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Working version of under-approximation

tempestpy_adaptions
Alexander Bork 5 years ago
parent
2bc79e6e07
commit
d814942997
4 changed files with 232 additions and 67 deletions
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  1. 3
      src/storm-pomdp-cli/storm-pomdp.cpp
  2. 2
      src/storm-pomdp/CMakeLists.txt
  3. 247
      src/storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.cpp
  4. 39
      src/storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.h

3
src/storm-pomdp-cli/storm-pomdp.cpp
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@ -23,6 +23,7 @@
#include "storm/settings/modules/AbstractionSettings.h"
#include "storm/settings/modules/BuildSettings.h"
#include "storm/settings/modules/JitBuilderSettings.h"
#include "storm/settings/modules/TopologicalEquationSolverSettings.h"
#include "storm/settings/modules/MultiObjectiveSettings.h"
#include "storm-pomdp-cli/settings/modules/POMDPSettings.h"
@ -63,7 +64,7 @@ void initializeSettings() {
storm::settings::addModule<storm::settings::modules::ExplorationSettings>();
storm::settings::addModule<storm::settings::modules::ResourceSettings>();
storm::settings::addModule<storm::settings::modules::JitBuilderSettings>();
storm::settings::addModule<storm::settings::modules::TopologicalEquationSolverSettings>();
storm::settings::addModule<storm::settings::modules::POMDPSettings>();

2
src/storm-pomdp/CMakeLists.txt
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@ -17,7 +17,7 @@ set_target_properties(storm-pomdp PROPERTIES DEFINE_SYMBOL "")
list(APPEND STORM_TARGETS storm-pomdp)
set(STORM_TARGETS ${STORM_TARGETS} PARENT_SCOPE)
target_link_libraries(storm-pomdp PUBLIC storm ${STORM_POMDP_LINK_LIBRARIES})
target_link_libraries(storm-pomdp PUBLIC storm storm-parsers ${STORM_POMDP_LINK_LIBRARIES})
# Install storm headers to include directory.
foreach(HEADER ${STORM_POMDP_HEADERS})

247
src/storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.cpp
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@ -1,6 +1,17 @@
#include <storm/utility/ConstantsComparator.h>
#include "ApproximatePOMDPModelchecker.h"
#include <boost/algorithm/string.hpp>
#include "storm/utility/ConstantsComparator.h"
#include "storm/models/sparse/Dtmc.h"
#include "storm/modelchecker/prctl/SparseDtmcPrctlModelChecker.h"
#include "storm/utility/vector.h"
#include "storm/modelchecker/results/CheckResult.h"
#include "storm/modelchecker/results/ExplicitQualitativeCheckResult.h"
#include "storm/modelchecker/results/ExplicitQuantitativeCheckResult.h"
#include "storm/api/properties.h"
#include "storm-parsers/api/storm-parsers.h"
namespace storm {
namespace pomdp {
@ -14,35 +25,42 @@ namespace storm {
/*std::unique_ptr<POMDPCheckResult>*/ void
ApproximatePOMDPModelchecker<ValueType, RewardModelType>::computeReachabilityProbability(
storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp,
std::set<uint32_t> target_observations, bool min, uint64_t gridResolution) {
std::set<uint32_t> targetObservations, bool min, uint64_t gridResolution) {
//TODO add timing
uint64_t maxIterations = 100;
bool finished = false;
uint64_t iteration = 0;
std::vector<storm::pomdp::Belief<ValueType>> beliefList;
std::vector<bool> beliefIsTarget;
uint64_t nextId = 0;
// Initial belief always has ID 0
storm::pomdp::Belief<ValueType> initialBelief = getInitialBelief(pomdp, nextId);
++nextId;
beliefList.push_back(initialBelief);
beliefIsTarget.push_back(
targetObservations.find(initialBelief.observation) != targetObservations.end());
std::vector<storm::pomdp::Belief<ValueType>> beliefGrid;
std::vector<bool> beliefIsKnown;
constructBeliefGrid(pomdp, target_observations, gridResolution, beliefList, beliefGrid, beliefIsKnown,
constructBeliefGrid(pomdp, targetObservations, gridResolution, beliefList, beliefGrid, beliefIsTarget,
nextId);
nextId = beliefList.size();
// ID -> Value
std::map<uint64_t, ValueType> result;
std::map<uint64_t, ValueType> result_backup;
// ID -> ActionIndex
