public virtual double TryEta(AbstractStochasticCachingDiffUpdateFunction function, double[] initial, int[] sample, double eta)
{
int numBatches = sample.Length / bSize;
double[] w = new double[initial.Length];
double wscale = 1;
System.Array.Copy(initial, 0, w, 0, w.Length);
int[] sampleBatch = new int[bSize];
int sampleIndex = 0;
for (int batch = 0; batch < numBatches; batch++)
{
for (int i = 0; i < bSize; i++)
{
sampleBatch[i] = sample[(sampleIndex + i) % sample.Length];
}
sampleIndex += bSize;
double gain = eta / wscale;
function.CalculateStochasticUpdate(w, wscale, sampleBatch, gain);
wscale *= (1 - eta * lambda * bSize);
}
double obj = GetObjective(function, w, wscale, sample);
return(obj);
}
public virtual double GetObjective(AbstractStochasticCachingDiffUpdateFunction function, double[] w, double wscale, int[] sample)
{
double wnorm = GetNorm(w) * wscale * wscale;
double obj = function.ValueAt(w, wscale, sample);
// Calculate objective with L2 regularization
return(obj + 0.5 * sample.Length * lambda * wnorm);
}
/// <summary>Finds a good learning rate to start with.</summary>
/// <remarks>
/// Finds a good learning rate to start with.
/// eta = 1/(lambda*(t0+t)) - we find good t0
/// </remarks>
/// <param name="function"/>
/// <param name="initial"/>
/// <param name="sampleSize"/>
/// <param name="seta"/>
public virtual double Tune(AbstractStochasticCachingDiffUpdateFunction function, double[] initial, int sampleSize, double seta)
{
Timing timer = new Timing();
int[] sample = function.GetSample(sampleSize);
double sobj = GetObjective(function, initial, 1, sample);
double besteta = 1;
double bestobj = sobj;
double eta = seta;
int totest = 10;
double factor = 2;
bool phase2 = false;
while (totest > 0 || !phase2)
{
double obj = TryEta(function, initial, sample, eta);
bool okay = (obj < sobj);
Sayln(" Trying eta=" + eta + " obj=" + obj + ((okay) ? "(possible)" : "(too large)"));
if (okay)
{
totest -= 1;
if (obj < bestobj)
{
bestobj = obj;
besteta = eta;
}
}
if (!phase2)
{
if (okay)
{
eta = eta * factor;
}
else
{
phase2 = true;
eta = seta;
}
}
if (phase2)
{
eta = eta / factor;
}
}
// take it on the safe side (implicit regularization)
besteta /= factor;
// determine t
t0 = (int)(1 / (besteta * lambda));
Sayln(" Taking eta=" + besteta + " t0=" + t0);
Sayln(" Tuning completed in: " + Timing.ToSecondsString(timer.Report()) + " s");
return(besteta);
}
public virtual double[] Minimize(IDiffFunction f, double functionTolerance, double[] initial, int maxIterations)
{
int totalSamples = 0;
Sayln("Using lambda=" + lambda);
if (f is AbstractStochasticCachingDiffUpdateFunction)
{
AbstractStochasticCachingDiffUpdateFunction func = (AbstractStochasticCachingDiffUpdateFunction)f;
func.sampleMethod = AbstractStochasticCachingDiffFunction.SamplingMethod.Shuffled;
totalSamples = func.DataDimension();
if (bSize > totalSamples)
{
log.Info("WARNING: Total number of samples=" + totalSamples + " is smaller than requested batch size=" + bSize + "!!!");
bSize = totalSamples;
Sayln("Using batch size=" + bSize);
}
if (bSize <= 0)
{
log.Info("WARNING: Requested batch size=" + bSize + " <= 0 !!!");
bSize = totalSamples;
Sayln("Using batch size=" + bSize);
}
}
x = new double[initial.Length];
double[] testUpdateCache = null;
double[] currentRateCache = null;
