Two heuristics for solving POMDPs having a delayed need to observe
A common heuristic for solving Partial ly Observable Markov Decision Problems POMDPs is to rst solve the underlying Markov Decision Process MDP and then con struct a POMDP policy by performing a xed depth lookahead search in the POMDP and evaluating the leaf nodes using the MDP value function A problem with this approximation is that it does not account for the need to choose actions in order to gain information about the state of the world particularly when those ob servation actions are needed at some point in the future This paper proposes two heuristics that are better than the MDP approximation in POMDPs where there is a delayed need to observe The rst approximation introduced in is the even odd POMDP in which the world is assumed to be fully observable every other time step The even odd POMDP can be converted into an equivalent MDP the even MDP whose value function captures some of the sensing costs of the original POMDP An online policy consisting in a step lookahead search com bined with the value function of the even MDP gives an approximation to the POMDP s value function that is at least as good as the method based on the value function of the underlying MDP The second POMDP approximation is applicable to a special kind of POMDP which we call the Cost Observable Markov Decision Problem COMDP In a COMDP the actions are partitioned into those that change the state of the world and those that are pure observa tion actions For such problems we describe the chain MDP algorithm which in many cases is able to capture more of the sensing costs than the even odd POMDP approximation We prove that both heuristics compute value functions that are upper bounded by i e bet ter than the value function of the underlying MDP and in the case of the even MDP also lower bounded by the POMDP s optimal value function We show cases where the chain MDP online policy is better equal or worse than the even MDP online policy