A Function Approximation Approach to Estimation of Policy Gradient for POMDP with Structured Policies

We consider the estimation of the policy gradient in partially observable Markov decision processes (POMDP) with a special class of structured policies that are finite-state controllers. We show that the gradient estimation can be done in the Actor-Critic framework, by making the critic compute a "value" function that does not depend on the states of POMDP. This function is the conditional mean of the true value function that depends on the states. We show that the critic can be implemented using temporal difference (TD) methods with linear function approximations, and the analytical results on TD and Actor-Critic can be transfered to this case. Although Actor-Critic algorithms have been used extensively in Markov decision processes (MDP), up to now they have not been proposed for POMDP as an alternative to the earlier proposal GPOMDP algorithm, an actor-only method. Furthermore, we show that the same idea applies to semi-Markov problems with a subset of finite-state controllers.