RProp (Resilient Back Propagation)
This is an implementation of the Resilient Backpropagation algorithm. See the wikipedia article for reference.
Usage
e["Solver"]["Type"] = "Optimizer/Rprop"
Results
These are the results produced by this solver:
- Best Gradient(x)
Usage: e[“Results”][“Best Gradient(x)”] = List of real number
Description: Values of dF(x) for the x parameters that produced the best F(x) found so far.
- Best F(x)
Usage: e[“Results”][“Best F(x)”] = real number
Description: Optimal value of F(x) found so far.
- Best Parameters
Usage: e[“Results”][“Best Parameters”] = List of real number
Description: Value for the x parameters that produced the best F(x).
Variable-Specific Settings
These are settings required by this module that are added to each of the experiment’s variables when this module is selected.
- Lower Bound
Usage: e[“Variables”][index][“Lower Bound”] = real number
Description: [Hint] Lower bound for the variable’s value.
- Upper Bound
Usage: e[“Variables”][index][“Upper Bound”] = real number
Description: [Hint] Upper bound for the variable’s value.
- Initial Value
Usage: e[“Variables”][index][“Initial Value”] = real number
Description: [Hint] Initial value at or around which the algorithm shall start looking for an optimum.
- Initial Mean
Usage: e[“Variables”][index][“Initial Mean”] = real number
Description: [Hint] Initial mean for the proposal distribution. This value must be defined between the variable’s Mininum and Maximum settings (by default, this value is given by the center of the variable domain).
- Initial Standard Deviation
Usage: e[“Variables”][index][“Initial Standard Deviation”] = real number
Description: [Hint] Initial standard deviation of the proposal distribution for a variable (by default, this value is given by 30% of the variable domain width).
- Minimum Standard Deviation Update
Usage: e[“Variables”][index][“Minimum Standard Deviation Update”] = real number
Description: [Hint] Lower bound for the standard deviation updates of the proposal distribution for a variable. Korali increases the scaling factor sigma if this value is undershot.
- Values
Usage: e[“Variables”][index][“Values”] = List of real number
Description: [Hint] Locations to evaluate the Objective Function.
Configuration
These are settings required by this module.
- Delta0
Usage: e[“Solver”][“Delta0”] = real number
Description: Initial Delta.
- Delta Min
Usage: e[“Solver”][“Delta Min”] = real number
Description: Minimum Delta, parameter for step size calibration.
- Delta Max
Usage: e[“Solver”][“Delta Max”] = real number
Description: Maximum Delta, parameter for step size calibration.
- Eta Minus
Usage: e[“Solver”][“Eta Minus”] = real number
Description: Parameter for step size calibration.
- Eta Plus
Usage: e[“Solver”][“Eta Plus”] = real number
Description: Parameter for step size calibration.
Termination Criteria
These are the customizable criteria that indicates whether the solver should continue or finish execution. Korali will stop when at least one of these conditions are met. The criteria is expressed in C++ since it is compiled and evaluated as seen here in the engine.
- Max Gradient Norm
Usage: e[“Solver”][“Max Gradient Norm”] = real number
Description: Maximum value of the norm of the gradient.
Criteria:
_normPreviousGradient < _maxGradientNorm
- Max Stall Generations
Usage: e[“Solver”][“Max Stall Generations”] = unsigned integer
Description: Maximum times stalled with function evaluation bigger than the best one.
Criteria: :code:` _maxStallCounter >= _maxStallGenerations`
- Parameter Relative Tolerance
Usage: e[“Solver”][“Parameter Relative Tolerance”] = real number
Description: Relative tolerance in parameter difference between generations.
Criteria:
_xDiff<_parameterRelativeTolerance && _xDiff>0
- Max Value
Usage: e[“Solver”][“Max Value”] = real number
Description: Specifies the maximum target fitness to stop maximization.
Criteria:
_k->_currentGeneration > 1 && (+_bestEverValue > _maxValue)
- Min Value Difference Threshold
Usage: e[“Solver”][“Min Value Difference Threshold”] = real number
Description: Specifies the minimum fitness differential between two consecutive generations before stopping execution.
Criteria:
_k->_currentGeneration > 1 && (fabs(_currentBestValue - _previousBestValue) < _minValueDifferenceThreshold)
- Max Model Evaluations
Usage: e[“Solver”][“Max Model Evaluations”] = unsigned integer
Description: Specifies the maximum allowed evaluations of the computational model.
Criteria:
_maxModelEvaluations <= _modelEvaluationCount
- Max Generations
Usage: e[“Solver”][“Max Generations”] = unsigned integer
Description: Determines how many solver generations to run before stopping execution. Execution can be resumed at a later moment.
Criteria:
_k->_currentGeneration > _maxGenerations
Default Configuration
These following configuration will be assigned by default. Any settings defined by the user will override the given settings specified in these defaults.
{ "Delta Max": 50, "Delta Min": 1e-06, "Delta0": 0.1, "Eta Minus": 0.5, "Eta Plus": 1.2, "Model Evaluation Count": 0, "Termination Criteria": { "Max Generations": 10000000000, "Max Gradient Norm": 0.0, "Max Model Evaluations": 1000000000, "Max Stall Generations": 20, "Max Value": Infinity, "Min Value Difference Threshold": -Infinity, "Parameter Relative Tolerance": 0.0001 }, "Variable Count": 0 }
Variable Defaults
These following configuration will be assigned to each of the experiment variables by default. Any settings defined by the user will override the given settings specified in these defaults.
{ "Initial Mean": NaN, "Initial Standard Deviation": NaN, "Initial Value": NaN, "Lower Bound": -Infinity, "Minimum Standard Deviation Update": 0.0, "Upper Bound": Infinity, "Values": [] }