Geometry and Determinism of Optimal Stationary Control in Partially Observable Markov Decision Processes
This work addresses the challenge of efficient policy optimization in POMDPs, which is incremental as it builds on known limitations of stochastic policies.
The paper tackles the problem of finding optimal memoryless policies in partially observable Markov decision processes (POMDPs), showing that such policies can have limited stochasticity, which reduces search space dimensionality and leads to better and faster convergence in policy gradient experiments.
It is well known that for any finite state Markov decision process (MDP) there is a memoryless deterministic policy that maximizes the expected reward. For partially observable Markov decision processes (POMDPs), optimal memoryless policies are generally stochastic. We study the expected reward optimization problem over the set of memoryless stochastic policies. We formulate this as a constrained linear optimization problem and develop a corresponding geometric framework. We show that any POMDP has an optimal memoryless policy of limited stochasticity, which allows us to reduce the dimensionality of the search space. Experiments demonstrate that this approach enables better and faster convergence of the policy gradient on the evaluated systems.