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quantiles: Better code re-usage, better structure, support for 'open' and 'non-open' dimensions, single dimensional quantiles should work now.

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TimQu 7 years ago
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3 changed files with 236 additions and 35 deletions
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  1. 2
      src/storm/modelchecker/prctl/SparseMdpPrctlModelChecker.cpp
  2. 238
      src/storm/modelchecker/prctl/helper/rewardbounded/QuantileHelper.cpp
  3. 31
      src/storm/modelchecker/prctl/helper/rewardbounded/QuantileHelper.h

2
src/storm/modelchecker/prctl/SparseMdpPrctlModelChecker.cpp
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@ -233,7 +233,7 @@ namespace storm {
uint64_t initialState = *this->getModel().getInitialStates().begin();
helper::rewardbounded::QuantileHelper<SparseMdpModelType> qHelper(this->getModel(), checkTask.getFormula());
auto res = qHelper.computeMultiDimensionalQuantile(env);
auto res = qHelper.computeQuantile(env);
if (res.size() == 1 && res.front().size() == 1) {
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(initialState, std::move(res.front().front())));

238
src/storm/modelchecker/prctl/helper/rewardbounded/QuantileHelper.cpp
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@ -4,12 +4,14 @@
#include <vector>
#include <memory>
#include <boost/optional.hpp>
#include <storm/exceptions/NotSupportedException.h>
#include "storm/models/sparse/Mdp.h"
#include "storm/modelchecker/prctl/helper/rewardbounded/MultiDimensionalRewardUnfolding.h"
#include "storm/storage/expressions/ExpressionManager.h"
#include "storm/storage/expressions/Expressions.h"
#include "storm/storage/BitVector.h"
#include "storm/storage/MaximalEndComponentDecomposition.h"
#include "storm/utility/vector.h"
#include "storm/logic/ProbabilityOperatorFormula.h"
@ -23,11 +25,23 @@ namespace storm {
template<typename ModelType>
QuantileHelper<ModelType>::QuantileHelper(ModelType const& model, storm::logic::QuantileFormula const& quantileFormula) : model(model), quantileFormula(quantileFormula) {
// Intentionally left empty
/* Todo: Current assumption:
* Subformula is always prob operator with bounded until
* Each bound variable occurs at most once (change this?)
* cost bounds can either be <= or > (the epochs returned by the reward unfolding assume this. One could translate them, though)
* 'reasonable' quantile (e.g. not quantile(max B, Pmax>0.5 [F <=B G]) (we could also filter out these things early on)
*/
}
std::shared_ptr<storm::logic::ProbabilityOperatorFormula> replaceBoundsByGreaterEqZero(storm::logic::ProbabilityOperatorFormula const& boundedUntilOperator, storm::storage::BitVector const& dimensionsToReplace) {
enum class BoundTransformation {
None,
GreaterZero,
GreaterEqualZero,
LessEqualZero
};
std::shared_ptr<storm::logic::ProbabilityOperatorFormula> transformBoundedUntilOperator(storm::logic::ProbabilityOperatorFormula const& boundedUntilOperator, std::vector<BoundTransformation> const& transformations) {
auto const& origBoundedUntil = boundedUntilOperator.getSubformula().asBoundedUntilFormula();
STORM_LOG_ASSERT(dimensionsToReplace.size() == origBoundedUntil.getDimension(), "Tried to replace the bound of a dimension that is higher than the number of dimensions of the formula.");
STORM_LOG_ASSERT(transformations.size() == origBoundedUntil.getDimension(), "Tried to replace the bound of a dimension that is higher than the number of dimensions of the formula.");
std::vector<std::shared_ptr<storm::logic::Formula const>> leftSubformulas, rightSubformulas;
std::vector<boost::optional<storm::logic::TimeBound>> lowerBounds, upperBounds;
std::vector<storm::logic::TimeBoundReference> timeBoundReferences;
@ -36,7 +50,19 @@ namespace storm {
leftSubformulas.push_back(origBoundedUntil.getLeftSubformula(dim).asSharedPointer());
