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org.deeplearning4j.optimize.solvers.BackTrackLineSearch Maven / Gradle / Ivy
/*
* ******************************************************************************
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* *
* * This program and the accompanying materials are made available under the
* * terms of the Apache License, Version 2.0 which is available at
* * https://www.apache.org/licenses/LICENSE-2.0.
* *
* * See the NOTICE file distributed with this work for additional
* * information regarding copyright ownership.
* * 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.
* *
* * SPDX-License-Identifier: Apache-2.0
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package org.deeplearning4j.optimize.solvers;
import org.apache.commons.math3.util.FastMath;
import org.deeplearning4j.exception.InvalidStepException;
import org.deeplearning4j.nn.api.Model;
import org.deeplearning4j.nn.conf.stepfunctions.NegativeGradientStepFunction;
import org.deeplearning4j.optimize.api.ConvexOptimizer;
import org.deeplearning4j.optimize.api.LineOptimizer;
import org.deeplearning4j.optimize.api.StepFunction;
import org.deeplearning4j.optimize.stepfunctions.NegativeDefaultStepFunction;
import org.nd4j.linalg.api.blas.Level1;
import org.nd4j.linalg.api.buffer.DataType;
import org.nd4j.linalg.api.ndarray.INDArray;
import org.nd4j.linalg.api.ops.impl.scalar.comparison.ScalarSetValue;
import org.nd4j.linalg.api.ops.impl.transforms.comparison.Eps;
import org.nd4j.linalg.api.shape.Shape;
import org.nd4j.linalg.factory.Nd4j;
import org.deeplearning4j.nn.workspace.LayerWorkspaceMgr;
import org.slf4j.Logger;
import org.slf4j.LoggerFactory;
import static org.nd4j.linalg.ops.transforms.Transforms.abs;
public class BackTrackLineSearch implements LineOptimizer {
private static final Logger log = LoggerFactory.getLogger(BackTrackLineSearch.class);
private Model layer;
private StepFunction stepFunction;
private ConvexOptimizer optimizer;
private int maxIterations;
double stepMax = 100;
private boolean minObjectiveFunction = true;
// termination conditions: either
// a) abs(delta x/x) < REL_TOLX for all coordinates
// b) abs(delta x) < ABS_TOLX for all coordinates
// c) sufficient function increase (uses ALF)
private double relTolx = 1e-7f;
private double absTolx = 1e-4f; // tolerance on absolute value difference
protected final double ALF = 1e-4f;
/**
* @param layer
* @param stepFunction
* @param optimizer
*/
public BackTrackLineSearch(Model layer, StepFunction stepFunction, ConvexOptimizer optimizer) {
this.layer = layer;
this.stepFunction = stepFunction;
this.optimizer = optimizer;
this.maxIterations = layer.conf().getMaxNumLineSearchIterations();
}
/**
* @param optimizable
* @param optimizer
*/
public BackTrackLineSearch(Model optimizable, ConvexOptimizer optimizer) {
this(optimizable, new NegativeDefaultStepFunction(), optimizer);
}
public void setStepMax(double stepMax) {
this.stepMax = stepMax;
}
public double getStepMax() {
return stepMax;
}
/**
* Sets the tolerance of relative diff in function value.
* Line search converges if abs(delta x / x) < tolx
* for all coordinates.
*/
public void setRelTolx(double tolx) {
relTolx = tolx;
}
/**
* Sets the tolerance of absolute diff in function value.
* Line search converges if abs(delta x) < tolx
* for all coordinates.
