Representation Policy Iteration

Understand

This paper addresses a fundamental issue central to approximation methods for solving large Markov decision processes (MDPs): how to automatically learn the underlying representation for value function approximation? A novel theoretically rigorous framework is proposed that automatically generates geometrically customized orthonormal sets of basis functions, which can be used with any approximate MDP solver like least squares policy iteration (LSPI).

• The key innovation is a coordinate-free representation of value functions, using the theory of smooth functions on a Riemannian manifold.
• Hodge theory yields a constructive method for generating basis functions for approximating value functions based on the eigenfunctions of the self-adjoint (Laplace-Beltrami) operator on manifolds.
• In effect, this approach performs a global Fourier analysis on the state space graph to approximate value functions, where the basis functions reflect the largescale topology of the underlying state space.