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LP-based long run average rewards for MDPs

main
TimQu 8 years ago
parent
2646097d8e
commit
aebe9fa3c3
5 changed files with 52 additions and 19 deletions
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  1. 2
      src/storm/modelchecker/csl/SparseMarkovAutomatonCslModelChecker.cpp
  2. 11
      src/storm/modelchecker/prctl/SparseMdpPrctlModelChecker.cpp
  3. 1
      src/storm/modelchecker/prctl/SparseMdpPrctlModelChecker.h
  4. 48
      src/storm/modelchecker/prctl/helper/SparseMdpPrctlHelper.cpp
  5. 9
      src/storm/modelchecker/prctl/helper/SparseMdpPrctlHelper.h

2
src/storm/modelchecker/csl/SparseMarkovAutomatonCslModelChecker.cpp
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@ -111,7 +111,7 @@ namespace storm {
std::unique_ptr<CheckResult> SparseMarkovAutomatonCslModelChecker<SparseMarkovAutomatonModelType>::computeLongRunAverageRewards(storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::LongRunAverageRewardFormula, ValueType> const& checkTask) {
STORM_LOG_THROW(checkTask.isOptimizationDirectionSet(), storm::exceptions::InvalidPropertyException, "Formula needs to specify whether minimal or maximal values are to be computed on nondeterministic model.");
STORM_LOG_THROW(this->getModel().isClosed(), storm::exceptions::InvalidPropertyException, "Unable to compute long run average rewards in non-closed Markov automaton.");
std::vector<ValueType> result = storm::modelchecker::helper::SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards<ValueType, RewardModelType>(checkTask.getOptimizationDirection(), this->getModel().getTransitionMatrix(), this->getModel().getBackwardTransitions(), this->getModel().getExitRates(), this->getModel().getMarkovianStates(), checkTask.isRewardModelSet() ? this->getModel().getRewardModel(checkTask.getRewardModel()) : this->getModel().getRewardModel(""), *minMaxLinearEquationSolverFactory);
std::vector<ValueType> result = storm::modelchecker::helper::SparseMarkovAutomatonCslHelper::computeLongRunAverageRewards<ValueType, RewardModelType>(checkTask.getOptimizationDirection(), this->getModel().getTransitionMatrix(), this->getModel().getBackwardTransitions(), this->getModel().getExitRates(), this->getModel().getMarkovianStates(), checkTask.isRewardModelSet() ? this->getModel().getRewardModel(checkTask.getRewardModel()) : this->getModel().getUniqueRewardModel(), *minMaxLinearEquationSolverFactory);
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(std::move(result)));
}

11
src/storm/modelchecker/prctl/SparseMdpPrctlModelChecker.cpp
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@ -43,7 +43,7 @@ namespace storm {
template<typename SparseMdpModelType>
bool SparseMdpPrctlModelChecker<SparseMdpModelType>::canHandle(CheckTask<storm::logic::Formula, ValueType> const& checkTask) const {
storm::logic::Formula const& formula = checkTask.getFormula();
if(formula.isInFragment(storm::logic::prctl().setLongRunAverageRewardFormulasAllowed(false).setLongRunAverageProbabilitiesAllowed(true).setConditionalProbabilityFormulasAllowed(true).setOnlyEventuallyFormuluasInConditionalFormulasAllowed(true))) {
if(formula.isInFragment(storm::logic::prctl().setLongRunAverageRewardFormulasAllowed(true).setLongRunAverageProbabilitiesAllowed(true).setConditionalProbabilityFormulasAllowed(true).setOnlyEventuallyFormuluasInConditionalFormulasAllowed(true))) {
return true;
} else {
// Check whether we consider a multi-objective formula
@ -162,6 +162,15 @@ namespace storm {
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(std::move(numericResult)));
}
template<typename SparseMdpModelType>
std::unique_ptr<CheckResult> SparseMdpPrctlModelChecker<SparseMdpModelType>::computeLongRunAverageRewards(storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::LongRunAverageRewardFormula, ValueType> const& checkTask) {
STORM_LOG_THROW(checkTask.isOptimizationDirectionSet(), storm::exceptions::InvalidPropertyException, "Formula needs to specify whether minimal or maximal values are to be computed on nondeterministic model.");
std::vector<ValueType> result = storm::modelchecker::helper::SparseMdpPrctlHelper<ValueType>::computeLongRunAverageRewards(checkTask.getOptimizationDirection(), this->getModel().getTransitionMatrix(), this->getModel().getBackwardTransitions(), checkTask.isRewardModelSet() ? this->getModel().getRewardModel(checkTask.getRewardModel()) : this->getModel().getUniqueRewardModel(), *minMaxLinearEquationSolverFactory);
return std::unique_ptr<CheckResult>(new ExplicitQuantitativeCheckResult<ValueType>(std::move(result)));
}
template<typename SparseMdpModelType>
std::unique_ptr<CheckResult> SparseMdpPrctlModelChecker<SparseMdpModelType>::checkMultiObjectiveFormula(CheckTask<storm::logic::MultiObjectiveFormula, ValueType> const& checkTask) {
return multiobjective::performMultiObjectiveModelChecking(this->getModel(), checkTask.getFormula());