*/
public void setAbsTolx(double tolx) {
absTolx = tolx;
}
public int getMaxIterations() {
return maxIterations;
}
public void setMaxIterations(int maxIterations) {
this.maxIterations = maxIterations;
}
public double setScoreFor(INDArray parameters, LayerWorkspaceMgr workspaceMgr) {
layer.setParams(parameters);
layer.computeGradientAndScore(workspaceMgr);
return layer.score();
}
// returns fraction of step size if found a good step
// returns 0.0 if could not step in direction
// step == alam and score == f in book
/**
* @param parameters the parameters to optimize
* @param gradients the line/rate of change
* @param searchDirection the point for the line search to go in
* @return the next step size
* @throws InvalidStepException
*/
@Override
public double optimize(INDArray parameters, INDArray gradients, INDArray searchDirection, LayerWorkspaceMgr workspaceMgr)
throws InvalidStepException {
double test, stepMin, step, step2, oldStep, tmpStep;
double rhs1, rhs2, a, b, disc, score, scoreAtStart, score2;
minObjectiveFunction = (stepFunction instanceof NegativeDefaultStepFunction
|| stepFunction instanceof NegativeGradientStepFunction);
parameters = parameters.reshape(parameters.length());
Level1 l1Blas = Nd4j.getBlasWrapper().level1();
double sum = l1Blas.nrm2(searchDirection);
double slope = -1f * Nd4j.getBlasWrapper().dot(searchDirection, gradients);
log.debug("slope = {}", slope);
INDArray maxOldParams = abs(parameters);
Nd4j.getExecutioner().exec(new ScalarSetValue(maxOldParams, 1));
INDArray testMatrix = abs(gradients).divi(maxOldParams);
test = testMatrix.max(Integer.MAX_VALUE).getDouble(0);
step = 1.0; // initially, step = 1.0, i.e. take full Newton step
stepMin = relTolx / test; // relative convergence tolerance
oldStep = 0.0;
step2 = 0.0;
score = score2 = scoreAtStart = layer.score();
double bestScore = score;
double bestStepSize = 1.0;
if (log.isTraceEnabled()) {
double norm1 = l1Blas.asum(searchDirection);
int infNormIdx = l1Blas.iamax(searchDirection);
double infNorm = FastMath.max(Float.NEGATIVE_INFINITY, searchDirection.getDouble(infNormIdx));
log.trace("ENTERING BACKTRACK\n");
log.trace("Entering BackTrackLineSearch, value = " + scoreAtStart + ",\ndirection.oneNorm:" + norm1
+ " direction.infNorm:" + infNorm);
}
if (sum > stepMax) {
log.warn("Attempted step too big. scaling: sum= {}, stepMax= {}", sum, stepMax);
searchDirection.muli(stepMax / sum);
}
// if (slope >= 0.0) {
// throw new InvalidStepException("Slope " + slope + " is >= 0.0. Expect slope < 0.0 when minimizing objective function");
// }
// find maximum lambda
// converge when (delta x) / x < REL_TOLX for all coordinates.
// the largest step size that triggers this threshold is precomputed and saved in stepMin
// look for step size in direction given by "line"
INDArray candidateParameters = null;
for (int iteration = 0; iteration < maxIterations; iteration++) {
if (log.isTraceEnabled()) {
log.trace("BackTrack loop iteration {} : step={}, oldStep={}", iteration, step, oldStep);
log.trace("before step, x.1norm: {} \nstep: {} \noldStep: {}", parameters.norm1(Integer.MAX_VALUE),
step, oldStep);
}
if (step == oldStep)
throw new IllegalArgumentException("Current step == oldStep");
// step
candidateParameters = parameters.dup('f');
stepFunction.step(candidateParameters, searchDirection, step);
oldStep = step;
if (log.isTraceEnabled()) {
double norm1 = l1Blas.asum(candidateParameters);
log.trace("after step, x.1norm: " + norm1);
}
// check for convergence on delta x
if ((step < stepMin) || Nd4j.getExecutioner()
.exec(new Eps(parameters, candidateParameters,Nd4j.createUninitialized(DataType.BOOL, candidateParameters.shape(), candidateParameters.ordering())))
.castTo(DataType.DOUBLE).sumNumber().longValue() != candidateParameters.length()) {
score = setScoreFor(parameters, workspaceMgr);
log.debug("EXITING BACKTRACK: Jump too small (stepMin = {}). Exiting and using original params. Score = {}",
stepMin, score);
return 0.0;
}
score = setScoreFor(candidateParameters, workspaceMgr);
log.debug("Model score after step = {}", score);
//Score best step size for use if we terminate on maxIterations
if ((minObjectiveFunction && score < bestScore) || (!minObjectiveFunction && score > bestScore)) {