double[] bCache = null;
sumGradSquare = new double[initial.Length];
prevGrad = new double[initial.Length];
prevDeltaX = new double[initial.Length];
if (useAdaDelta)
{
sumDeltaXSquare = new double[initial.Length];
if (prior != SGDWithAdaGradAndFOBOS.Prior.None && prior != SGDWithAdaGradAndFOBOS.Prior.Gaussian)
{
throw new NotSupportedException("useAdaDelta is currently only supported for Prior.NONE or Prior.GAUSSIAN");
}
}
int[][] featureGrouping = null;
if (prior != SGDWithAdaGradAndFOBOS.Prior.Lasso && prior != SGDWithAdaGradAndFOBOS.Prior.None)
{
testUpdateCache = new double[initial.Length];
currentRateCache = new double[initial.Length];
}
if (prior != SGDWithAdaGradAndFOBOS.Prior.Lasso && prior != SGDWithAdaGradAndFOBOS.Prior.Ridge && prior != SGDWithAdaGradAndFOBOS.Prior.Gaussian)
{
if (!(f is IHasFeatureGrouping))
{
throw new NotSupportedException("prior is specified to be ae-lasso or g-lasso, but function does not support feature grouping");
}
featureGrouping = ((IHasFeatureGrouping)f).GetFeatureGrouping();
}
if (prior == SGDWithAdaGradAndFOBOS.Prior.sgLASSO)
{
bCache = new double[initial.Length];
}
System.Array.Copy(initial, 0, x, 0, x.Length);
int numBatches = 1;
if (f is AbstractStochasticCachingDiffUpdateFunction)
{
if (totalSamples > 0)
{
numBatches = totalSamples / bSize;
}
}
bool have_max = (maxIterations > 0 || numPasses > 0);
if (!have_max)
{
throw new NotSupportedException("No maximum number of iterations has been specified.");
}
else
{
maxIterations = Math.Max(maxIterations, numPasses * numBatches);
}
Sayln(" Batch size of: " + bSize);
Sayln(" Data dimension of: " + totalSamples);
Sayln(" Batches per pass through data: " + numBatches);
Sayln(" Number of passes is = " + numPasses);
Sayln(" Max iterations is = " + maxIterations);
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// Loop
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Timing total = new Timing();
Timing current = new Timing();
total.Start();
current.Start();
int iters = 0;
double gValue = 0;
double wValue = 0;
double currentRate = 0;
double testUpdate = 0;
double realUpdate = 0;
IList <double> values = null;
double oldObjVal = 0;
for (int pass = 0; pass < numPasses; pass++)
{
bool doEval = (pass > 0 && evaluateIters > 0 && pass % evaluateIters == 0);
double evalScore = double.NegativeInfinity;
if (doEval)
{
evalScore = DoEvaluation(x);
if (useEvalImprovement && !ToContinue(x, evalScore))
{
break;
}
}
// TODO: currently objVal is only updated for GAUSSIAN prior
// when other priors are used, objVal only reflects the un-regularized obj value
double objVal = double.NegativeInfinity;
double objDelta = double.NegativeInfinity;
Say("Iter: " + iters + " pass " + pass + " batch 1 ... ");
int numOfNonZero = 0;
int numOfNonZeroGroup = 0;
string gSizeStr = string.Empty;
for (int batch = 0; batch < numBatches; batch++)
{
iters++;
//Get the next gradients
// log.info("getting gradients");
double[] gradients = null;
if (f is AbstractStochasticCachingDiffUpdateFunction)
{
AbstractStochasticCachingDiffUpdateFunction func = (AbstractStochasticCachingDiffUpdateFunction)f;
if (bSize == totalSamples)
{
objVal = func.ValueAt(x);
gradients = func.GetDerivative();
objDelta = objVal - oldObjVal;
oldObjVal = objVal;
if (values == null)
{
values = new List <double>();
}