1
src/storm/modelchecker/prctl/SparseMdpPrctlModelChecker.h
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@ -27,6 +27,7 @@ namespace storm {
virtual std::unique_ptr<CheckResult> computeInstantaneousRewards(storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::InstantaneousRewardFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeReachabilityRewards(storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::EventuallyFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeLongRunAverageProbabilities(CheckTask<storm::logic::StateFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> computeLongRunAverageRewards(storm::logic::RewardMeasureType rewardMeasureType, CheckTask<storm::logic::LongRunAverageRewardFormula, ValueType> const& checkTask) override;
virtual std::unique_ptr<CheckResult> checkMultiObjectiveFormula(CheckTask<storm::logic::MultiObjectiveFormula, ValueType> const& checkTask) override;
private:

48
src/storm/modelchecker/prctl/helper/SparseMdpPrctlHelper.cpp
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@ -503,17 +503,31 @@ namespace storm {
template<typename ValueType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeLongRunAverageProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
// If there are no goal states, we avoid the computation and directly return zero.
uint_fast64_t numberOfStates = transitionMatrix.getRowGroupCount();
if (psiStates.empty()) {
return std::vector<ValueType>(numberOfStates, storm::utility::zero<ValueType>());
return std::vector<ValueType>(transitionMatrix.getRowGroupCount(), storm::utility::zero<ValueType>());
}
// Likewise, if all bits are set, we can avoid the computation and set.
if ((~psiStates).empty()) {
return std::vector<ValueType>(numberOfStates, storm::utility::one<ValueType>());
if (psiStates.full()) {
return std::vector<ValueType>(transitionMatrix.getRowGroupCount(), storm::utility::one<ValueType>());
}
// Reduce long run average probabilities to long run average rewards by
// building a reward model assigning one reward to every psi state
std::vector<ValueType> stateRewards(psiStates.size(), storm::utility::zero<ValueType>());
storm::utility::vector::setVectorValues(stateRewards, psiStates, storm::utility::one<ValueType>());
storm::models::sparse::StandardRewardModel<ValueType> rewardModel(std::move(stateRewards));
return computeLongRunAverageRewards(dir, transitionMatrix, backwardTransitions, rewardModel, minMaxLinearEquationSolverFactory);
}
template<typename ValueType>
template<typename RewardModelType>
std::vector<ValueType> SparseMdpPrctlHelper<ValueType>::computeLongRunAverageRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, RewardModelType const& rewardModel, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory) {
uint64_t numberOfStates = transitionMatrix.getRowGroupCount();
// Start by decomposing the MDP into its MECs.
storm::storage::MaximalEndComponentDecomposition<ValueType> mecDecomposition(transitionMatrix, backwardTransitions);
@ -529,7 +543,7 @@ namespace storm {
for (uint_fast64_t currentMecIndex = 0; currentMecIndex < mecDecomposition.size(); ++currentMecIndex) {
storm::storage::MaximalEndComponent const& mec = mecDecomposition[currentMecIndex];
lraValuesForEndComponents[currentMecIndex] = computeLraForMaximalEndComponent(dir, transitionMatrix, psiStates, mec);
lraValuesForEndComponents[currentMecIndex] = computeLraForMaximalEndComponent(dir, transitionMatrix, rewardModel, mec);
// Gather information for later use.
for (auto const& stateChoicesPair : mec) {
@ -555,7 +569,9 @@ namespace storm {
// Finally, we are ready to create the SSP matrix and right-hand side of the SSP.
std::vector<ValueType> b;
typename storm::storage::SparseMatrixBuilder<ValueType> sspMatrixBuilder(0, 0, 0, false, true, numberOfStatesNotInMecs + mecDecomposition.size());
uint64_t numberOfSspStates = numberOfStatesNotInMecs + mecDecomposition.size();
typename storm::storage::SparseMatrixBuilder<ValueType> sspMatrixBuilder(0, numberOfSspStates, 0, false, true, numberOfSspStates);
// If the source state is not contained in any MEC, we copy its choices (and perform the necessary modifications).
uint_fast64_t currentChoice = 0;
@ -596,10 +612,9 @@ namespace storm {
boost::container::flat_set<uint_fast64_t> const& choicesInMec = stateChoicesPair.second;
for (uint_fast64_t choice = nondeterministicChoiceIndices[state]; choice < nondeterministicChoiceIndices[state + 1]; ++choice) {
std::vector<ValueType> auxiliaryStateToProbabilityMap(mecDecomposition.size());
// If the choice is not contained in the MEC itself, we have to add a similar distribution to the auxiliary state.
if (choicesInMec.find(choice) == choicesInMec.end()) {
std::vector<ValueType> auxiliaryStateToProbabilityMap(mecDecomposition.size());
b.push_back(storm::utility::zero<ValueType>());
for (auto element : transitionMatrix.getRow(choice)) {
@ -631,9 +646,9 @@ namespace storm {
}
// Finalize the matrix and solve the corresponding system of equations.