rightSubformulas.push_back(origBoundedUntil.getRightSubformula(dim).asSharedPointer());
timeBoundReferences.push_back(origBoundedUntil.getTimeBoundReference(dim));
if (dimensionsToReplace.get(dim)) {
if (transformations[dim] == BoundTransformation::None) {
if (origBoundedUntil.hasLowerBound()) {
lowerBounds.push_back(storm::logic::TimeBound(origBoundedUntil.isLowerBoundStrict(dim), origBoundedUntil.getLowerBound(dim)));
} else {
lowerBounds.push_back(boost::none);
}
if (origBoundedUntil.hasUpperBound()) {
upperBounds.push_back(storm::logic::TimeBound(origBoundedUntil.isUpperBoundStrict(dim), origBoundedUntil.getUpperBound(dim)));
} else {
upperBounds.push_back(boost::none);
}
} else {
// We need a zero expression in all other cases
storm::expressions::Expression zero;
if (origBoundedUntil.hasLowerBound(dim)) {
zero = origBoundedUntil.getLowerBound(dim).getManager().rational(0.0);
@ -44,17 +70,12 @@ namespace storm {
STORM_LOG_THROW(origBoundedUntil.hasUpperBound(dim), storm::exceptions::InvalidOperationException, "The given bounded until formula has no cost-bound for one dimension.");
zero = origBoundedUntil.getUpperBound(dim).getManager().rational(0.0);
}
lowerBounds.push_back(storm::logic::TimeBound(false, zero));
upperBounds.push_back(boost::none);
} else {
if (origBoundedUntil.hasLowerBound()) {
lowerBounds.push_back(storm::logic::TimeBound(origBoundedUntil.isLowerBoundStrict(dim), origBoundedUntil.getLowerBound(dim)));
} else {
if (transformations[dim] == BoundTransformation::LessEqualZero) {
lowerBounds.push_back(boost::none);
}
if (origBoundedUntil.hasUpperBound()) {
lowerBounds.push_back(storm::logic::TimeBound(origBoundedUntil.isUpperBoundStrict(dim), origBoundedUntil.getUpperBound(dim)));
upperBounds.push_back(storm::logic::TimeBound(false, zero));
} else {
STORM_LOG_ASSERT(transformations[dim] == BoundTransformation::GreaterZero || transformations[dim] == BoundTransformation::GreaterEqualZero, "Unhandled bound transformation.");
lowerBounds.push_back(storm::logic::TimeBound(transformations[dim] == BoundTransformation::GreaterZero, zero));
upperBounds.push_back(boost::none);
}
}
@ -63,15 +84,36 @@ namespace storm {
return std::make_shared<storm::logic::ProbabilityOperatorFormula>(newBoundedUntil, boundedUntilOperator.getOperatorInformation());
}
template<typename ModelType>
uint64_t QuantileHelper<ModelType>::getDimension() const {
return quantileFormula.getSubformula().asProbabilityOperatorFormula().getSubformula().asBoundedUntilFormula().getDimension();
}
template<typename ModelType>
storm::storage::BitVector QuantileHelper<ModelType>::getDimensionsForVariable(storm::expressions::Variable const& var) {
storm::storage::BitVector QuantileHelper<ModelType>::getOpenDimensions() const {
auto const& boundedUntil = quantileFormula.getSubformula().asProbabilityOperatorFormula().getSubformula().asBoundedUntilFormula();
storm::storage::BitVector res(getDimension());
for (uint64_t dim = 0; dim < getDimension(); ++dim) {
res.set(dim, boundedUntil.hasLowerBound(dim) ? boundedUntil.getLowerBound(dim).containsVariables() : boundedUntil.getUpperBound(dim).containsVariables());
}
return res;
}
template<typename ModelType>
storm::solver::OptimizationDirection const& QuantileHelper<ModelType>::getOptimizationDirForDimension(uint64_t const& dim) const {
auto const& boundedUntil = quantileFormula.getSubformula().asProbabilityOperatorFormula().getSubformula().asBoundedUntilFormula();
storm::expressions::Variable const& dimVar = (boundedUntil.hasLowerBound() ? boundedUntil.getLowerBound(dim) : boundedUntil.getUpperBound(dim)).getBaseExpression().asVariableExpression().getVariable();
for (auto const& boundVar : quantileFormula.getBoundVariables()) {
if (boundVar.second == dimVar) {
return boundVar.first;
}
}
STORM_LOG_THROW(false, storm::exceptions::InvalidOperationException, "The bound variable '" << dimVar.getName() << "' is not specified within the quantile formula '" << quantileFormula << "'.");
return quantileFormula.getOptimizationDirection();
