/// <summary>
/// Finds approximate minimum of the function
/// </summary>
/// <param name="function">Function to minimize</param>
/// <param name="initial">Initial point</param>
/// <param name="result">Approximate minimum</param>
public void Minimize(DifferentiableFunction function, ref VBuffer <Float> initial, ref VBuffer <Float> result)
{
Contracts.Check(FloatUtils.IsFinite(initial.Values, initial.Count), "The initial vector contains NaNs or infinite values.");
LineFunc lineFunc = new LineFunc(function, ref initial, UseCG);
VBuffer <Float> prev = default(VBuffer <Float>);
initial.CopyTo(ref prev);
for (int n = 0; _maxSteps == 0 || n < _maxSteps; ++n)
{
Float step = LineSearch.Minimize(lineFunc.Eval, lineFunc.Value, lineFunc.Deriv);
var newPoint = lineFunc.NewPoint;
bool terminateNow = n > 0 && TerminateTester.ShouldTerminate(ref newPoint, ref prev);
if (terminateNow || Terminate(ref newPoint))
{
break;
}
newPoint.CopyTo(ref prev);
lineFunc.ChangeDir();
}
lineFunc.NewPoint.CopyTo(ref result);
}
/// <summary>
/// Minimize the function represented by <paramref name="f"/>.
/// </summary>
/// <param name="f">Stochastic gradients of function to minimize</param>
/// <param name="initial">Initial point</param>
/// <param name="result">Approximate minimum of <paramref name="f"/></param>
public void Minimize(DStochasticGradient f, ref VBuffer <Float> initial, ref VBuffer <Float> result)
{
Contracts.Check(FloatUtils.IsFinite(initial.Values, initial.Count), "The initial vector contains NaNs or infinite values.");
int dim = initial.Length;
VBuffer <Float> grad = VBufferUtils.CreateEmpty <Float>(dim);
VBuffer <Float> step = VBufferUtils.CreateEmpty <Float>(dim);
VBuffer <Float> x = default(VBuffer <Float>);
initial.CopyTo(ref x);
VBuffer <Float> prev = default(VBuffer <Float>);
VBuffer <Float> avg = VBufferUtils.CreateEmpty <Float>(dim);
for (int n = 0; _maxSteps == 0 || n < _maxSteps; ++n)
{
if (_momentum == 0)
{
step = new VBuffer <Float>(step.Length, 0, step.Values, step.Indices);
}
else
{
VectorUtils.ScaleBy(ref step, _momentum);
}
Float stepSize;
switch (_rateSchedule)
{
case RateScheduleType.Constant:
stepSize = 1 / _t0;
break;
case RateScheduleType.Sqrt:
stepSize = 1 / (_t0 + MathUtils.Sqrt(n));
break;
case RateScheduleType.Linear:
stepSize = 1 / (_t0 + n);
break;
default:
throw Contracts.Except();
}
Float scale = (1 - _momentum) / _batchSize;
for (int i = 0; i < _batchSize; ++i)
{
f(ref x, ref grad);
VectorUtils.AddMult(ref grad, scale, ref step);
}
if (_averaging)
{
Utils.Swap(ref avg, ref prev);
VectorUtils.ScaleBy(prev, ref avg, (Float)n / (n + 1));
VectorUtils.AddMult(ref step, -stepSize, ref x);
VectorUtils.AddMult(ref x, (Float)1 / (n + 1), ref avg);
if ((n > 0 && TerminateTester.ShouldTerminate(ref avg, ref prev)) || _terminate(ref avg))
{
result = avg;
return;
}
}
else
{
Utils.Swap(ref x, ref prev);
VectorUtils.AddMult(ref step, -stepSize, ref prev, ref x);
if ((n > 0 && TerminateTester.ShouldTerminate(ref x, ref prev)) || _terminate(ref x))
{
result = x;
return;
}
}
}
result = _averaging ? avg : x;
}