of a
gradient.
+ * @param stepSize Initial step size for the first step.
+ * @param convergenceTol Tolerance for convergence of the optimization
algorithm. When the norm of
+ * the change in weight vectors between successive
iterations falls below
+ * this relative tolerance, optimization is
complete.
+ * @param numIterations Maximum number of iterations to run the
algorithm.
+ * @param regParam The regularization parameter.
+ * @param initialWeights The initial weight values.
+ *
+ * @return A tuple containing two elements. The first element is a
Vector containing the optimized
+ * weight for each feature, and the second element is an array
containing the approximate
+ * loss computed on each iteration.
+ */
+ def run(
+ data: RDD[(Double, Vector)],
+ gradient: Gradient,
+ updater: Updater,
+ stepSize: Double,
+ convergenceTol: Double,
+ numIterations: Int,
+ regParam: Double,
+ initialWeights: Vector): (Vector, Array[Double]) = {
+
+ /** Returns the loss function and gradient for the provided weights
'x'. */
+ def applySmooth(x: BDV[Double]): (Double, BDV[Double]) = {
+ val bcX = data.context.broadcast(Vectors.fromBreeze(x))
+
+ // Sum the loss function and gradient computed for each training
example.
+ val (loss, grad, count) = data.treeAggregate((0.0,
BDV.zeros[Double](x.size), 0L))(
+ seqOp = (c, v) => (c, v) match { case ((loss, grad, count),
(label, features)) =>
+ val l = gradient.compute(features, label, bcX.value,
Vectors.fromBreeze(grad))
+ (loss + l, grad, count + 1)
+ },
+ combOp = (c1, c2) => (c1, c2) match {
+ case ((loss1, grad1, count1), (loss2, grad2, count2)) =>
+ (loss1 + loss2, grad1 += grad2, count1 + count2)
+ })
+
+ // Divide the summed loss and gradient by the number of training
examples.
+ (loss / count, grad / (count: Double))
+ }
+
+ /**
+ * Returns the regularization loss and updates weights according to
the gradient and the
+ * proximity operator.
+ */
+ def applyProjector(x: BDV[Double], g: BDV[Double], step: Double):
(Double, BDV[Double]) = {
+ val (weights, regularization) =
updater.compute(Vectors.fromBreeze(x),
+
Vectors.fromBreeze(g),
+ step,
+ iter = 1, // Passing
1 avoids step size
+ //
rescaling within the updater.
+ regParam)
+ (regularization, BDV[Double](weights.toArray))
+ }
+
+ var x = BDV[Double](initialWeights.toArray)
+ var z = x
+ val L = 1.0 / stepSize // Infer a (global) Lipshitz bound from the
provided stepSize.
+ var theta = Double.PositiveInfinity
+ var hasConverged = false
+ val lossHistory = new ArrayBuffer[Double](numIterations)
+
+ for (i <- 1 to numIterations if !hasConverged) {
+
+ // Auslender and Teboulle's accelerated method.
+ val (x_old, z_old) = (x, z)
+ theta = 2.0 / (1.0 + math.sqrt(1.0 + 4.0 / (theta * theta)))
+ val y = x_old * (1.0 - theta) + z_old * theta
+ val (f_y, g_y) = applySmooth(y)
+ val step = 1.0 / (theta * L)
+ z = applyProjector(z_old, g_y, step)._2
+ x = x_old * (1.0 - theta) + z * theta
+ val d_x = x - x_old
+
+ // Track loss history using the loss function at y, since f_y is
already avaialble and
--- End diff --
Oops looks like a typo: 'avaialble'
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