1. Witness Algorithm Presented by Alp Sardağ

2. 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)}.

3. 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 81 10 a kadar olan formüller

4. 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

5. 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.

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

7. Sayfa 85 teki LP kopyalanacak. Constructing Q a t

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

9. 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.