storm::storage::SparseMatrix<ValueType> sspMatrix = sspMatrixBuilder.build(currentChoice);
storm::storage::SparseMatrix<ValueType> sspMatrix = sspMatrixBuilder.build(currentChoice, numberOfSspStates, numberOfSspStates);
std::vector<ValueType> sspResult(numberOfStatesNotInMecs + mecDecomposition.size());
std::vector<ValueType> sspResult(numberOfSspStates);
std::unique_ptr<storm::solver::MinMaxLinearEquationSolver<ValueType>> solver = minMaxLinearEquationSolverFactory.create(std::move(sspMatrix));
solver->solveEquations(dir, sspResult, b);
@ -652,7 +667,8 @@ namespace storm {
}
template<typename ValueType>
ValueType SparseMdpPrctlHelper<ValueType>::computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& psiStates, storm::storage::MaximalEndComponent const& mec) {
template<typename RewardModelType>
ValueType SparseMdpPrctlHelper<ValueType>::computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec) {
std::shared_ptr<storm::solver::LpSolver> solver = storm::utility::solver::getLpSolver("LRA for MEC");
solver->setOptimizationDirection(invert(dir));
@ -672,14 +688,11 @@ namespace storm {
// Now, based on the type of the state, create a suitable constraint.
for (auto choice : stateChoicesPair.second) {
storm::expressions::Expression constraint = -lambda;
ValueType r = 0;
for (auto element : transitionMatrix.getRow(choice)) {
constraint = constraint + stateToVariableMap.at(element.getColumn()) * solver->getConstant(storm::utility::convertNumber<double>(element.getValue()));
if (psiStates.get(element.getColumn())) {
r += element.getValue();
}
}
typename RewardModelType::ValueType r = rewardModel.getTotalStateActionReward(state, choice, transitionMatrix);
constraint = solver->getConstant(storm::utility::convertNumber<double>(r)) + constraint;
if (dir == OptimizationDirection::Minimize) {
@ -803,6 +816,8 @@ namespace storm {
template std::vector<double> SparseMdpPrctlHelper<double>::computeCumulativeRewards(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, uint_fast64_t stepBound, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template MDPSparseModelCheckingHelperReturnType<double> SparseMdpPrctlHelper<double>::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative, bool produceScheduler, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory, ModelCheckerHint const& hint);
template MDPSparseModelCheckingHelperReturnType<double> SparseMdpPrctlHelper<double>::computeReachabilityRewards(storm::solver::SolveGoal const& goal, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative, bool produceScheduler, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory, ModelCheckerHint const& hint);
template std::vector<double> SparseMdpPrctlHelper<double>::computeLongRunAverageRewards(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::storage::SparseMatrix<double> const& backwardTransitions, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::solver::MinMaxLinearEquationSolverFactory<double> const& minMaxLinearEquationSolverFactory);
template double SparseMdpPrctlHelper<double>::computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<double> const& transitionMatrix, storm::models::sparse::StandardRewardModel<double> const& rewardModel, storm::storage::MaximalEndComponent const& mec);
#ifdef STORM_HAVE_CARL
template class SparseMdpPrctlHelper<storm::RationalNumber>;
@ -810,6 +825,9 @@ namespace storm {
template std::vector<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeCumulativeRewards(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, uint_fast64_t stepBound, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template MDPSparseModelCheckingHelperReturnType<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeReachabilityRewards(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative, bool produceScheduler, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory, ModelCheckerHint const& hint);
template MDPSparseModelCheckingHelperReturnType<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeReachabilityRewards(storm::solver::SolveGoal const& goal, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::BitVector const& targetStates, bool qualitative, bool produceScheduler, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory, ModelCheckerHint const& hint);
template std::vector<storm::RationalNumber> SparseMdpPrctlHelper<storm::RationalNumber>::computeLongRunAverageRewards(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::storage::SparseMatrix<storm::RationalNumber> const& backwardTransitions, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::solver::MinMaxLinearEquationSolverFactory<storm::RationalNumber> const& minMaxLinearEquationSolverFactory);
template storm::RationalNumber SparseMdpPrctlHelper<storm::RationalNumber>::computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<storm::RationalNumber> const& transitionMatrix, storm::models::sparse::StandardRewardModel<storm::RationalNumber> const& rewardModel, storm::storage::MaximalEndComponent const& mec);
#endif
}
}

