// [cdm 2012: The version that used to be here was clearly buggy;
// I changed it a little, but didn't test it. It's now more correct, but
// I think it is still conceptually faulty, since it will keep growing the
// batch size so long as any minute improvement in the function value is
// obtained, whereas the whole point of using a small batch is to get speed
// at the cost of small losses.]
public virtual int TuneBatch(Func function, double[] initial, long msPerTest, int bStart)
{
double[] xTest = new double[initial.Length];
int bOpt = 0;
double min = double.PositiveInfinity;
this.maxTime = msPerTest;
double prev = double.PositiveInfinity;
// check for stochastic derivatives
if (!(function is AbstractStochasticCachingDiffFunction))
{
throw new NotSupportedException();
}
AbstractStochasticCachingDiffFunction dFunction = (AbstractStochasticCachingDiffFunction)function;
int b = bStart;
bool toContinue = true;
do
{
System.Array.Copy(initial, 0, xTest, 0, initial.Length);
log.Info(string.Empty);
log.Info("Testing with batch size: " + b);
bSize = b;
ShutUp();
this.Minimize(function, 1e-5, xTest);
double result = dFunction.ValueAt(xTest);
if (result < min)
{
min = result;
bOpt = bSize;
b *= 2;
prev = result;
}
else
{
if (result < prev)
{
b *= 2;
prev = result;
}
else
{
if (result > prev)
{
toContinue = false;
}
}
}
log.Info(string.Empty);
log.Info("Final value is: " + nf.Format(result));
log.Info("Optimal so far is: batch size: " + bOpt);
}while (toContinue);
return(bOpt);
}
/// <summary>
/// This function tests to make sure that the sum of the stochastic calculated gradients is equal to the
/// full gradient.
/// </summary>
/// <remarks>
/// This function tests to make sure that the sum of the stochastic calculated gradients is equal to the
/// full gradient. This requires using ordered sampling, so if the ObjectiveFunction itself randomizes
/// the inputs this function will likely fail.
/// </remarks>
/// <param name="x">is the point to evaluate the function at</param>
/// <param name="functionTolerance">is the tolerance to place on the infinity norm of the gradient and value</param>
/// <returns>boolean indicating success or failure.</returns>
public virtual bool TestSumOfBatches(double[] x, double functionTolerance)
{
bool ret = false;
log.Info("Making sure that the sum of stochastic gradients equals the full gradient");
AbstractStochasticCachingDiffFunction.SamplingMethod tmpSampleMethod = thisFunc.sampleMethod;
StochasticCalculateMethods tmpMethod = thisFunc.method;
//Make sure that our function is using ordered sampling. Otherwise we have no gaurentees.
thisFunc.sampleMethod = AbstractStochasticCachingDiffFunction.SamplingMethod.Ordered;
if (thisFunc.method == StochasticCalculateMethods.NoneSpecified)
{
log.Info("No calculate method has been specified");
}
approxValue = 0;
approxGrad = new double[x.Length];
curGrad = new double[x.Length];
fullGrad = new double[x.Length];
double percent = 0.0;
//This loop runs through all the batches and sums of the calculations to compare against the full gradient
for (int i = 0; i < numBatches; i++)
{
percent = 100 * ((double)i) / (numBatches);
// update the value
approxValue += thisFunc.ValueAt(x, v, testBatchSize);
// update the gradient
thisFunc.returnPreviousValues = true;
System.Array.Copy(thisFunc.DerivativeAt(x, v, testBatchSize), 0, curGrad, 0, curGrad.Length);
//Update Approximate
approxGrad = ArrayMath.PairwiseAdd(approxGrad, curGrad);
double norm = ArrayMath.Norm(approxGrad);
System.Console.Error.Printf("%5.1f percent complete %6.2f \n", percent, norm);
}
// !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// Get the full gradient and value, these should equal the approximates
// !!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
log.Info("About to calculate the full derivative and value");
System.Array.Copy(thisFunc.DerivativeAt(x), 0, fullGrad, 0, fullGrad.Length);
thisFunc.returnPreviousValues = true;
fullValue = thisFunc.ValueAt(x);
diff = new double[x.Length];
if ((ArrayMath.Norm_inf(diff = ArrayMath.PairwiseSubtract(fullGrad, approxGrad))) < functionTolerance)
{
Sayln(string.Empty);
Sayln("Success: sum of batch gradients equals full gradient");
ret = true;
}
else
{
diffNorm = ArrayMath.Norm(diff);
Sayln(string.Empty);
Sayln("Failure: sum of batch gradients minus full gradient has norm " + diffNorm);
ret = false;
}
if (System.Math.Abs(approxValue - fullValue) < functionTolerance)
{
Sayln(string.Empty);
Sayln("Success: sum of batch values equals full value");
ret = true;
}
else
{
Sayln(string.Empty);
Sayln("Failure: sum of batch values minus full value has norm " + System.Math.Abs(approxValue - fullValue));
ret = false;
}
thisFunc.sampleMethod = tmpSampleMethod;
thisFunc.method = tmpMethod;
return(ret);
}
public virtual double[] Minimize(Func function, double functionTolerance, double[] initial, int maxIterations)
{
// check for stochastic derivatives
if (!(function is AbstractStochasticCachingDiffFunction))
{
throw new NotSupportedException();
}
AbstractStochasticCachingDiffFunction dfunction = (AbstractStochasticCachingDiffFunction)function;
dfunction.method = StochasticCalculateMethods.GradientOnly;
/* ---
* StochasticDiffFunctionTester sdft = new StochasticDiffFunctionTester(dfunction);
* ArrayMath.add(initial, gen.nextDouble() ); // to make sure that priors are working.
