Witness Algorithm

Presented by Alp Sardağ

Witness Algorithm

• Like other algorithms, start with a set of vectors, V*t-1={0(t-1),..., M(t-1)}.– Sayfa 81 deki ilk formül

• The output of the algorithm will be a set of vectors, V*t-1={0(t-1),..., N(t-1)}.

Witness Algorithm

• Let Qat the set of vectors

representing PLWC value function, for performing action a at time t and performing optimally there after.

• Qat = {0

a(t),..., Na(t)}

• There will be a separate Qat for each

action a.– Sayfa 81 10 a kadar olan formüller

Witness Algorithm

• The algorithm first constructs the Qa

t sets

• Then constructs the desired V*t set of vectors.

• In constructing Qat set, the

algorithm incrementally build up.• Note that:

– Sayfa 81 son formül

Constructing Qat

• Begin with an empty set Qat, choose

any belief point and construct the vector using:– Formula 10 buraya kopyalanacak.

• Determine if there exist a belief state * (like Sondik’s):– Sayfa 82 formüllerin ilk iki satırı

kopyala.

• Once the new vector found, it is added to the list of vectors.

• How the algorithm finds the new belief point?

• Sayfa 83 ün sonu ve 84 ün 4 formülü kopyalanacak.

Constructing Qat

• Sayfa 85 teki LP kopyalanacak.

Constructing Qat

• The algorithm for constructing Qat

is as follows:

• Sayfa 85 pseudocode copy paste edilecek.

Constructing Qat

Witness Algorithm Reduction Phase

• Once all Qat sets found for each action a, then combine them to form the set V*t that is the optimal value function.

• The algorithm uses reduction phase of Monahan’s algorithm.

– Monahan’s reduction LP si kopyalanacak.