std::map<uint64_t, uint64_t> chosenActions;
std::vector<std::vector<std::map<uint32_t, ValueType>>> observationProbabilities;
std::vector<std::vector<std::map<uint32_t, uint64_t>>> nextBelieves;
// ID -> Observation -> Probability
std::map<uint64_t, std::vector<std::map<uint32_t, ValueType>>> observationProbabilities;
// current ID -> action -> next ID
std::map<uint64_t, std::vector<std::map<uint32_t, uint64_t>>> nextBelieves;
for (size_t i = 0; i < beliefGrid.size(); ++i) {
auto currentBelief = beliefGrid[i];
bool isTarget = beliefIsKnown[i];
bool isTarget = beliefIsTarget[currentBelief.id];
if (isTarget) {
result.emplace(std::make_pair(currentBelief.id, storm::utility::one<ValueType>()));
result_backup.emplace(std::make_pair(currentBelief.id, storm::utility::one<ValueType>()));
@ -64,6 +82,8 @@ namespace storm {
uint32_t observation = iter->first;
actionObservationBelieves[observation] = getBeliefAfterActionAndObservation(pomdp,
beliefList,
beliefIsTarget,
targetObservations,
currentBelief,
action,
observation,
@ -73,8 +93,9 @@ namespace storm {
observationProbabilitiesInAction.push_back(actionObservationProbabilities);
nextBelievesInAction.push_back(actionObservationBelieves);
}
observationProbabilities.push_back(observationProbabilitiesInAction);
nextBelieves.push_back(nextBelievesInAction);
observationProbabilities.emplace(
std::make_pair(currentBelief.id, observationProbabilitiesInAction));
nextBelieves.emplace(std::make_pair(currentBelief.id, nextBelievesInAction));
}
}
// Value Iteration
@ -83,9 +104,9 @@ namespace storm {
STORM_LOG_DEBUG("Iteration " << iteration + 1);
bool improvement = false;
for (size_t i = 0; i < beliefGrid.size(); ++i) {
bool isTarget = beliefIsKnown[i];
if (!isTarget) {
storm::pomdp::Belief<ValueType> currentBelief = beliefGrid[i];
bool isTarget = beliefIsTarget[currentBelief.id];
if (!isTarget) {
// we can take any state with the observation as they have the same number of choices
uint64_t numChoices = pomdp.getNumberOfChoices(
pomdp.getStatesWithObservation(currentBelief.observation).front());
@ -97,17 +118,17 @@ namespace storm {
for (uint64_t action = 0; action < numChoices; ++action) {
currentValue = storm::utility::zero<ValueType>(); // simply change this for rewards?
for (auto iter = observationProbabilities[i][action].begin();
iter != observationProbabilities[i][action].end(); ++iter) {
for (auto iter = observationProbabilities[currentBelief.id][action].begin();
iter != observationProbabilities[currentBelief.id][action].end(); ++iter) {
uint32_t observation = iter->first;
storm::pomdp::Belief<ValueType> nextBelief = beliefList[nextBelieves[i][action][observation]];
storm::pomdp::Belief<ValueType> nextBelief = beliefList[nextBelieves[currentBelief.id][action][observation]];
// compute subsimplex and lambdas according to the Lovejoy paper to approximate the next belief
std::pair<std::vector<std::vector<ValueType>>, std::vector<ValueType>> temp = computeSubSimplexAndLambdas(
nextBelief.probabilities, gridResolution);
std::vector<std::vector<ValueType>> subSimplex = temp.first;
std::vector<ValueType> lambdas = temp.second;
ValueType sum = storm::utility::zero<ValueType>();
auto sum = storm::utility::zero<ValueType>();
for (size_t j = 0; j < lambdas.size(); ++j) {
if (lambdas[j] != storm::utility::zero<ValueType>()) {
sum += lambdas[j] * result_backup.at(
@ -117,12 +138,19 @@ namespace storm {
currentValue += iter->second * sum;
}
// Update the selected actions
// Update the selected actions TODO make this nicer
if ((min && cc.isLess(storm::utility::zero<ValueType>(), chosenValue - currentValue)) ||
(!min &&
cc.isLess(storm::utility::zero<ValueType>(), currentValue - chosenValue))) {
chosenValue = currentValue;
chosenActionIndex = action;
} else if ((min && cc.isEqual(storm::utility::zero<ValueType>(),
chosenValue - currentValue)) ||
(!min &&
cc.isEqual(storm::utility::zero<ValueType>(),
currentValue - chosenValue))) {
chosenValue = currentValue;
chosenActionIndex = action;
}
// TODO tie breaker?