values.Add(objVal);
}
else
{
func.CalculateStochasticGradient(x, bSize);
gradients = func.GetDerivative();
}
}
else
{
if (f is AbstractCachingDiffFunction)
{
AbstractCachingDiffFunction func = (AbstractCachingDiffFunction)f;
gradients = func.DerivativeAt(x);
}
}
// log.info("applying regularization");
if (prior == SGDWithAdaGradAndFOBOS.Prior.None || prior == SGDWithAdaGradAndFOBOS.Prior.Gaussian)
{
// Gaussian prior is also handled in objective
for (int index = 0; index < x.Length; index++)
{
gValue = gradients[index];
currentRate = ComputeLearningRate(index, gValue);
// arrive at x(t+1/2)
wValue = x[index];
testUpdate = wValue - (currentRate * gValue);
realUpdate = testUpdate;
UpdateX(x, index, realUpdate);
}
}
else
{
// x[index] = testUpdate;
if (prior == SGDWithAdaGradAndFOBOS.Prior.Lasso || prior == SGDWithAdaGradAndFOBOS.Prior.Ridge)
{
double testUpdateSquaredSum = 0;
ICollection <int> paramRange = null;
if (f is IHasRegularizerParamRange)
{
paramRange = ((IHasRegularizerParamRange)f).GetRegularizerParamRange(x);
}
else
{
paramRange = new HashSet <int>();
for (int i = 0; i < x.Length; i++)
{
paramRange.Add(i);
}
}
foreach (int index in paramRange)
{
gValue = gradients[index];
currentRate = ComputeLearningRate(index, gValue);
// arrive at x(t+1/2)
wValue = x[index];
testUpdate = wValue - (currentRate * gValue);
double currentLambda = currentRate * lambda;
// apply FOBOS
if (prior == SGDWithAdaGradAndFOBOS.Prior.Lasso)
{
realUpdate = Math.Signum(testUpdate) * Pospart(Math.Abs(testUpdate) - currentLambda);
UpdateX(x, index, realUpdate);
if (realUpdate != 0)
{
numOfNonZero++;
}
}
else
{
if (prior == SGDWithAdaGradAndFOBOS.Prior.Ridge)
{
testUpdateSquaredSum += testUpdate * testUpdate;
testUpdateCache[index] = testUpdate;
currentRateCache[index] = currentRate;
}
}
}
// } else if (prior == Prior.GAUSSIAN) { // GAUSSIAN prior is assumed to be handled in the objective directly
// realUpdate = testUpdate / (1 + currentLambda);
// updateX(x, index, realUpdate);
// // update objVal
// objVal += currentLambda * wValue * wValue;
if (prior == SGDWithAdaGradAndFOBOS.Prior.Ridge)
{
double testUpdateNorm = Math.Sqrt(testUpdateSquaredSum);
for (int index_1 = 0; index_1 < testUpdateCache.Length; index_1++)
{
realUpdate = testUpdateCache[index_1] * Pospart(1 - currentRateCache[index_1] * lambda / testUpdateNorm);
UpdateX(x, index_1, realUpdate);
if (realUpdate != 0)
{
numOfNonZero++;
}
}
}
}
else
{
// log.info("featureGroup.length: " + featureGrouping.length);
foreach (int[] gFeatureIndices in featureGrouping)
{
// if (gIndex % 100 == 0) log.info(gIndex+" ");
double testUpdateSquaredSum = 0;
double testUpdateAbsSum = 0;
double M = gFeatureIndices.Length;
double dm = Math.Log(M);
foreach (int index in gFeatureIndices)
{
gValue = gradients[index];
currentRate = ComputeLearningRate(index, gValue);
// arrive at x(t+1/2)
wValue = x[index];
testUpdate = wValue - (currentRate * gValue);
testUpdateSquaredSum += testUpdate * testUpdate;
testUpdateAbsSum += Math.Abs(testUpdate);
testUpdateCache[index] = testUpdate;
currentRateCache[index] = currentRate;
}
if (prior == SGDWithAdaGradAndFOBOS.Prior.gLASSO)
{
double testUpdateNorm = Math.Sqrt(testUpdateSquaredSum);
bool groupHasNonZero = false;
foreach (int index_1 in gFeatureIndices)
{