}
template<typename ModelType>
storm::storage::BitVector QuantileHelper<ModelType>::getDimensionsForVariable(storm::expressions::Variable const& var) const {
auto const& boundedUntil = quantileFormula.getSubformula().asProbabilityOperatorFormula().getSubformula().asBoundedUntilFormula();
storm::storage::BitVector result(boundedUntil.getDimension(), false);
for (uint64_t dim = 0; dim < boundedUntil.getDimension(); ++dim) {
@ -86,24 +128,166 @@ namespace storm {
}
template<typename ModelType>
std::vector<std::vector<typename ModelType::ValueType>> QuantileHelper<ModelType>::computeMultiDimensionalQuantile(Environment const& env) {
std::vector<std::vector<typename ModelType::ValueType>> QuantileHelper<ModelType>::computeQuantile(Environment const& env) {
std::vector<std::vector<ValueType>> result;
if (!computeUnboundedValue(env)) {
if (getOpenDimensions().getNumberOfSetBits() == 1) {
uint64_t dimension = *getOpenDimensions().begin();
auto const& boundedUntilOperator = quantileFormula.getSubformula().asProbabilityOperatorFormula();
bool maxProbSatisfiesFormula = boundedUntilOperator.getBound().isSatisfied(computeExtremalValue(env, storm::storage::BitVector(getDimension(), false)));
bool minProbSatisfiesFormula = boundedUntilOperator.getBound().isSatisfied(computeExtremalValue(env, getOpenDimensions()));
if (maxProbSatisfiesFormula != minProbSatisfiesFormula) {
auto quantileRes = computeQuantileForDimension(env, dimension);
result = {{storm::utility::convertNumber<ValueType>(quantileRes.first) * quantileRes.second}};
} else if (maxProbSatisfiesFormula) {
// i.e., all bound values satisfy the formula
bool minimizingRewardBound = storm::solver::minimize(getOptimizationDirForDimension(dimension));
bool upperCostBound = boundedUntilOperator.getSubformula().asBoundedUntilFormula().hasUpperBound(dimension);
if (minimizingRewardBound) {
result = {{ (upperCostBound ? storm::utility::zero<ValueType>() : -storm::utility::one<ValueType>())}};
} else {
result = {{ storm::utility::infinity<ValueType>()}};
}
} else {
// i.e., no bound value satisfies the formula
result = {{}};
}
} else if (getOpenDimensions().getNumberOfSetBits() == 2) {
} else {
STORM_LOG_THROW(false, storm::exceptions::NotSupportedException, "The quantile formula considers " << getOpenDimensions().getNumberOfSetBits() << " open dimensions. Only one- or two-dimensional quantiles are supported.");
}
return result;
/*
return unboundedFormula->getBound().isSatisfied(numericResult);
if (!checkUnboundedValue(env)) {
STORM_LOG_INFO("Bound is not satisfiable.");
result.emplace_back();
for (auto const& bv : quantileFormula.getBoundVariables()) {
result.front().push_back(storm::solver::minimize(bv.first) ? storm::utility::infinity<ValueType>() : -storm::utility::infinity<ValueType>());
}
} else {
std::vector<bool> limitProbCheckResults;
for (uint64_t dim = 0; dim < getDimension(); ++dim) {
storm::storage::BitVector dimAsBitVector(getDimension(), false);
dimAsBitVector.set(dim, true);
limitProbCheckResults.push_back(checkLimitProbability(env, dimAsBitVector));
auto quantileRes = computeQuantileForDimension(env, dim);
std::cout << "Quantile for dim " << dim << " is " << (storm::utility::convertNumber<ValueType>(quantileRes.first) * quantileRes.second) << std::endl;
}
result = {{27}};
}
return result;
return result;*/
}
template<typename ModelType>
bool QuantileHelper<ModelType>::computeUnboundedValue(Environment const& env) {
auto unboundedFormula = replaceBoundsByGreaterEqZero(quantileFormula.getSubformula().asProbabilityOperatorFormula(), storm::storage::BitVector(getDimension(), true));
MultiDimensionalRewardUnfolding<ValueType, true> rewardUnfolding(model, unboundedFormula);
std::pair<uint64_t, typename ModelType::ValueType> QuantileHelper<ModelType>::computeQuantileForDimension(Environment const& env, uint64_t dimension) const {
// We assume that their is one bound value that violates the quantile and one bound value that satisfies it.