}
@ -148,8 +176,8 @@ namespace storm {
STORM_PRINT("Grid approximation took " << iteration << " iterations" << std::endl);
beliefGrid.push_back(initialBelief);
beliefIsKnown.push_back(
target_observations.find(initialBelief.observation) != target_observations.end());
beliefIsTarget.push_back(
targetObservations.find(initialBelief.observation) != targetObservations.end());
std::pair<std::vector<std::vector<ValueType>>, std::vector<ValueType>> temp = computeSubSimplexAndLambdas(
initialBelief.probabilities, gridResolution);
@ -167,92 +195,197 @@ namespace storm {
// Now onto the under-approximation
std::set<uint64_t> visitedBelieves;
std::deque<uint64_t> believesToBeExpanded;
std::map<uint64_t, uint64_t> beliefStateMap;
std::vector<std::map<uint64_t, ValueType>> transitions;
std::vector<uint64_t> targetStates;
uint64_t stateId = 0;
beliefStateMap[initialBelief.id] = stateId;
++stateId;
// Expand the believes TODO capsuling
visitedBelieves.insert(initialBelief.id);
believesToBeExpanded.push_back(initialBelief.id);
while (!believesToBeExpanded.empty()) {
auto currentBeliefId = believesToBeExpanded.front();
std::map<uint64_t, ValueType> transitionsInState;
STORM_LOG_DEBUG("Exploring Belief " << beliefList[currentBeliefId].observation << "||"
<< beliefList[currentBeliefId].probabilities);
if (beliefIsTarget[currentBeliefId]) {
// add a self-loop to target states and save them
transitionsInState[beliefStateMap[currentBeliefId]] = storm::utility::one<ValueType>();
targetStates.push_back(beliefStateMap[currentBeliefId]);
} else {
if (chosenActions.find(currentBeliefId) == chosenActions.end()) {
// If the current Belief is not part of the grid, we have not computed the action to choose yet
chosenActions[currentBeliefId] = extractBestAction(pomdp, beliefList, beliefIsTarget,
targetObservations,
observationProbabilities,
nextBelieves, result, gridResolution,
currentBeliefId, beliefList.size(), min);
}
for (auto iter = observationProbabilities[currentBeliefId][chosenActions[currentBeliefId]].begin();
iter !=
observationProbabilities[currentBeliefId][chosenActions[currentBeliefId]].end(); ++iter) {
uint32_t observation = iter->first;
uint64_t nextBeliefId = nextBelieves[currentBeliefId][chosenActions[currentBeliefId]][observation];
if (visitedBelieves.insert(nextBeliefId).second) {
beliefStateMap[nextBeliefId] = stateId;
++stateId;
believesToBeExpanded.push_back(nextBeliefId);
}
transitionsInState[beliefStateMap[nextBeliefId]] = iter->second;
}
}
transitions.push_back(transitionsInState);
believesToBeExpanded.pop_front();
}
for (size_t i = 0; i < transitions.size(); ++i) {
for (auto const &transition : transitions[i]) {
STORM_LOG_DEBUG(
"Transition: " << i << " -- " << transition.second << "--> " << transition.first);
}
}
storm::models::sparse::StateLabeling labeling(transitions.size());
labeling.addLabel("init");
labeling.addLabel("target");
labeling.addLabelToState("init", 0);
for (auto targetState : targetStates) {
labeling.addLabelToState("target", targetState);
}
storm::storage::sparse::ModelComponents<ValueType, RewardModelType> modelComponents(
buildTransitionMatrix(transitions), labeling);
storm::models::sparse::Dtmc<ValueType, RewardModelType> underApproxDtmc(modelComponents);
auto model = std::make_shared<storm::models::sparse::Dtmc<ValueType, RewardModelType>>(underApproxDtmc);
model->printModelInformationToStream(std::cout);
std::string propertyString = min ? "Pmin=? [F \"target\"]" : "Pmax=? [F \"target\"]";
std::vector<storm::jani::Property> propertyVector = storm::api::parseProperties(propertyString);
std::shared_ptr<storm::logic::Formula const> property = storm::api::extractFormulasFromProperties(
propertyVector).front();
std::unique_ptr<storm::modelchecker::CheckResult> res(
storm::api::verifyWithSparseEngine<ValueType>(model, storm::api::createTask<ValueType>(property,
true)));
STORM_LOG_ASSERT(res, "Result does not exist.");
res->filter(storm::modelchecker::ExplicitQualitativeCheckResult(model->getInitialStates()));