realUpdate = testUpdateCache[index_1] * Pospart(1 - currentRateCache[index_1] * lambda * dm / testUpdateNorm);
UpdateX(x, index_1, realUpdate);
if (realUpdate != 0)
{
numOfNonZero++;
groupHasNonZero = true;
}
}
if (groupHasNonZero)
{
numOfNonZeroGroup++;
}
}
else
{
if (prior == SGDWithAdaGradAndFOBOS.Prior.aeLASSO)
{
int nonZeroCount = 0;
bool groupHasNonZero = false;
foreach (int index_1 in gFeatureIndices)
{
double tau = currentRateCache[index_1] * lambda / (1 + currentRateCache[index_1] * lambda * M) * testUpdateAbsSum;
realUpdate = Math.Signum(testUpdateCache[index_1]) * Pospart(Math.Abs(testUpdateCache[index_1]) - tau);
UpdateX(x, index_1, realUpdate);
if (realUpdate != 0)
{
numOfNonZero++;
nonZeroCount++;
groupHasNonZero = true;
}
}
if (groupHasNonZero)
{
numOfNonZeroGroup++;
}
}
else
{
// gSizeStr += nonZeroCount+",";
if (prior == SGDWithAdaGradAndFOBOS.Prior.sgLASSO)
{
double bSquaredSum = 0;
double b = 0;
foreach (int index_1 in gFeatureIndices)
{
b = Math.Signum(testUpdateCache[index_1]) * Pospart(Math.Abs(testUpdateCache[index_1]) - currentRateCache[index_1] * alpha * lambda);
bCache[index_1] = b;
bSquaredSum += b * b;
}
double bNorm = Math.Sqrt(bSquaredSum);
int nonZeroCount = 0;
bool groupHasNonZero = false;
foreach (int index_2 in gFeatureIndices)
{
realUpdate = bCache[index_2] * Pospart(1 - currentRateCache[index_2] * (1.0 - alpha) * lambda * dm / bNorm);
UpdateX(x, index_2, realUpdate);
if (realUpdate != 0)
{
numOfNonZero++;
nonZeroCount++;
groupHasNonZero = true;
}
}
if (groupHasNonZero)
{
numOfNonZeroGroup++;
}
}
}
}
}
}
}
// gSizeStr += nonZeroCount+",";
// log.info();
// update gradient and lastX
for (int index_3 = 0; index_3 < x.Length; index_3++)
{
prevGrad[index_3] = gradients[index_3];
}
}
// if (hessSampleSize > 0) {
// approxHessian();
// }
try
{
ArrayMath.AssertFinite(x, "x");
}
catch (ArrayMath.InvalidElementException e)
{
log.Info(e.ToString());
for (int i = 0; i < x.Length; i++)
{
x[i] = double.NaN;
}
break;
}
Sayln(numBatches.ToString() + ", n0-fCount:" + numOfNonZero + ((prior != SGDWithAdaGradAndFOBOS.Prior.Lasso && prior != SGDWithAdaGradAndFOBOS.Prior.Ridge) ? ", n0-gCount:" + numOfNonZeroGroup : string.Empty) + ((evalScore != double.NegativeInfinity
) ? ", evalScore:" + evalScore : string.Empty) + (objVal != double.NegativeInfinity ? ", obj_val:" + nf.Format(objVal) + ", obj_delta:" + objDelta : string.Empty));
if (values != null && useAvgImprovement && iters > 5)
{
int size = values.Count;
double previousVal = (size >= 10 ? values[size - 10] : values[0]);
double averageImprovement = (previousVal - objVal) / (size >= 10 ? 10 : size);
if (System.Math.Abs(averageImprovement / objVal) < Tol)
{
Sayln("Online Optmization completed, due to average improvement: | newest_val - previous_val | / |newestVal| < TOL ");
break;
}
}
if (iters >= maxIterations)
{
Sayln("Online Optimization complete. Stopped after max iterations");
break;
}
if (total.Report() >= maxTime)
{
Sayln("Online Optimization complete. Stopped after max time");
break;
}
}
if (evaluateIters > 0)
{
// do final evaluation
double evalScore = (useEvalImprovement ? DoEvaluation(xBest) : DoEvaluation(x));
Sayln("final evalScore is: " + evalScore);
}
Sayln("Completed in: " + Timing.ToSecondsString(total.Report()) + " s");
return(useEvalImprovement ? xBest : x);
}
