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Witness Algorithm Presented by Alp Sardağ

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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)}.

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Witness Algorithm Let Q a t the set of vectors representing PLWC value function, for performing action a at time t and performing optimally there after. Q a t = { 0 a (t),..., N a (t)} There will be a separate Q a t for each action a. –Sayfa a kadar olan formüller

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Witness Algorithm The algorithm first constructs the Q a t sets Then constructs the desired V* t set of vectors. In constructing Q a t set, the algorithm incrementally build up. Note that: –Sayfa 81 son formül

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Constructing Q a t Begin with an empty set Q a t, 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.

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How the algorithm finds the new belief point? Sayfa 83 ün sonu ve 84 ün 4 formülü kopyalanacak. Constructing Q a t

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Sayfa 85 teki LP kopyalanacak. Constructing Q a t

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The algorithm for constructing Q a t is as follows: Sayfa 85 pseudocode copy paste edilecek. Constructing Q a t

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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.

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