ValueType resultValue = res->asExplicitQuantitativeCheckResult<ValueType>().getValueMap().begin()->second;
STORM_PRINT("Over-Approximation Result: " << overApprox << std::endl);
STORM_PRINT("Under-Approximation Result: " << resultValue << std::endl);
}
template<typename ValueType, typename RewardModelType>
storm::storage::SparseMatrix<ValueType>
ApproximatePOMDPModelchecker<ValueType, RewardModelType>::buildTransitionMatrix(
std::vector<std::map<uint64_t, ValueType>> transitions) {
uint_fast64_t currentRow = 0;
uint64_t nrEntries = 0;
for (auto const &map : transitions) {
nrEntries += map.size();
}
storm::storage::SparseMatrixBuilder<ValueType> smb(transitions.size(), transitions.size(), nrEntries);
for (auto const &map : transitions) {
for (auto const &transition : map) {
smb.addNextValue(currentRow, transition.first, transition.second);
}
++currentRow;
}
return smb.build();
}
/* All this has to be put into a separate function as we have to repeat it for other believes not in the grid
// first compute some things for the initial belief
template<typename ValueType, typename RewardModelType>
uint64_t ApproximatePOMDPModelchecker<ValueType, RewardModelType>::extractBestAction(
storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp,
std::vector<storm::pomdp::Belief<ValueType>> &beliefList,
std::vector<bool> &beliefIsTarget,
std::set<uint32_t> &targetObservations,
std::map<uint64_t, std::vector<std::map<uint32_t, ValueType>>> &observationProbabilities,
std::map<uint64_t, std::vector<std::map<uint32_t, uint64_t>>> &nextBelieves,
std::map<uint64_t, ValueType> &result,
uint64_t gridResolution, uint64_t currentBeliefId, uint64_t nextId, bool min) {
auto cc = storm::utility::ConstantsComparator<ValueType>();
storm::pomdp::Belief<ValueType> currentBelief = beliefList[currentBeliefId];
std::vector<std::map<uint32_t, ValueType>> observationProbabilitiesInAction;
std::vector<std::map<uint32_t, uint64_t>> nextBelievesInAction;
uint64_t initialNumChoices = pomdp.getNumberOfChoices(
pomdp.getStatesWithObservation(initialBelief.observation).front());
for (uint64_t action = 0; action < initialNumChoices; ++action) {
uint64_t numChoices = pomdp.getNumberOfChoices(
pomdp.getStatesWithObservation(currentBelief.observation).front());
for (uint64_t action = 0; action < numChoices; ++action) {
std::map<uint32_t, ValueType> actionObservationProbabilities = computeObservationProbabilitiesAfterAction(
pomdp, initialBelief, action);
pomdp, currentBelief, action);
std::map<uint32_t, uint64_t> actionObservationBelieves;
for (auto iter = actionObservationProbabilities.begin();
iter != actionObservationProbabilities.end(); ++iter) {
uint32_t observation = iter->first;
actionObservationBelieves[observation] = getBeliefAfterActionAndObservation(pomdp,
beliefList,
initialBelief,
beliefIsTarget,
targetObservations,
currentBelief,
action,
observation,
nextId);
nextId = beliefList.size();
}
observationProbabilitiesInAction.push_back(actionObservationProbabilities);
nextBelievesInAction.push_back(actionObservationBelieves);
}
observationProbabilities.push_back(observationProbabilitiesInAction);
nextBelieves.push_back(nextBelievesInAction);
//STORM_LOG_DEBUG("ID " << currentBeliefId << " add " << observationProbabilitiesInAction);
observationProbabilities.emplace(std::make_pair(currentBeliefId, observationProbabilitiesInAction));
nextBelieves.emplace(std::make_pair(currentBeliefId, nextBelievesInAction));
// do one step here to get the best action in the initial state
// choose the action which results in the value computed by the over-approximation
ValueType chosenValue = min ? storm::utility::infinity<ValueType>()
: -storm::utility::infinity<ValueType>();
uint64_t chosenActionIndex = std::numeric_limits<uint64_t>::infinity();
ValueType currentValue;
for (uint64_t action = 0; action < initialNumChoices; ++action) {
for (uint64_t action = 0; action < numChoices; ++action) {
currentValue = storm::utility::zero<ValueType>(); // simply change this for rewards?
