/// <inheritdoc/>
private protected override void TrainWithoutLock(IProgressChannelProvider progress, FloatLabelCursor.Factory cursorFactory, Random rand,
IdToIdxLookup idToIdx, int numThreads, DualsTableBase duals, float[] biasReg, float[] invariants, float lambdaNInv,
VBuffer <float>[] weights, float[] biasUnreg, VBuffer <float>[] l1IntermediateWeights, float[] l1IntermediateBias, float[] featureNormSquared)
{
Contracts.AssertValueOrNull(progress);
Contracts.Assert(SdcaTrainerOptions.L1Regularization.HasValue);
Contracts.AssertValueOrNull(idToIdx);
Contracts.AssertValueOrNull(invariants);
Contracts.AssertValueOrNull(featureNormSquared);
int numClasses = Utils.Size(weights);
Contracts.Assert(Utils.Size(biasReg) == numClasses);
Contracts.Assert(Utils.Size(biasUnreg) == numClasses);
int maxUpdateTrials = 2 * numThreads;
var l1Threshold = SdcaTrainerOptions.L1Regularization.Value;
bool l1ThresholdZero = l1Threshold == 0;
var lr = SdcaTrainerOptions.BiasLearningRate * SdcaTrainerOptions.L2Regularization.Value;
var pch = progress != null?progress.StartProgressChannel("Dual update") : null;
using (pch)
using (var cursor = SdcaTrainerOptions.Shuffle ? cursorFactory.Create(rand) : cursorFactory.Create())
{
long rowCount = 0;
if (pch != null)
{
pch.SetHeader(new ProgressHeader("examples"), e => e.SetProgress(0, rowCount));
}
Func <DataViewRowId, long> getIndexFromId = GetIndexFromIdGetter(idToIdx, biasReg.Length);
while (cursor.MoveNext())
{
Host.CheckAlive();
long idx = getIndexFromId(cursor.Id);
long dualIndexInitPos = idx * numClasses;
var features = cursor.Features;
var label = (int)cursor.Label;
float invariant;
float normSquared;
if (invariants != null)
{
invariant = invariants[idx];
Contracts.AssertValue(featureNormSquared);
normSquared = featureNormSquared[idx];
}
else
{
normSquared = VectorUtils.NormSquared(in features);
if (SdcaTrainerOptions.BiasLearningRate == 0)
{
normSquared += 1;
}
invariant = _loss.ComputeDualUpdateInvariant(2 * normSquared * lambdaNInv * GetInstanceWeight(cursor));
}
// The output for the label class using current weights and bias.
var labelOutput = WDot(in features, in weights[label], biasReg[label] + biasUnreg[label]);
var instanceWeight = GetInstanceWeight(cursor);
// This will be the new dual variable corresponding to the label class.
float labelDual = 0;
// This will be used to update the weights and regularized bias corresponding to the label class.
float labelPrimalUpdate = 0;
// This will be used to update the unregularized bias corresponding to the label class.
float labelAdjustment = 0;
// Iterates through all classes.
for (int iClass = 0; iClass < numClasses; iClass++)
{
// Skip the dual/weights/bias update for label class. Will be taken care of at the end.
if (iClass == label)
{
continue;
}
var weightsEditor = VBufferEditor.CreateFromBuffer(ref weights[iClass]);
var l1IntermediateWeightsEditor =
!l1ThresholdZero?VBufferEditor.CreateFromBuffer(ref l1IntermediateWeights[iClass]) :
default;
// Loop trials for compare-and-swap updates of duals.
// In general, concurrent update conflict to the same dual variable is rare
// if data is shuffled.
for (int numTrials = 0; numTrials < maxUpdateTrials; numTrials++)
{
long dualIndex = iClass + dualIndexInitPos;
var dual = duals[dualIndex];
var output = labelOutput + labelPrimalUpdate * normSquared - WDot(in features, in weights[iClass], biasReg[iClass] + biasUnreg[iClass]);
var dualUpdate = _loss.DualUpdate(output, 1, dual, invariant, numThreads);
// The successive over-relaxation approach to adjust the sum of dual variables (biasReg) to zero.
