Representation Policy Iteration
This addresses a fundamental issue in reinforcement learning for researchers and practitioners dealing with large-scale MDPs, offering a theoretically rigorous method for representation learning, though it appears incremental in its application to existing solvers.
The paper tackles the problem of automatically learning representations for value function approximation in large Markov decision processes by proposing a novel framework that generates customized orthonormal basis functions using Riemannian manifold theory and Hodge theory. The result is a new algorithm, Representation Policy Iteration (RPI), which outperforms least squares policy iteration with handcoded basis functions in illustrative experiments.
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. A new class of algorithms called Representation Policy Iteration (RPI) are presented that automatically learn both basis functions and approximately optimal policies. Illustrative experiments compare the performance of RPI with that of LSPI using two handcoded basis functions (RBF and polynomial state encodings).