for (auto iter = observationProbabilities[initialBelief.id][action].begin();
iter != observationProbabilities[initialBelief.id][action].end(); ++iter) {
for (auto iter = observationProbabilities[currentBelief.id][action].begin();
iter != observationProbabilities[currentBelief.id][action].end(); ++iter) {
uint32_t observation = iter->first;
storm::pomdp::Belief<ValueType> nextBelief = beliefList[nextBelieves[initialBelief.id][action][observation]];
storm::pomdp::Belief<ValueType> nextBelief = beliefList[nextBelieves[currentBelief.id][action][observation]];
// compute subsimplex and lambdas according to the Lovejoy paper to approximate the next belief
temp = computeSubSimplexAndLambdas(
auto temp = computeSubSimplexAndLambdas(
nextBelief.probabilities, gridResolution);
std::vector<std::vector<ValueType>> subSimplex = temp.first;
std::vector<ValueType> lambdas = temp.second;
ValueType sum = storm::utility::zero<ValueType>();
auto sum = storm::utility::zero<ValueType>();
for (size_t j = 0; j < lambdas.size(); ++j) {
if (lambdas[j] != storm::utility::zero<ValueType>()) {
sum += lambdas[j] * result.at(
getBeliefIdInVector(beliefGrid, observation, subSimplex[j]));
getBeliefIdInVector(beliefList, observation, subSimplex[j]));
}
}
currentValue += iter->second * sum;
}
// Update the selected actions
// Update the selected actions TODO make this nicer
if ((min && cc.isLess(storm::utility::zero<ValueType>(), chosenValue - currentValue)) ||
(!min &&
cc.isLess(storm::utility::zero<ValueType>(), currentValue - chosenValue))) {
chosenValue = currentValue;
chosenActionIndex = action;
} else if ((min && cc.isEqual(storm::utility::zero<ValueType>(), chosenValue - currentValue)) ||
(!min &&
cc.isEqual(storm::utility::zero<ValueType>(), currentValue - chosenValue))) {
chosenValue = currentValue;
chosenActionIndex = action;
}
}
chosenActions[initialBelief.id] = chosenActionIndex;*/
std::set<uint64_t> exploredBelieves;
std::deque<uint64_t> believesToBeExplored;
exploredBelieves.insert(initialBelief.id);
believesToBeExplored.push_back(initialBelief.id);
while (!believesToBeExplored.empty()) {
auto currentBeliefId = believesToBeExplored.front();
if (chosenActions.find(currentBeliefId) != chosenActions.end()) {
} else {
}
believesToBeExplored.pop_front();
return chosenActionIndex;
}
STORM_PRINT("Over-Approximation Result: " << overApprox << std::endl);
}
template<typename ValueType, typename RewardModelType>
uint64_t ApproximatePOMDPModelchecker<ValueType, RewardModelType>::getBeliefIdInVector(
std::vector<storm::pomdp::Belief<ValueType>> &grid, uint32_t observation,
@ -260,12 +393,10 @@ namespace storm {
for (auto const &belief : grid) {
if (belief.observation == observation) {
if (belief.probabilities == probabilities) {
STORM_LOG_DEBUG("Found belief with id " << std::to_string(belief.id));
return belief.id;
}
}
}
STORM_LOG_DEBUG("Did not find the belief in the grid");
return -1;
}
@ -482,7 +613,8 @@ namespace storm {
template<typename ValueType, typename RewardModelType>
uint64_t ApproximatePOMDPModelchecker<ValueType, RewardModelType>::getBeliefAfterActionAndObservation(
storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp,
std::vector<storm::pomdp::Belief<ValueType>> &beliefList, storm::pomdp::Belief<ValueType> belief,
std::vector<storm::pomdp::Belief<ValueType>> &beliefList, std::vector<bool> &beliefIsTarget,
