From f8fbf7ace40f85330798d9f380191a4069edbbd2 Mon Sep 17 00:00:00 2001 From: Tim Quatmann Date: Tue, 3 Mar 2020 17:50:27 +0100 Subject: [PATCH] Refactored unif+ implementation (introduced relative precision criterion) --- .../helper/SparseMarkovAutomatonCslHelper.cpp | 329 +++++++++++++++++- 1 file changed, 321 insertions(+), 8 deletions(-) diff --git a/src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.cpp b/src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.cpp index f39606107..131c3cf44 100644 --- a/src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.cpp +++ b/src/storm/modelchecker/csl/helper/SparseMarkovAutomatonCslHelper.cpp @@ -16,6 +16,7 @@ #include "storm/environment/solver/TopologicalSolverEnvironment.h" #include "storm/environment/solver/LongRunAverageSolverEnvironment.h" #include "storm/environment/solver/EigenSolverEnvironment.h" +#include "storm/environment/solver/TimeBoundedSolverEnvironment.h" #include "storm/utility/macros.h" #include "storm/utility/vector.h" @@ -26,6 +27,7 @@ #include "storm/storage/expressions/Expression.h" #include "storm/storage/expressions/ExpressionManager.h" +#include "storm/solver/Multiplier.h" #include "storm/solver/MinMaxLinearEquationSolver.h" #include "storm/solver/LpSolver.h" @@ -37,7 +39,309 @@ namespace storm { namespace modelchecker { namespace helper { + + template + class UnifPlusHelper { + public: + UnifPlusHelper(storm::storage::SparseMatrix const& transitionMatrix, std::vector const& exitRateVector, storm::storage::BitVector const& markovianStates) : transitionMatrix(transitionMatrix), exitRateVector(exitRateVector), markovianStates(markovianStates) { + // Intentionally left empty + } + + std::vector computeBoundedUntilProbabilities(storm::Environment const& env, OptimizationDirection dir, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, ValueType const& upperTimeBound) { + // Since there is no lower time bound, we can treat the psiStates as if they are absorbing. + + // Compute some important subsets of states + storm::storage::BitVector maybeStates = ~(getProb0States(dir, phiStates, psiStates) | psiStates); + storm::storage::BitVector markovianMaybeStates = markovianStates & maybeStates; + storm::storage::BitVector probabilisticMaybeStates = ~markovianStates & maybeStates; + + // Catch the case where this is query can be solved by solving the untimed variant instead. + // This is the case if there is no Markovian maybe state (e.g. if the initial state is already a psi state) of if the time bound is infinity. + if (markovianMaybeStates.empty() || storm::utility::isInfinity(upperTimeBound)) { + return SparseMarkovAutomatonCslHelper::computeUntilProbabilities(env, dir, transitionMatrix, transitionMatrix.transpose(true), phiStates, psiStates, false, false).values; + } + + // Split the transitions into various part + // Transitions from Markovian maybe states to all other maybe states. Insert Diagonal entries to apply uniformization later. + storm::storage::SparseMatrix markovianToMaybeTransitions = transitionMatrix.getSubmatrix(true, markovianMaybeStates, maybeStates, true); + // The probabilities to go from a Markovian state to a psi state in one step + std::vector> markovianToPsiProbabilities = getSparseOneStepProbabilities(markovianMaybeStates, psiStates); + // Transitions from probabilistic maybe states to probabilistic maybe states. + storm::storage::SparseMatrix probabilisticToProbabilisticTransitions = transitionMatrix.getSubmatrix(true, probabilisticMaybeStates, probabilisticMaybeStates, false); + // Transitions from probabilistic maybe states to Markovian maybe states. + storm::storage::SparseMatrix probabilisticToMarkovianTransitions = transitionMatrix.getSubmatrix(true, probabilisticMaybeStates, markovianMaybeStates, false); + // The probabilities to go from a probabilistic state to a psi state in one step + std::vector> probabilisticToPsiProbabilities = getSparseOneStepProbabilities(probabilisticMaybeStates, psiStates); + + // Get the exit rates restricted to only markovian maybe states. + std::vector markovianExitRates = storm::utility::vector::filterVector(exitRateVector, markovianMaybeStates); + + // Obtain parameters of the algorithm + // Truncation error + ValueType kappa = storm::utility::convertNumber(env.solver().timeBounded().getUnifPlusKappa()); + // Precision to be achieved + ValueType epsilon = storm::utility::convertNumber(env.solver().timeBounded().getPrecision()); + bool relativePrecision = env.solver().timeBounded().getRelativeTerminationCriterion(); + // Uniformization rate + ValueType lambda = *std::max_element(markovianExitRates.begin(), markovianExitRates.end()); + STORM_LOG_DEBUG("Initial lambda is " << lambda << "."); + + // Uniformize the Markovian transitions for the first time + uniformize(markovianToMaybeTransitions, markovianToPsiProbabilities, markovianExitRates, lambda); + + // Set up a solver for the transitions between probabilistic states (if there are some) + auto solver = setUpProbabilisticStatesSolver(env, dir, probabilisticToProbabilisticTransitions); + + // Allocate auxiliary memory that can be used during the iterations + std::vector maybeStatesValuesLower(maybeStates.getNumberOfSetBits(), storm::utility::zero()); // should be zero initially + std::vector maybeStatesValuesWeightedUpper(maybeStates.getNumberOfSetBits(), storm::utility::zero()); // should be zero initially + std::vector maybeStatesValuesUpper(maybeStates.getNumberOfSetBits(), storm::utility::zero()); // should be zero initially + std::vector nextMarkovianStateValues = std::move(markovianExitRates); // At this point, the markovianExitRates are no longer needed, so we 'move' them away instead of allocating new memory + std::vector nextProbabilisticStateValues(probabilisticToProbabilisticTransitions.getRowGroupCount()); + std::vector eqSysRhs(probabilisticToProbabilisticTransitions.getRowCount()); + + // Start the outer iterations which increase the uniformization rate until lower and upper bound on the result vector is sufficiently small + storm::utility::ProgressMeasurement progressIterations("iterations"); + uint64_t iteration = 0; + progressIterations.startNewMeasurement(iteration); + bool converged = false; + while (!converged) { + // Maximal step size + uint64_t N = storm::utility::ceil(lambda * upperTimeBound * std::exp(2) - storm::utility::log(kappa * epsilon)); + + // Compute poisson distribution. + // The division by 8 is similar to what is done for CTMCs (probably to reduce numerical impacts?) + auto foxGlynnResult = storm::utility::numerical::foxGlynn(lambda * upperTimeBound, epsilon * kappa / storm::utility::convertNumber(8.0)); + // Scale the weights so they sum to one. + storm::utility::vector::scaleVectorInPlace(foxGlynnResult.weights, storm::utility::one() / foxGlynnResult.totalWeight); + + // Set up multiplier + auto markovianToMaybeMultiplier = storm::solver::MultiplierFactory().create(env, markovianToMaybeTransitions); + auto probabilisticToMarkovianMultiplier = storm::solver::MultiplierFactory().create(env, probabilisticToMarkovianTransitions); + + //Perform inner iterations + // Iteration k = N will be performed by implicitly assuming value 0 for all states. + STORM_LOG_ASSERT(!storm::utility::vector::hasNonZeroEntry(maybeStatesValuesUpper), "Current values need to be initialized with zero."); + // Iterations k < N + for (bool computeLowerBound : {false, true}) { + ValueType targetValue = computeLowerBound ? storm::utility::zero() : storm::utility::one(); + storm::utility::ProgressMeasurement progressSteps("steps in iteration " + std::to_string(iteration) + " for " + std::string(computeLowerBound ? "lower" : "upper") + " bounds."); + progressSteps.setMaxCount(N); + progressSteps.startNewMeasurement(0); + for (int64_t k = N - 1; k >= 0; --k) { + auto& maybeStatesValues = computeLowerBound ? maybeStatesValuesLower : maybeStatesValuesWeightedUpper; + + // Compute the values at Markovian maybe states. + if (static_cast(k) == N - 1) { + // If we are in the very first (inner) iteration, we have to set set all values to zero, since we are in the 'last' time epoch before the bound is