When the reward function is defined as R(a,s), the value function is defined as max_{a in A} (rho(a,b) + ...), where A is the set of actions, b is the current belief state and rho(a,b) is the expected reward w.r.t. b. But what does the definition of the value function look like when the reward function looks like R(s,a,s') , where a is performed in state s and the agent ends up in state s'?
Gavin Rens
Thanks, Xy Huang! In other words, one can determine R(a,s) = sum_{s' \in S} R(s,a,s')*T(s,a,s'), where T is the transition function. Then one can use rho(a,s), the expected value of R(a,s).
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