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/*
* 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 org.scalatest.FunSuite
import org.scalatest.matchers.ShouldMatchers
import org.apache.spark.mllib.regression.LabeledPoint
import org.apache.spark.mllib.linalg.Vectors
import org.apache.spark.mllib.util.LocalSparkContext
class LBFGSSuite extends FunSuite with LocalSparkContext with ShouldMatchers {
val nPoints = 10000
val A = 2.0
val B = -1.5
val initialB = -1.0
val initialWeights = Array(initialB)
val gradient = new LogisticGradient()
val numCorrections = 10
val miniBatchFrac = 1.0
val simpleUpdater = new SimpleUpdater()
val squaredL2Updater = new SquaredL2Updater()
// Add an extra variable consisting of all 1.0's for the intercept.
val testData = GradientDescentSuite.generateGDInput(A, B, nPoints, 42)
val data = testData.map { case LabeledPoint(label, features) =>
label -> Vectors.dense(1.0, features.toArray: _*)
}
lazy val dataRDD = sc.parallelize(data, 2).cache()
def compareDouble(x: Double, y: Double, tol: Double = 1E-3): Boolean = {
math.abs(x - y) / (math.abs(y) + 1e-15) < tol
}
test("LBFGS loss should be decreasing and match the result of Gradient Descent.") {
val regParam = 0
val initialWeightsWithIntercept = Vectors.dense(1.0, initialWeights: _*)
val convergenceTol = 1e-12
val maxNumIterations = 10
val (_, loss) = LBFGS.runMiniBatchLBFGS(
dataRDD,
gradient,
simpleUpdater,
numCorrections,
convergenceTol,
maxNumIterations,
regParam,
miniBatchFrac,
initialWeightsWithIntercept)
// Since the cost function is convex, the loss is guaranteed to be monotonically decreasing
// with L-BFGS optimizer.
// (SGD doesn't guarantee this, and the loss will be fluctuating in the optimization process.)
assert((loss, loss.tail).zipped.forall(_ > _), "loss should be monotonically decreasing.")
val stepSize = 1.0
// Well, GD converges slower, so it requires more iterations!
val numGDIterations = 50
val (_, lossGD) = GradientDescent.runMiniBatchSGD(
dataRDD,
gradient,
simpleUpdater,
stepSize,
numGDIterations,
regParam,
miniBatchFrac,
initialWeightsWithIntercept)
// GD converges a way slower than L-BFGS. To achieve 1% difference,
// it requires 90 iterations in GD. No matter how hard we increase
// the number of iterations in GD here, the lossGD will be always
// larger than lossLBFGS. This is based on observation, no theoretically guaranteed
assert(Math.abs((lossGD.last - loss.last) / loss.last) < 0.02,
"LBFGS should match GD result within 2% difference.")
}
test("LBFGS and Gradient Descent with L2 regularization should get the same result.") {
val regParam = 0.2
// Prepare another non-zero weights to compare the loss in the first iteration.
val initialWeightsWithIntercept = Vectors.dense(0.3, 0.12)
val convergenceTol = 1e-12
val maxNumIterations = 10
val (weightLBFGS, lossLBFGS) = LBFGS.runMiniBatchLBFGS(
dataRDD,
gradient,
squaredL2Updater,
numCorrections,
convergenceTol,
maxNumIterations,
regParam,
miniBatchFrac,
initialWeightsWithIntercept)
val numGDIterations = 50
val stepSize = 1.0
val (weightGD, lossGD) = GradientDescent.runMiniBatchSGD(
dataRDD,
gradient,
squaredL2Updater,
stepSize,
numGDIterations,
regParam,
miniBatchFrac,
initialWeightsWithIntercept)
assert(compareDouble(lossGD(0), lossLBFGS(0)),
"The first losses of LBFGS and GD should be the same.")
// The 2% difference here is based on observation, but is not theoretically guaranteed.
assert(compareDouble(lossGD.last, lossLBFGS.last, 0.02),
"The last losses of LBFGS and GD should be within 2% difference.")
assert(compareDouble(weightLBFGS(0), weightGD(0), 0.02) &&
compareDouble(weightLBFGS(1), weightGD(1), 0.02),
"The weight differences between LBFGS and GD should be within 2%.")
}
test("The convergence criteria should work as we expect.") {
val regParam = 0.0
/**
* For the first run, we set the convergenceTol to 0.0, so that the algorithm will
* run up to the maxNumIterations which is 8 here.
*/
val initialWeightsWithIntercept = Vectors.dense(0.0, 0.0)
val maxNumIterations = 8
var convergenceTol = 0.0
val (_, lossLBFGS1) = LBFGS.runMiniBatchLBFGS(
dataRDD,
gradient,
squaredL2Updater,
numCorrections,
convergenceTol,
maxNumIterations,
regParam,
miniBatchFrac,
initialWeightsWithIntercept)
// Note that the first loss is computed with initial weights,
// so the total numbers of loss will be numbers of iterations + 1
assert(lossLBFGS1.length == 9)
convergenceTol = 0.1
val (_, lossLBFGS2) = LBFGS.runMiniBatchLBFGS(
dataRDD,
gradient,
squaredL2Updater,
numCorrections,
convergenceTol,
maxNumIterations,
regParam,
miniBatchFrac,
initialWeightsWithIntercept)
// Based on observation, lossLBFGS2 runs 3 iterations, no theoretically guaranteed.
assert(lossLBFGS2.length == 4)
assert((lossLBFGS2(2) - lossLBFGS2(3)) / lossLBFGS2(2) < convergenceTol)
convergenceTol = 0.01
val (_, lossLBFGS3) = LBFGS.runMiniBatchLBFGS(
dataRDD,
gradient,
squaredL2Updater,
numCorrections,
convergenceTol,
maxNumIterations,
regParam,
miniBatchFrac,
initialWeightsWithIntercept)
// With smaller convergenceTol, it takes more steps.
assert(lossLBFGS3.length > lossLBFGS2.length)
// Based on observation, lossLBFGS2 runs 5 iterations, no theoretically guaranteed.
assert(lossLBFGS3.length == 6)
assert((lossLBFGS3(4) - lossLBFGS3(5)) / lossLBFGS3(4) < convergenceTol)
}
}
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