exceeded. + std::fill(nextMarkovianStateValues.begin(), nextMarkovianStateValues.end(), storm::utility::zero()); + } else { + markovianToMaybeMultiplier->multiply(env, maybeStatesValues, nullptr, nextMarkovianStateValues); + for (auto const& oneStepProb : markovianToPsiProbabilities) { + nextMarkovianStateValues[oneStepProb.first] += oneStepProb.second * targetValue; + } + } + + // Update the value when reaching a psi state. + // This has to be done after updating the Markovian state values since we needed the 'old' target value above. + if (computeLowerBound && static_cast(k) >= foxGlynnResult.left && static_cast(k) <=foxGlynnResult.right) { + targetValue += foxGlynnResult.weights[k - foxGlynnResult.left]; + } + + // Compute the values at probabilistic states. + probabilisticToMarkovianMultiplier->multiply(env, nextMarkovianStateValues, nullptr, eqSysRhs); + for (auto const& oneStepProb : probabilisticToPsiProbabilities) { + eqSysRhs[oneStepProb.first] += oneStepProb.second * targetValue; + } + if (solver) { + solver->solveEquations(env, dir, nextProbabilisticStateValues, eqSysRhs); + } else { + storm::utility::vector::reduceVectorMinOrMax(dir, eqSysRhs, nextMarkovianStateValues, probabilisticToProbabilisticTransitions.getRowGroupIndices()); + } + + // Create the new values for the maybestates + // Fuse the results together + storm::utility::vector::setVectorValues(maybeStatesValues, markovianMaybeStates, nextMarkovianStateValues); + storm::utility::vector::setVectorValues(maybeStatesValues, probabilisticMaybeStates, nextProbabilisticStateValues); + if (!computeLowerBound) { + // Add the scaled values to the actual result vector + uint64_t i = N-1-k; + if (i >= foxGlynnResult.left && i <= foxGlynnResult.right) { + ValueType const& weight = foxGlynnResult.weights[i - foxGlynnResult.left]; + storm::utility::vector::addScaledVector(maybeStatesValuesUpper, maybeStatesValuesWeightedUpper, weight); + } + } + progressSteps.updateProgress(N-k); + } + // Check if the lower and upper bound are sufficiently close to each other + // TODO: apply this only to relevant values? + converged = checkConvergence(maybeStatesValuesLower, maybeStatesValuesUpper, boost::none, epsilon, relativePrecision, kappa); + if (converged) { + break; + } + } + + if (!converged) { + // Increase the uniformization rate and prepare the next run + + // Double lambda. + ValueType oldLambda = lambda; + lambda *= storm::utility::convertNumber(2.0); + STORM_LOG_DEBUG("Increased lambda to " << lambda << "."); + + if (relativePrecision) { + // Reduce kappa a bit + ValueType minValue = *std::min_element(maybeStatesValuesUpper.begin(), maybeStatesValuesUpper.end()); + kappa *= std::max(storm::utility::convertNumber("1/10"), minValue); + } + + // Apply uniformization with new rate + uniformize(markovianToMaybeTransitions, markovianToPsiProbabilities, oldLambda, lambda); + + // Reset the values of the maybe states to zero. + std::fill(maybeStatesValuesUpper.begin(), maybeStatesValuesUpper.end(), storm::utility::zero()); + } + progressIterations.updateProgress(++iteration); + } + + // We take the average of the lower and upper bounds + auto two = storm::utility::convertNumber(2.0); + storm::utility::vector::applyPointwise(maybeStatesValuesLower, maybeStatesValuesUpper, maybeStatesValuesLower, [&two] (ValueType const& a, ValueType const& b) -> ValueType { return (a + b) / two; }); + + std::vector result(transitionMatrix.getRowGroupCount(), storm::utility::zero()); + storm::utility::vector::setVectorValues(result, psiStates, storm::utility::one()); + storm::utility::vector::setVectorValues(result, maybeStates, maybeStatesValuesLower); + return result; + } + + private: + + bool checkConvergence(std::vector const& lower, std::vector const& upper, boost::optional const& relevantValues, ValueType const& epsilon, bool relative, ValueType& kappa) { + if (!relative) { + if (relevantValues) { + return storm::utility::vector::equalModuloPrecision(lower, upper, relevantValues.get(), epsilon * (storm::utility::one() - kappa), false); + } else { + return storm::utility::vector::equalModuloPrecision(lower, upper, epsilon * (storm::utility::one() - kappa), false); + } + } + ValueType truncationError = epsilon * kappa; + ValueType twoTimestruncationError = storm::utility::convertNumber(2.0) * truncationError; + for (uint64_t i = 0; i < lower.size(); ++i) { + if (lower[i] == upper[i]) { + continue; + } + if (lower[i] <= truncationError) { + return false; + } + ValueType absDiff = upper[i] - lower[i] + twoTimestruncationError; + ValueType relDiff = absDiff / (lower[i] - truncationError); + if (relDiff > epsilon) { + return false; + } + STORM_LOG_ASSERT(absDiff > storm::utility::zero(), "Upper bound " << upper[i] << " is smaller than lower bound " << lower[i] << "."); + } + return true; + } + + void uniformize(storm::storage::SparseMatrix& matrix, std::vector>& oneSteps, std::vector const& oldRates, ValueType uniformizationRate) { + for (uint64_t row = 0; row < matrix.getRowCount(); ++row) { + ValueType const& oldExitRate = oldRates[row]; + if (oldExitRate == uniformizationRate) { + // Already uniformized. + continue; + } + for (auto& v : matrix.getRow(row)) { + if (v.getColumn() == row) { + ValueType newSelfLoop = uniformizationRate - oldExitRate + v.getValue() * oldExitRate; + v.setValue(newSelfLoop / uniformizationRate); + } else { + v.setValue(v.getValue() * oldExitRate / uniformizationRate); + } + } + } + for (auto& oneStep : oneSteps) { + oneStep.second *= oldRates[oneStep.first] / uniformizationRate; + } + } + + void uniformize(storm::storage::SparseMatrix& matrix, std::vector>& oneSteps, ValueType oldUniformizationRate, ValueType newUniformizationRate) { + if (oldUniformizationRate != newUniformizationRate) { + assert(oldUniformizationRate < newUniformizationRate); + ValueType rateDiff = newUniformizationRate - oldUniformizationRate; + ValueType rateFraction = oldUniformizationRate / newUniformizationRate; + for (uint64_t row = 0; row < matrix.getRowCount(); ++row) { + for (auto& v : matrix.getRow(row)) { + if (v.getColumn() == row) { + ValueType newSelfLoop = rateDiff + v.getValue() * oldUniformizationRate; + v.setValue(newSelfLoop / newUniformizationRate); + } else { + v.setValue(v.getValue() * rateFraction); + } + } + } + for (auto& oneStep : oneSteps) { + oneStep.second *= rateFraction; + } + } + } + + std::unique_ptr> setUpProbabilisticStatesSolver(storm::Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix const& transitions) const { + std::unique_ptr> solver; + if (transitions.getNonzeroEntryCount() > 0) { + storm::solver::GeneralMinMaxLinearEquationSolverFactory factory; + solver = factory.create(env, transitions); + solver->setHasUniqueSolution(true); // Assume non-zeno MA + solver->setHasNoEndComponents(true); // assume non-zeno MA + solver->setLowerBound(storm::utility::zero()); + solver->setUpperBound(storm::utility::one()); + solver->setCachingEnabled(true); + solver->setRequirementsChecked(true); + auto req = solver->getRequirements(env, dir); + req.clearBounds(); + req.clearUniqueSolution(); + STORM_LOG_THROW(!req.hasEnabledCriticalRequirement(), storm::exceptions::UncheckedRequirementException, "The solver requirement " << req.getEnabledRequirementsAsString() << " has not been checked."); + } + return solver; + } + + storm::storage::BitVector getProb0States(OptimizationDirection dir, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates) const { + if (dir == storm::solver::OptimizationDirection::Maximize) { + return storm::utility::graph::performProb0A(transitionMatrix.transpose(true), phiStates, psiStates); + } else { + return storm::utility::graph::performProb0E(transitionMatrix, transitionMatrix.getRowGroupIndices(), transitionMatrix.transpose(true), phiStates, psiStates); + } + } + + /*! + * Returns a vector with pairs of state indices and non-zero probabilities to move from the corresponding state to a target state. + * The state indices are with respect to the number of states satisfying the sourceStateConstraint, i.e. the indices are in the range [0, sourceStateConstraint.getNumberOfSetBits()) + */ + std::vector> getSparseOneStepProbabilities(storm::storage::BitVector