* sdft.testSumOfBatches(initial, 1e-4);
* System.exit(1);
* --- */
x = initial;
grad = new double[x.Length];
newX = new double[x.Length];
gradList = new List <double[]>();
numBatches = dfunction.DataDimension() / bSize;
outputFrequency = (int)System.Math.Ceil(((double)numBatches) / ((double)outputFrequency));
Init(dfunction);
InitFiles();
bool have_max = (maxIterations > 0 || numPasses > 0);
if (!have_max)
{
throw new NotSupportedException("No maximum number of iterations has been specified.");
}
else
{
maxIterations = System.Math.Max(maxIterations, numPasses) * numBatches;
}
Sayln(" Batchsize of: " + bSize);
Sayln(" Data dimension of: " + dfunction.DataDimension());
Sayln(" Batches per pass through data: " + numBatches);
Sayln(" Max iterations is = " + maxIterations);
if (outputIterationsToFile)
{
infoFile.Println(function.DomainDimension() + "; DomainDimension ");
infoFile.Println(bSize + "; batchSize ");
infoFile.Println(maxIterations + "; maxIterations");
infoFile.Println(numBatches + "; numBatches ");
infoFile.Println(outputFrequency + "; outputFrequency");
}
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// Loop
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Timing total = new Timing();
Timing current = new Timing();
total.Start();
current.Start();
for (k = 0; k < maxIterations; k++)
{
try
{
bool doEval = (k > 0 && evaluateIters > 0 && k % evaluateIters == 0);
if (doEval)
{
DoEvaluation(x);
}
int pass = k / numBatches;
int batch = k % numBatches;
Say("Iter: " + k + " pass " + pass + " batch " + batch);
// restrict number of saved gradients
// (recycle memory of first gradient in list for new gradient)
if (k > 0 && gradList.Count >= memory)
{
newGrad = gradList.Remove(0);
}
else
{
newGrad = new double[grad.Length];
}
dfunction.hasNewVals = true;
System.Array.Copy(dfunction.DerivativeAt(x, v, bSize), 0, newGrad, 0, newGrad.Length);
ArrayMath.AssertFinite(newGrad, "newGrad");
gradList.Add(newGrad);
grad = Smooth(gradList);
//Get the next X
TakeStep(dfunction);
ArrayMath.AssertFinite(newX, "newX");
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// THIS IS FOR DEBUG ONLY
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
if (outputIterationsToFile && (k % outputFrequency == 0) && k != 0)
{
double curVal = dfunction.ValueAt(x);
Say(" TrueValue{ " + curVal + " } ");
file.Println(k + " , " + curVal + " , " + total.Report());
}
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
// END OF DEBUG STUFF
//!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
if (k >= maxIterations)
{
Sayln("Stochastic Optimization complete. Stopped after max iterations");
x = newX;
break;
}
if (total.Report() >= maxTime)
{
Sayln("Stochastic Optimization complete. Stopped after max time");
x = newX;
break;
}
System.Array.Copy(newX, 0, x, 0, x.Length);
Say("[" + (total.Report()) / 1000.0 + " s ");
Say("{" + (current.Restart() / 1000.0) + " s}] ");
Say(" " + dfunction.LastValue());
if (quiet)
{
log.Info(".");
}
else
{
Sayln(string.Empty);
}
}
catch (ArrayMath.InvalidElementException e)
{
log.Info(e.ToString());
for (int i = 0; i < x.Length; i++)
{
x[i] = double.NaN;
}
break;
}
}
if (evaluateIters > 0)
{
// do final evaluation
DoEvaluation(x);
}
if (outputIterationsToFile)
{
infoFile.Println(k + "; Iterations");
infoFile.Println((total.Report()) / 1000.0 + "; Completion Time");
infoFile.Println(dfunction.ValueAt(x) + "; Finalvalue");
infoFile.Close();
file.Close();
log.Info("Output Files Closed");
}
//System.exit(1);
Say("Completed in: " + (total.Report()) / 1000.0 + " s");
return(x);
}
public virtual double TuneDouble(Func function, double[] initial, long msPerTest, StochasticMinimizer.IPropertySetter <double> ps, double lower, double upper, double Tol)
{
double[] xtest = new double[initial.Length];
this.maxTime = msPerTest;
// check for stochastic derivatives
if (!(function is AbstractStochasticCachingDiffFunction))