// 'Drop' all other open bounds
std::vector<BoundTransformation> bts(getDimension(), BoundTransformation::None);
for (auto const& d : getOpenDimensions()) {
if (d != dimension) {
bts[d] = BoundTransformation::GreaterEqualZero;
}
}
auto transformedFormula = transformBoundedUntilOperator(quantileFormula.getSubformula().asProbabilityOperatorFormula(), bts);
MultiDimensionalRewardUnfolding<ValueType, true> rewardUnfolding(model, transformedFormula);
bool upperCostBound = transformedFormula->getSubformula().asBoundedUntilFormula().hasUpperBound(dimension);
// bool lowerProbabilityBound = storm::logic::isLowerBound(transformedFormula->getBound().comparisonType);
bool minimizingRewardBound = storm::solver::minimize(getOptimizationDirForDimension(dimension));
// initialize data that will be needed for each epoch
auto lowerBound = rewardUnfolding.getLowerObjectiveBound();
auto upperBound = rewardUnfolding.getUpperObjectiveBound();
std::vector<ValueType> x, b;
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> minMaxSolver;
int64_t epochValue = 0; // -1 is actally allowed since we express >=0 as >-1
std::set<typename EpochManager::Epoch> exploredEpochs;
while (true) {
auto currEpoch = rewardUnfolding.getStartEpoch(true);
rewardUnfolding.getEpochManager().setDimensionOfEpoch(currEpoch, dimension, (uint64_t) epochValue);
auto epochOrder = rewardUnfolding.getEpochComputationOrder(currEpoch);
for (auto const& epoch : epochOrder) {
if (exploredEpochs.count(epoch) == 0) {
auto& epochModel = rewardUnfolding.setCurrentEpoch(epoch);
rewardUnfolding.setSolutionForCurrentEpoch(epochModel.analyzeSingleObjective(env, quantileFormula.getSubformula().asProbabilityOperatorFormula().getOptimalityType(), x, b, minMaxSolver, lowerBound, upperBound));
exploredEpochs.insert(epoch);
}
}
ValueType currValue = rewardUnfolding.getInitialStateResult(currEpoch);
std::cout << "Numeric result for epoch " << rewardUnfolding.getEpochManager().toString(currEpoch) << " is " << currValue << std::endl;
bool propertySatisfied = transformedFormula->getBound().isSatisfied(currValue);
// If the reward bound should be as small as possible, we should stop as soon as the property is satisfied.
// If the reward bound should be as large as possible, we should stop as soon as sthe property is violated and then go a step backwards
if (minimizingRewardBound && propertySatisfied) {
break;
} else if (!minimizingRewardBound && !propertySatisfied) {
STORM_LOG_ASSERT(epochValue > 0 || !upperCostBound, "The property does not seem to be satisfiable. This case should have been treated earlier.");
--epochValue;
break;
}
++epochValue;
}
return {epochValue, rewardUnfolding.getDimension(dimension).scalingFactor};
}
template<typename ModelType>
typename ModelType::ValueType QuantileHelper<ModelType>::computeExtremalValue(Environment const& env, storm::storage::BitVector const& minimizingDimensions) const {
// For maximizing in a dimension, we can simply 'drop' the bound by replacing it with >=0
// For minimizing an upper-bounded dimension, we can replace it with <=0
// For minimizing a lower-bounded dimension, the lower bound needs to approach infinity.
// To compute this limit probability, we only consider epoch steps that lie in an end component and check for the bound >0 instead.
// Notice, however, that this approach fails if we try to minimize for a lower and an upper bounded dimension
std::vector<BoundTransformation> bts(getDimension(), BoundTransformation::None);
storm::storage::BitVector minimizingLowerBoundedDimensions(getDimension(), false);
for (auto const& d : getOpenDimensions()) {
if (minimizingDimensions.get(d)) {
bool upperCostBound = quantileFormula.getSubformula().asProbabilityOperatorFormula().getSubformula().asBoundedUntilFormula().hasUpperBound(d);
if (upperCostBound) {
bts[d] = BoundTransformation::LessEqualZero;
STORM_LOG_ASSERT(std::find(bts.begin(), bts.end(), BoundTransformation::GreaterZero) == bts.end(), "Unable to compute extremal value for minimizing lower and upper bounded dimensions.");
} else {
bts[d] = BoundTransformation::GreaterZero;
minimizingLowerBoundedDimensions.set(d, true);
STORM_LOG_ASSERT(std::find(bts.begin(), bts.end(), BoundTransformation::LessEqualZero) == bts.end(), "Unable to compute extremal value for minimizing lower and upper bounded dimensions.");
}
} else {
bts[d] = BoundTransformation::GreaterEqualZero;
}
}
auto transformedFormula = transformBoundedUntilOperator(quantileFormula.getSubformula().asProbabilityOperatorFormula(), bts);
storm::storage::BitVector nonMecChoices;
if (!minimizingLowerBoundedDimensions.empty()) {
// Get the choices that do not lie on a mec
nonMecChoices.resize(model.getNumberOfChoices(), true);
auto mecDecomposition = storm::storage::MaximalEndComponentDecomposition<ValueType>(model);
for (auto const& mec : mecDecomposition) {
for (auto const& stateChoicesPair : mec) {
for (auto const& choice : stateChoicesPair.second) {
nonMecChoices.set(choice, false);
}
}
}
}
MultiDimensionalRewardUnfolding<ValueType, true> rewardUnfolding(model, transformedFormula, [&](std::vector<EpochManager::Epoch>& epochSteps, EpochManager const& epochManager) {
if (!minimizingLowerBoundedDimensions.empty()) {
for (auto const& choice : nonMecChoices) {
for (auto const& dim : minimizingLowerBoundedDimensions) {
epochManager.setDimensionOfEpoch(epochSteps[choice], dim, 0);
}
}
}
});
// Get lower and upper bounds for the solution.