// Reference to details: http://stat.rutgers.edu/home/tzhang/papers/ml02_dual.pdf, pp. 16-17.
var adjustment = l1ThresholdZero ? lr * biasReg[iClass] : lr * l1IntermediateBias[iClass];
dualUpdate -= adjustment;
bool success = false;
duals.ApplyAt(dualIndex, (long index, ref float value) =>
success = Interlocked.CompareExchange(ref value, dual + dualUpdate, dual) == dual);
if (success)
{
// Note: dualConstraint[iClass] = lambdaNInv * (sum of duals[iClass])
var primalUpdate = dualUpdate * lambdaNInv * instanceWeight;
labelDual -= dual + dualUpdate;
labelPrimalUpdate += primalUpdate;
biasUnreg[iClass] += adjustment * lambdaNInv * instanceWeight;
labelAdjustment -= adjustment;
if (l1ThresholdZero)
{
VectorUtils.AddMult(in features, weightsEditor.Values, -primalUpdate);
biasReg[iClass] -= primalUpdate;
}
else
{
//Iterative shrinkage-thresholding (aka. soft-thresholding)
//Update v=denseWeights as if there's no L1
//Thresholding: if |v[j]| < threshold, turn off weights[j]
//If not, shrink: w[j] = v[i] - sign(v[j]) * threshold
l1IntermediateBias[iClass] -= primalUpdate;
if (SdcaTrainerOptions.BiasLearningRate == 0)
{
biasReg[iClass] = Math.Abs(l1IntermediateBias[iClass]) - l1Threshold > 0.0
? l1IntermediateBias[iClass] - Math.Sign(l1IntermediateBias[iClass]) * l1Threshold
: 0;
}
var featureValues = features.GetValues();
if (features.IsDense)
{
CpuMathUtils.SdcaL1UpdateDense(-primalUpdate, featureValues.Length, featureValues, l1Threshold, l1IntermediateWeightsEditor.Values, weightsEditor.Values);
}
else if (featureValues.Length > 0)
{
CpuMathUtils.SdcaL1UpdateSparse(-primalUpdate, featureValues.Length, featureValues, features.GetIndices(), l1Threshold, l1IntermediateWeightsEditor.Values, weightsEditor.Values);
}
}
break;
}
}
}
// Updating with label class weights and dual variable.
duals[label + dualIndexInitPos] = labelDual;
biasUnreg[label] += labelAdjustment * lambdaNInv * instanceWeight;
if (l1ThresholdZero)
{
var weightsEditor = VBufferEditor.CreateFromBuffer(ref weights[label]);
VectorUtils.AddMult(in features, weightsEditor.Values, labelPrimalUpdate);
biasReg[label] += labelPrimalUpdate;
}
else
{
l1IntermediateBias[label] += labelPrimalUpdate;
var intermediateBias = l1IntermediateBias[label];
biasReg[label] = Math.Abs(intermediateBias) - l1Threshold > 0.0
? intermediateBias - Math.Sign(intermediateBias) * l1Threshold
: 0;
var weightsEditor = VBufferEditor.CreateFromBuffer(ref weights[label]);
var l1IntermediateWeightsEditor = VBufferEditor.CreateFromBuffer(ref l1IntermediateWeights[label]);
var featureValues = features.GetValues();
if (features.IsDense)
{
CpuMathUtils.SdcaL1UpdateDense(labelPrimalUpdate, featureValues.Length, featureValues, l1Threshold, l1IntermediateWeightsEditor.Values, weightsEditor.Values);
}
else if (featureValues.Length > 0)
{
CpuMathUtils.SdcaL1UpdateSparse(labelPrimalUpdate, featureValues.Length, featureValues, features.GetIndices(), l1Threshold, l1IntermediateWeightsEditor.Values, weightsEditor.Values);
}
}
rowCount++;
}
}
}
/// <inheritdoc/>
private protected override bool CheckConvergence(
IProgressChannel pch,
int iter,
FloatLabelCursor.Factory cursorFactory,
DualsTableBase duals,
IdToIdxLookup idToIdx,
VBuffer <Float>[] weights,
VBuffer <Float>[] bestWeights,
Float[] biasUnreg,
Float[] bestBiasUnreg,
Float[] biasReg,
Float[] bestBiasReg,
long count,
Double[] metrics,
ref Double bestPrimalLoss,
ref int bestIter)
{
Contracts.AssertValue(weights);
Contracts.AssertValue(duals);
int numClasses = weights.Length;
Contracts.Assert(duals.Length >= numClasses * count);
Contracts.AssertValueOrNull(idToIdx);
Contracts.Assert(Utils.Size(weights) == numClasses);
Contracts.Assert(Utils.Size(biasReg) == numClasses);
Contracts.Assert(Utils.Size(biasUnreg) == numClasses);
Contracts.Assert(Utils.Size(metrics) == 6);
var reportedValues = new Double?[metrics.Length + 1];
reportedValues[metrics.Length] = iter;
var lossSum = new CompensatedSum();
var dualLossSum = new CompensatedSum();
int numFeatures = weights[0].Length;
using (var cursor = cursorFactory.Create())
{
long row = 0;
Func <DataViewRowId, long, long> getIndexFromIdAndRow = GetIndexFromIdAndRowGetter(idToIdx, biasReg.Length);
// Iterates through data to compute loss function.