{
throw new NotSupportedException();
}
AbstractStochasticCachingDiffFunction dfunction = (AbstractStochasticCachingDiffFunction)function;
IList <Pair <double, double> > res = new List <Pair <double, double> >();
Pair <double, double> best = new Pair <double, double>(lower, double.PositiveInfinity);
//this is set to lower because the first it will always use the lower first, so it has to be best
Pair <double, double> low = new Pair <double, double>(lower, double.PositiveInfinity);
Pair <double, double> high = new Pair <double, double>(upper, double.PositiveInfinity);
Pair <double, double> cur = new Pair <double, double>();
Pair <double, double> tmp = new Pair <double, double>();
IList <double> queue = new List <double>();
queue.Add(lower);
queue.Add(upper);
//queue.add(0.5* (lower + upper));
bool toContinue = true;
this.numPasses = 10000;
do
{
System.Array.Copy(initial, 0, xtest, 0, initial.Length);
if (queue.Count != 0)
{
cur.first = queue.Remove(0);
}
else
{
cur.first = 0.5 * (low.First() + high.First());
}
ps.Set(cur.First());
log.Info(string.Empty);
log.Info("About to test with batch size: " + bSize + " gain: " + gain + " and " + ps.ToString() + " set to " + cur.First());
xtest = this.Minimize(function, 1e-100, xtest);
if (double.IsNaN(xtest[0]))
{
cur.second = double.PositiveInfinity;
}
else
{
cur.second = dfunction.ValueAt(xtest);
}
if (cur.Second() < best.Second())
{
CopyPair(best, tmp);
CopyPair(cur, best);
if (tmp.First() > best.First())
{
CopyPair(tmp, high);
}
else
{
// The old best is now the upper bound
CopyPair(tmp, low);
}
// The old best is now the lower bound
queue.Add(0.5 * (cur.First() + high.First()));
}
else
{
// check in the right interval next
if (cur.First() < best.First())
{
CopyPair(cur, low);
}
else
{
if (cur.First() > best.First())
{
CopyPair(cur, high);
}
}
}
if (System.Math.Abs(low.First() - high.First()) < Tol)
{
toContinue = false;
}
res.Add(new Pair <double, double>(cur.First(), cur.Second()));
log.Info(string.Empty);
log.Info("Final value is: " + nf.Format(cur.Second()));
log.Info("Optimal so far using " + ps.ToString() + " is: " + best.First());
}while (toContinue);
//output the results to screen.
log.Info("-------------");
log.Info(" RESULTS ");
log.Info(ps.GetType().ToString());
log.Info("-------------");
log.Info(" val , function after " + msPerTest + " ms");
foreach (Pair <double, double> re in res)
{
log.Info(re.First() + " , " + re.Second());
}
log.Info(string.Empty);
log.Info(string.Empty);
return(best.First());
}
// 0=MinErr 1=Bradley
public virtual double TuneFixedGain(Func function, double[] initial, long msPerTest, double fixedStart)
{
double[] xtest = new double[initial.Length];
double fOpt = 0.0;
double factor = 1.2;
double min = double.PositiveInfinity;
this.maxTime = msPerTest;
double prev = double.PositiveInfinity;
// check for stochastic derivatives
if (!(function is AbstractStochasticCachingDiffFunction))
{
throw new NotSupportedException();
}
AbstractStochasticCachingDiffFunction dfunction = (AbstractStochasticCachingDiffFunction)function;
int it = 1;
bool toContinue = true;
double f = fixedStart;
do
{
System.Array.Copy(initial, 0, xtest, 0, initial.Length);
log.Info(string.Empty);
this.fixedGain = f;
log.Info("Testing with batchsize: " + bSize + " gain: " + gain + " fixedGain: " + nf.Format(fixedGain));
this.numPasses = 10000;
this.Minimize(function, 1e-100, xtest);
double result = dfunction.ValueAt(xtest);
if (it == 1)
{
f = f / factor;
}
if (result < min)
{
min = result;
fOpt = this.fixedGain;
f = f / factor;
prev = result;
}
else
{
if (result < prev)
{
f = f / factor;
prev = result;
}
else
{
if (result > prev)
{
toContinue = false;
}
}
}
it += 1;
log.Info(string.Empty);
log.Info("Final value is: " + nf.Format(result));
log.Info("Optimal so far is: fixedgain: " + fOpt);
}while (toContinue);
return(fOpt);
}
