Exponential Family PCA for Belief Compression in POMDPs

Standard value function approaches to finding policies for Partially Observable Markov Decision Processes (POMDPs) are intractable for large models. The intractability of these algorithms is due to a great extent to their generating an optimal policy over the entire belief space. However, in real POMDP problems most belief states are unlikely, and there is a structured, low-dimensional manifold of plausible beliefs embedded in the high-dimensional belief space. We introduce a new method for solving large-scale POMDPs by taking advantage of belief space sparsity. We reduce the dimensionality of the belief space by exponential family Principal Components Analysis [1], which allows us to turn the sparse, high-dimensional belief space into a compact, low-dimensional representation in terms of learned features of the belief state. We then plan directly on the low-dimensional belief features. By planning in a low-dimensional space, we can find policies for POMDPs that are orders of magnitude larger than can be handled by conventional techniques. We demonstrate the use of this algorithm on a synthetic problem and also on a mobile robot navigation task.