public virtual double[] Minimize(IFunction f, double functionTolerance, double[] initial, int maxIterations)
{
if (!(f is AbstractStochasticCachingDiffUpdateFunction))
{
throw new NotSupportedException();
}
AbstractStochasticCachingDiffUpdateFunction function = (AbstractStochasticCachingDiffUpdateFunction)f;
int totalSamples = function.DataDimension();
int tuneSampleSize = Math.Min(totalSamples, tuningSamples);
if (tuneSampleSize < tuningSamples)
{
log.Info("WARNING: Total number of samples=" + totalSamples + " is smaller than requested tuning sample size=" + tuningSamples + "!!!");
}
lambda = 1.0 / (sigma * totalSamples);
Sayln("Using sigma=" + sigma + " lambda=" + lambda + " tuning sample size " + tuneSampleSize);
// tune(function, initial, tuneSampleSize, 0.1);
t0 = (int)(1 / (0.1 * lambda));
x = new double[initial.Length];
System.Array.Copy(initial, 0, x, 0, x.Length);
xscale = 1;
xnorm = GetNorm(x);
int numBatches = totalSamples / bSize;
Init(function);
bool have_max = (maxIterations > 0 || numPasses > 0);
if (!have_max)
{
throw new NotSupportedException("No maximum number of iterations has been specified.");
}
else
{
maxIterations = Math.Max(maxIterations, numPasses) * numBatches;
}
Sayln(" Batch size of: " + bSize);
Sayln(" Data dimension of: " + totalSamples);
Sayln(" Batches per pass through data: " + numBatches);
Sayln(" Number of passes is = " + numPasses);
Sayln(" Max iterations is = " + maxIterations);
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// Loop
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Timing total = new Timing();
Timing current = new Timing();
int t = t0;
int iters = 0;
for (int pass = 0; pass < numPasses; pass++)
{
bool doEval = (pass > 0 && evaluateIters > 0 && pass % evaluateIters == 0);
if (doEval)
{
Rescale();
DoEvaluation(x);
}
double totalValue = 0;
double lastValue = 0;
for (int batch = 0; batch < numBatches; batch++)
{
iters++;
//Get the next X
double eta = 1 / (lambda * t);
double gain = eta / xscale;
lastValue = function.CalculateStochasticUpdate(x, xscale, bSize, gain);
totalValue += lastValue;
// weight decay (for L2 regularization)
xscale *= (1 - eta * lambda * bSize);
t += bSize;
}
if (xscale < 1e-6)
{
Rescale();
}
try
{
ArrayMath.AssertFinite(x, "x");
}
catch (ArrayMath.InvalidElementException e)
{
log.Info(e.ToString());
for (int i = 0; i < x.Length; i++)
{
x[i] = double.NaN;
}
break;
}
xnorm = GetNorm(x) * xscale * xscale;
// Calculate loss based on L2 regularization
double loss = totalValue + 0.5 * xnorm * lambda * totalSamples;
Sayln("Iter: " + iters + " pass " + pass + " batch 1 ... " + numBatches.ToString() + " [" + (total.Report()) / 1000.0 + " s " + " {" + (current.Restart() / 1000.0) + " s}] " + lastValue + " " + totalValue + " " + loss);
if (iters >= maxIterations)
{
Sayln("Stochastic Optimization complete. Stopped after max iterations");
break;
}
if (total.Report() >= maxTime)
{
Sayln("Stochastic Optimization complete. Stopped after max time");
break;
}
}
Rescale();
if (evaluateIters > 0)
{
// do final evaluation
DoEvaluation(x);
}
Sayln("Completed in: " + Timing.ToSecondsString(total.Report()) + " s");
return(x);
}
//This can be filled if an extending class needs to initialize things.
protected internal virtual void Init(AbstractStochasticCachingDiffUpdateFunction func)
{
}