double JointBeliefSparse::Update(const MultiAgentDecisionProcessDiscreteInterface &pu,
Index lastJAI, Index newJOI)
{
//const TransitionModelDiscrete* T=pu.GetTransitionModelDiscretePtr();
const ObservationModelDiscrete* O=pu.GetObservationModelDiscretePtr();
//pointer to the transition probability Get funtion:
TGet* T = pu.GetTGet();
if(T==0)
{
return(UpdateSlow(pu,lastJAI,newJOI));
}
double Po_ba = 0.0; // P(o|b,a) with o=newJO
double Ps_ba, Po_as, Pso_ba;
size_t nrS = _m_b.size();
BS newJB_unnorm(nrS);
for(Index sI=0; sI < nrS; sI++)
{
//P(sI | b, a) = sum_(prec_s) P(sI | prec_s, a)*JB(prec_s)
Ps_ba = 0.0;
for(BScit it=_m_b.begin(); it!=_m_b.end(); ++it)
Ps_ba += T->Get(it.index(), lastJAI, sI) * *it;
if(Ps_ba>0) // if it is zero, Pso_ba will be zero anyway
{
//P(newJOI | lastJAI, sI) :
Po_as = O->Get(lastJAI, sI, newJOI);
//the new (unormalized) belief P(s,o|b,a)
Pso_ba = Po_as * Ps_ba;
if(Pso_ba>PROB_PRECISION) // we don't want to store very
// small probabilities in a
// sparse representation
{
newJB_unnorm[sI]=Pso_ba; //unnormalized new belief
Po_ba += Pso_ba; //running sum of P(o|b,a)
}
}
}
//normalize:
if(Po_ba>0)
for(BSit it=newJB_unnorm.begin(); it!=newJB_unnorm.end(); ++it)
*it/=Po_ba;
_m_b=newJB_unnorm;
#if JointBeliefSparse_doSanityCheckAfterEveryUpdate
if(!SanityCheck())
throw(E("JointBeliefSparse::Update SanityCheck failed"));
#endif
return(Po_ba);
}
double JointBeliefEventDriven::Update(const MultiAgentDecisionProcessDiscreteInterface &pu,
Index lastJAI, Index newJOI)
{
using namespace boost::numeric::ublas;
if(!pu.GetEventObservability())
throw E("Trying to use a JointBeliefEventDriven on a model without event observability.");
size_t nrS = pu.GetNrStates();
const TransitionModelMapping *T = dynamic_cast<const TransitionModelMapping *>(pu.GetTransitionModelDiscretePtr());
const EventObservationModelMapping *O = dynamic_cast<const EventObservationModelMapping *>(pu.GetObservationModelDiscretePtr());
double eta = 0;
if(T != 0 && O != 0)
{
using namespace boost::numeric::ublas;
//we need to break the abstraction here since we'll be using ublas over T and O.
//Ideally, we could have some kind of built in conversion.
const matrix<double>* Ta = T->GetMatrixPtr(lastJAI);
const matrix<double>* Oao = O->GetMatrixPtr(lastJAI,newJOI);
matrix<double>* Hao = new matrix<double>(element_prod(*Ta,*Oao));
matrix<double> H = *Hao;
double epsilon, last_epsilon = 0;
//We need b in ublas form.
boost::numeric::ublas::vector<double> b(nrS);
std::copy(_m_b.begin(), _m_b.end(), b.begin());
boost::numeric::ublas::vector<double> res = zero_vector<double>(nrS);
boost::numeric::ublas::vector<double> bUpdated = prod(b,H);
epsilon = JointBeliefEventDriven_convergenceTh;
if(_m_falseNegativeObs >= 0)
{
const matrix<double>* Oaf = O->GetMatrixPtr(lastJAI,_m_falseNegativeObs);
//At this point we have two |S|x|S| matrices
//What we want to do is;
//Hao = Ta.*Oao;
//Haf = Ta.*Oaf;
//b' = (b^T * (inv(I - Haf) * Hao))/n
//Since we can't compute the inverse of arbitrarily large matrices, we have to approximate this
//by cutting off the respective power series (I + Haf + Haf^2 + Haf^3 + ...) at some point.
//Since Ta, Oao, Oaf are defined over (s,s') and we want to avoid having to transpose,
//we have to left-multiply this by b^T to get the update
//We also cannot rely on determinant / trace, so we have to keep track of b' and see if it is converging.
matrix<double>* Haf = new matrix<double>(element_prod(*Ta,*Oaf));
for(int safety_s=0, safety_h=0;
epsilon >= JointBeliefEventDriven_convergenceTh && safety_h < JointBeliefEventDriven_hardCap;
safety_h++)
{
noalias(H) = prod(*Haf, H); //remember that we are implicitly using transposes.
res = prod(b,H);
bUpdated = bUpdated + res;
last_epsilon = epsilon;
if(sum(bUpdated) > 0)
epsilon = sum(res);
if(last_epsilon != 0 && epsilon >= last_epsilon){
safety_s++;
}else{
safety_s=0;
}
if(safety_s >= JointBeliefEventDriven_softCap){
cout << "Warning: Event-driven belief update not converging! - The system has non-observable chains." << endl;
break;
}
}
delete Haf;
}
//only the normalization factor remains
eta = sum(bUpdated);
if(eta > 0)
{
bUpdated = bUpdated / eta;
_m_b.clear();
_m_b.insert(_m_b.end(), bUpdated.begin(), bUpdated.end());
}
else
{
cout << "Event-driven belief update failed: The system is badly conditioned. There is 0 probability of observing this symbol given this belief." << endl;
}
delete Hao;
}
#if JointBeliefEventDriven_doSanityCheckAfterEveryUpdate
if(!SanityCheck())
throw(E("JointBeliefEventDriven::Update SanityCheck failed"));
#endif
return(eta);
}