9
src/storm/modelchecker/prctl/helper/SparseMdpPrctlHelper.h
View File

@ -65,12 +65,17 @@ namespace storm {
static std::vector<ValueType> computeLongRunAverageProbabilities(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& psiStates, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory);
template<typename RewardModelType>
static std::vector<ValueType> computeLongRunAverageRewards(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, RewardModelType const& rewardModel, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory);
static std::unique_ptr<CheckResult> computeConditionalProbabilities(OptimizationDirection dir, storm::storage::sparse::state_type initialState, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, storm::storage::BitVector const& targetStates, storm::storage::BitVector const& conditionStates, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory);
private:
static MDPSparseModelCheckingHelperReturnType<ValueType> computeReachabilityRewardsHelper(storm::solver::SolveGoal const& goal, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::SparseMatrix<ValueType> const& backwardTransitions, std::function<std::vector<ValueType>(uint_fast64_t, storm::storage::SparseMatrix<ValueType> const&, storm::storage::BitVector const&)> const& totalStateRewardVectorGetter, storm::storage::BitVector const& targetStates, bool qualitative, bool produceScheduler, storm::solver::MinMaxLinearEquationSolverFactory<ValueType> const& minMaxLinearEquationSolverFactory, ModelCheckerHint const& hint = ModelCheckerHint());
static ValueType computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, storm::storage::BitVector const& goalStates, storm::storage::MaximalEndComponent const& mec);
template<typename RewardModelType>
static ValueType computeLraForMaximalEndComponent(OptimizationDirection dir, storm::storage::SparseMatrix<ValueType> const& transitionMatrix, RewardModelType const& rewardModel, storm::storage::MaximalEndComponent const& mec);
};

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