while (cursor.MoveNext())
{
var instanceWeight = GetInstanceWeight(cursor);
var features = cursor.Features;
var label = (int)cursor.Label;
var labelOutput = WDot(in features, in weights[label], biasReg[label] + biasUnreg[label]);
Double subLoss = 0;
Double subDualLoss = 0;
long idx = getIndexFromIdAndRow(cursor.Id, row);
long dualIndex = idx * numClasses;
for (int iClass = 0; iClass < numClasses; iClass++)
{
if (iClass == label)
{
dualIndex++;
continue;
}
var currentClassOutput = WDot(in features, in weights[iClass], biasReg[iClass] + biasUnreg[iClass]);
subLoss += _loss.Loss(labelOutput - currentClassOutput, 1);
Contracts.Assert(dualIndex == iClass + idx * numClasses);
var dual = duals[dualIndex++];
subDualLoss += _loss.DualLoss(1, dual);
}
lossSum.Add(subLoss * instanceWeight);
dualLossSum.Add(subDualLoss * instanceWeight);
row++;
}
Host.Assert(idToIdx == null || row * numClasses == duals.Length);
}
Contracts.Assert(Args.L2Const.HasValue);
Contracts.Assert(Args.L1Threshold.HasValue);
Double l2Const = Args.L2Const.Value;
Double l1Threshold = Args.L1Threshold.Value;
Double weightsL1Norm = 0;
Double weightsL2NormSquared = 0;
Double biasRegularizationAdjustment = 0;
for (int iClass = 0; iClass < numClasses; iClass++)
{
weightsL1Norm += VectorUtils.L1Norm(in weights[iClass]) + Math.Abs(biasReg[iClass]);
weightsL2NormSquared += VectorUtils.NormSquared(weights[iClass]) + biasReg[iClass] * biasReg[iClass];
biasRegularizationAdjustment += biasReg[iClass] * biasUnreg[iClass];
}
Double l1Regularizer = Args.L1Threshold.Value * l2Const * weightsL1Norm;
var l2Regularizer = l2Const * weightsL2NormSquared * 0.5;
var newLoss = lossSum.Sum / count + l2Regularizer + l1Regularizer;
var newDualLoss = dualLossSum.Sum / count - l2Regularizer - l2Const * biasRegularizationAdjustment;
var dualityGap = newLoss - newDualLoss;
metrics[(int)MetricKind.Loss] = newLoss;
metrics[(int)MetricKind.DualLoss] = newDualLoss;
metrics[(int)MetricKind.DualityGap] = dualityGap;
metrics[(int)MetricKind.BiasUnreg] = biasUnreg[0];
metrics[(int)MetricKind.BiasReg] = biasReg[0];
metrics[(int)MetricKind.L1Sparsity] = Args.L1Threshold == 0 ? 1 : weights.Sum(
weight => weight.GetValues().Count(w => w != 0)) / (numClasses * numFeatures);
bool converged = dualityGap / newLoss < Args.ConvergenceTolerance;
if (metrics[(int)MetricKind.Loss] < bestPrimalLoss)
{
for (int iClass = 0; iClass < numClasses; iClass++)
{
// Maintain a copy of weights and bias with best primal loss thus far.
// This is some extra work and uses extra memory, but it seems worth doing it.
// REVIEW: Sparsify bestWeights?
weights[iClass].CopyTo(ref bestWeights[iClass]);
bestBiasReg[iClass] = biasReg[iClass];
bestBiasUnreg[iClass] = biasUnreg[iClass];
}
bestPrimalLoss = metrics[(int)MetricKind.Loss];
bestIter = iter;
}
for (int i = 0; i < metrics.Length; i++)
{
reportedValues[i] = metrics[i];
}
if (pch != null)
{
pch.Checkpoint(reportedValues);
}
return(converged);
}