bestScore = score;
bestStepSize = step;
}
//Sufficient decrease in cost/loss function (Wolfe condition / Armijo condition)
if (minObjectiveFunction && score <= scoreAtStart + ALF * step * slope) {
log.debug("Sufficient decrease (Wolfe cond.), exiting backtrack on iter {}: score={}, scoreAtStart={}",
iteration, score, scoreAtStart);
if (score > scoreAtStart)
throw new IllegalStateException("Function did not decrease: score = " + score + " > " + scoreAtStart
+ " = oldScore");
return step;
}
//Sufficient increase in cost/loss function (Wolfe condition / Armijo condition)
if (!minObjectiveFunction && score >= scoreAtStart + ALF * step * slope) {
log.debug("Sufficient increase (Wolfe cond.), exiting backtrack on iter {}: score={}, bestScore={}",
iteration, score, scoreAtStart);
if (score < scoreAtStart)
throw new IllegalStateException("Function did not increase: score = " + score + " < " + scoreAtStart
+ " = scoreAtStart");
return step;
}
// if value is infinite, i.e. we've jumped to unstable territory, then scale down jump
else if (Double.isInfinite(score) || Double.isInfinite(score2) || Double.isNaN(score)
|| Double.isNaN(score2)) {
log.warn("Value is infinite after jump. oldStep={}. score={}, score2={}. Scaling back step size...",
oldStep, score, score2);
tmpStep = .2 * step;
if (step < stepMin) { //convergence on delta x
score = setScoreFor(parameters, workspaceMgr);
log.warn("EXITING BACKTRACK: Jump too small (step={} < stepMin={}). Exiting and using previous parameters. Value={}",
step, stepMin, score);
return 0.0;
}
}
// backtrack
else if (minObjectiveFunction) {
if (step == 1.0) // first time through
tmpStep = -slope / (2.0 * (score - scoreAtStart - slope));
else {
rhs1 = score - scoreAtStart - step * slope;
rhs2 = score2 - scoreAtStart - step2 * slope;
if (step == step2)
throw new IllegalStateException("FAILURE: dividing by step-step2 which equals 0. step=" + step);
double stepSquared = step * step;
double step2Squared = step2 * step2;
a = (rhs1 / stepSquared - rhs2 / step2Squared) / (step - step2);
b = (-step2 * rhs1 / stepSquared + step * rhs2 / step2Squared) / (step - step2);
if (a == 0.0)
tmpStep = -slope / (2.0 * b);
else {
disc = b * b - 3.0 * a * slope;
if (disc < 0.0) {
tmpStep = 0.5 * step;
} else if (b <= 0.0)
tmpStep = (-b + FastMath.sqrt(disc)) / (3.0 * a);
else
tmpStep = -slope / (b + FastMath.sqrt(disc));
}
if (tmpStep > 0.5 * step)
tmpStep = 0.5 * step; // lambda <= 0.5 lambda_1
}
} else {
if (step == 1.0) // first time through
tmpStep = -slope / (2.0 * (scoreAtStart - score - slope));
else {
rhs1 = scoreAtStart - score - step * slope;
rhs2 = scoreAtStart - score2 - step2 * slope;
if (step == step2)
throw new IllegalStateException("FAILURE: dividing by step-step2 which equals 0. step=" + step);
double stepSquared = step * step;
double step2Squared = step2 * step2;
a = (rhs1 / stepSquared - rhs2 / step2Squared) / (step - step2);
b = (-step2 * rhs1 / stepSquared + step * rhs2 / step2Squared) / (step - step2);
if (a == 0.0)
tmpStep = -slope / (2.0 * b);
else {
disc = b * b - 3.0 * a * slope;
if (disc < 0.0) {
tmpStep = 0.5 * step;
} else if (b <= 0.0)
tmpStep = (-b + FastMath.sqrt(disc)) / (3.0 * a);
else
tmpStep = -slope / (b + FastMath.sqrt(disc));
}
if (tmpStep > 0.5 * step)
tmpStep = 0.5 * step; // lambda <= 0.5 lambda_1
}
}
step2 = step;
score2 = score;
log.debug("tmpStep: {}", tmpStep);
step = Math.max(tmpStep, .1f * step); // lambda >= .1*Lambda_1
}
if (minObjectiveFunction && bestScore < scoreAtStart) {
//Return best step size
log.debug("Exited line search after maxIterations termination condition; bestStepSize={}, bestScore={}, scoreAtStart={}",
bestStepSize, bestScore, scoreAtStart);
return bestStepSize;
} else if (!minObjectiveFunction && bestScore > scoreAtStart) {
//Return best step size
log.debug("Exited line search after maxIterations termination condition; bestStepSize={}, bestScore={}, scoreAtStart={}",
bestStepSize, bestScore, scoreAtStart);
return bestStepSize;
} else {
log.debug("Exited line search after maxIterations termination condition; score did not improve (bestScore={}, scoreAtStart={}). Resetting parameters",
bestScore, scoreAtStart);
setScoreFor(parameters, workspaceMgr);
return 0.0;
}
}
}
