  Standard value function approaches to finding policies for Partially
Observable Markov Decision Processes (POMDPs) are generally considered to be
intractable for large models. The intractability of these algorithms is to a
large extent a consequence of computing an exact, optimal policy over the
entire belief space. However, in real-world POMDP problems, computing the
optimal policy for the full belief space is often unnecessary for good control
even for problems with complicated policy classes. The beliefs experienced by
the controller often lie near a structured, low-dimensional subspace embedded
in the high-dimensional belief space. Finding a good approximation to the
optimal value function for only this subspace can be much easier than computing
the full value function. We introduce a new method for solving large-scale
POMDPs by reducing the dimensionality of the belief space. We use Exponential
family Principal Components Analysis (Collins, Dasgupta and Schapire, 2002) to
represent sparse, high-dimensional belief spaces using small sets of learned
features of the belief state. We then plan only in terms of the low-dimensional
belief features. By planning in this low-dimensional space, we can find
policies for POMDP models that are orders of magnitude larger than models that
can be handled by conventional techniques. We demonstrate the use of this
algorithm on a synthetic problem and on mobile robot navigation tasks.