std::set<uint32_t> &targetObservations, storm::pomdp::Belief<ValueType> belief,
uint64_t actionIndex, uint32_t observation, uint64_t id) {
std::vector<ValueType> distributionAfter(pomdp.getNumberOfStates(), storm::utility::zero<ValueType>());
for (uint64_t state = 0; state < pomdp.getNumberOfStates(); ++state) {
@ -508,6 +640,7 @@ namespace storm {
return getBeliefIdInVector(beliefList, observation, distributionAfter);
} else {
beliefList.push_back(storm::pomdp::Belief<ValueType>{id, observation, distributionAfter});
beliefIsTarget.push_back(targetObservations.find(observation) != targetObservations.end());
return id;
}
}

39
src/storm-pomdp/modelchecker/ApproximatePOMDPModelchecker.h
View File

@ -1,22 +1,24 @@
#include <cstdlib>
#include "storm/modelchecker/CheckTask.h"
#include "storm/api/storm.h"
#include "storm/models/sparse/Pomdp.h"
#include "storm/utility/logging.h"
#include "storm-pomdp/storage/Belief.h"
#include "storm/storage/jani/Property.h"
namespace storm {
namespace pomdp {
namespace modelchecker {
class POMDPCheckResult;
template<class ValueType, typename RewardModelType = models::sparse::StandardRewardModel <ValueType>>
template<class ValueType, typename RewardModelType = models::sparse::StandardRewardModel<ValueType>>
class ApproximatePOMDPModelchecker {
public:
explicit ApproximatePOMDPModelchecker();
/*std::unique_ptr<POMDPCheckResult>*/ void
computeReachabilityProbability(storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp,
std::set<uint32_t> target_observations, bool min,
std::set<uint32_t> targetObservations, bool min,
uint64_t gridResolution);
std::unique_ptr<POMDPCheckResult>
@ -24,6 +26,29 @@ namespace storm {
std::set<uint32_t> target_observations, uint64_t gridResolution);
private:
/**
* TODO
* @param pomdp
* @param beliefList
* @param observationProbabilities
* @param nextBelieves
* @param result
* @param gridResolution
* @param currentBeliefId
* @param nextId
* @param min
* @return
*/
uint64_t extractBestAction(storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp,
std::vector<storm::pomdp::Belief<ValueType>> &beliefList,
std::vector<bool> &beliefIsTarget,
std::set<uint32_t> &target_observations,
std::map<uint64_t, std::vector<std::map<uint32_t, ValueType>>> &observationProbabilities,
std::map<uint64_t, std::vector<std::map<uint32_t, uint64_t>>> &nextBelieves,
std::map<uint64_t, ValueType> &result,
uint64_t gridResolution, uint64_t currentBeliefId, uint64_t nextId,
bool min);
/**
*
* @param pomdp
@ -82,8 +107,11 @@ namespace storm {
* @return the resulting belief (observation and distribution)
*/
uint64_t
getBeliefAfterActionAndObservation(const models::sparse::Pomdp <ValueType, RewardModelType> &pomdp,
getBeliefAfterActionAndObservation(
storm::models::sparse::Pomdp<ValueType, RewardModelType> const &pomdp,
std::vector<storm::pomdp::Belief<ValueType>> &beliefList,
std::vector<bool> &beliefIsTarget,
std::set<uint32_t> &targetObservations,
storm::pomdp::Belief<ValueType> belief,
uint64_t actionIndex, uint32_t observation, uint64_t id);
@ -108,6 +136,9 @@ namespace storm {
*/
uint64_t getBeliefIdInVector(std::vector<storm::pomdp::Belief<ValueType>> &grid, uint32_t observation,
std::vector<ValueType> probabilities);
storm::storage::SparseMatrix<ValueType>
buildTransitionMatrix(std::vector<std::map<uint64_t, ValueType>> transitions);
};
}

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