auto lowerBound = rewardUnfolding.getLowerObjectiveBound();
@ -112,20 +296,20 @@ namespace storm {
// Initialize epoch models
auto initEpoch = rewardUnfolding.getStartEpoch();
auto epochOrder = rewardUnfolding.getEpochComputationOrder(initEpoch);
STORM_LOG_ASSERT(epochOrder.size() == 1, "unexpected epoch order size.");
// initialize data that will be needed for each epoch
std::vector<ValueType> x, b;
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> minMaxSolver;
auto& epochModel = rewardUnfolding.setCurrentEpoch(initEpoch);
rewardUnfolding.setSolutionForCurrentEpoch(epochModel.analyzeSingleObjective(env, quantileFormula.getSubformula().asProbabilityOperatorFormula().getOptimalityType(), x, b, minMaxSolver, lowerBound, upperBound));
for (auto const& epoch : epochOrder) {
auto& epochModel = rewardUnfolding.setCurrentEpoch(epoch);
rewardUnfolding.setSolutionForCurrentEpoch(epochModel.analyzeSingleObjective(env, quantileFormula.getSubformula().asProbabilityOperatorFormula().getOptimalityType(), x, b, minMaxSolver, lowerBound, upperBound));
}
ValueType numericResult = rewardUnfolding.getInitialStateResult(initEpoch);
std::cout << "Numeric result is " << numericResult;
return unboundedFormula->getBound().isSatisfied(numericResult);
STORM_LOG_TRACE("Extremal probability for minimizing dimensions " << minimizingDimensions << " is " << numericResult << ".");
return transformedFormula->getBound().isSatisfied(numericResult);
}
template class QuantileHelper<storm::models::sparse::Mdp<double>>;
template class QuantileHelper<storm::models::sparse::Mdp<storm::RationalNumber>>;

31
src/storm/modelchecker/prctl/helper/rewardbounded/QuantileHelper.h
View File

@ -19,16 +19,33 @@ namespace storm {
public:
QuantileHelper(ModelType const& model, storm::logic::QuantileFormula const& quantileFormula);
std::vector<std::vector<ValueType>> computeMultiDimensionalQuantile(Environment const& env);
std::vector<std::vector<ValueType>> computeQuantile(Environment const& env);
private:
bool computeUnboundedValue(Environment const& env);
/*!
* Computes the infimum over bound values in minimizing dimensions / the supremum over bound values in maximizing dimensions
* @param minimizingDimensions marks dimensions which should be minimized. The remaining dimensions are either not open or maximizing.
*/
ValueType computeExtremalValue(Environment const& env, storm::storage::BitVector const& minimizingDimensions) const;
/// Computes the quantile with respect to the given dimension
std::pair<uint64_t, typename ModelType::ValueType> computeQuantileForDimension(Environment const& env, uint64_t dim) const;
/*!
* Gets the number of dimensions of the underlying boudned until formula
*/
uint64_t getDimension() const;
storm::storage::BitVector getDimensionsForVariable(storm::expressions::Variable const& var);
/*!
* Gets the dimensions that are open, i.e., for which the bound value is not fixed
* @return
*/
storm::storage::BitVector getOpenDimensions() const;
storm::storage::BitVector getDimensionsForVariable(storm::expressions::Variable const& var) const;
storm::solver::OptimizationDirection const& getOptimizationDirForDimension(uint64_t const& dim) const;
ModelType const& model;
storm::logic::QuantileFormula const& quantileFormula;

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