const& sourceStateConstraint, storm::storage::BitVector const& targetStateConstraint) const { + auto denseResult = transitionMatrix.getConstrainedRowGroupSumVector(sourceStateConstraint, targetStateConstraint); + std::vector> sparseResult; + for (uint64 i = 0; i < denseResult.size(); ++i) { + auto const& val = denseResult[i]; + if (!storm::utility::isZero(val)) { + sparseResult.emplace_back(i, val); + } + } + return sparseResult; + } + + void performMarkovianStep(storm::Environment const& env, storm::storage::SparseMatrix const& markovianTransitions, std::vector> const& oneStepToGoalProbabilities, std::vector const& currentMaybeStatesValues, ValueType const& currentGoalValue) const { + // Set up a multiplier for the transitions emerging at Markovian states + auto multiplier = storm::solver::MultiplierFactory().create(env, markovianTransitions); + } + + storm::storage::SparseMatrix const& transitionMatrix; + std::vector const& exitRateVector; + storm::storage::BitVector const& markovianStates; + }; + + + + /** * Data structure holding result vectors (vLower, vUpper, wUpper) for Unif+. */ @@ -186,7 +490,7 @@ namespace storm { } if (resVectorNew[successor] == -1) { - calculateUnifPlusVector(env, k, successor, calcLower, lambda, numberOfProbabilisticStates, relativeReachability, dir, unifVectors, fullTransitionMatrix, markovianStates, psiStates, solver, poisson, cycleFree); + calculateUnifPlusVector(env, k, successor, calcLower, lambda, numberOfProbabilisticChoices, relativeReachability, dir, unifVectors, fullTransitionMatrix, markovianStates, psiStates, solver, poisson, cycleFree); } res += relativeReachability[j][stateCount] * resVectorNew[successor]; ++stateCount; @@ -608,18 +912,27 @@ namespace storm { template ::SupportsExponential, int>::type> std::vector SparseMarkovAutomatonCslHelper::computeBoundedUntilProbabilities(Environment const& env, OptimizationDirection dir, storm::storage::SparseMatrix const& transitionMatrix, std::vector const& exitRateVector, storm::storage::BitVector const& markovianStates, storm::storage::BitVector const& phiStates, storm::storage::BitVector const& psiStates, std::pair const& boundsPair) { - auto const& settings = storm::settings::getModule(); - if (settings.getMarkovAutomatonBoundedReachabilityMethod() == storm::settings::modules::MinMaxEquationSolverSettings::MarkovAutomatonBoundedReachabilityMethod::Imca) { - return computeBoundedUntilProbabilitiesImca(env, dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair); + // Choose the applicable method + auto method = env.solver().timeBounded().getMaMethod(); + if (method == storm::solver::MaBoundedReachabilityMethod::Imca) { + if (!phiStates.full()) { + STORM_LOG_WARN("Using Unif+ method because IMCA method does not support (phi Until psi) for non-trivial phi"); + method = storm::solver::MaBoundedReachabilityMethod::UnifPlus; + } } else { - STORM_LOG_ASSERT(settings.getMarkovAutomatonBoundedReachabilityMethod() == storm::settings::modules::MinMaxEquationSolverSettings::MarkovAutomatonBoundedReachabilityMethod::UnifPlus, "Unknown solution method."); + STORM_LOG_ASSERT(method == storm::solver::MaBoundedReachabilityMethod::UnifPlus, "Unknown solution method."); if (!storm::utility::isZero(boundsPair.first)) { STORM_LOG_WARN("Using IMCA method because Unif+ does not support a lower bound > 0."); - return computeBoundedUntilProbabilitiesImca(env, dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair); - } else { - return computeBoundedUntilProbabilitiesUnifPlus(env, dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair); + method = storm::solver::MaBoundedReachabilityMethod::Imca; } } + + if (method == storm::solver::MaBoundedReachabilityMethod::Imca) { + return computeBoundedUntilProbabilitiesImca(env, dir, transitionMatrix, exitRateVector, markovianStates, psiStates, boundsPair); + } else { + UnifPlusHelper helper(transitionMatrix, exitRateVector, markovianStates); + return helper.computeBoundedUntilProbabilities(env, dir, phiStates, psiStates, boundsPair.second); + } } template ::SupportsExponential, int>::type>