Optimistic Initialization and Greediness Lead to Polynomial Time Learning in Factored MDPs - Extended Version

TL;DR

This paper introduces FOIM, an algorithm for polynomial-time reinforcement learning in factored MDPs, using optimistic initialization and greediness to ensure efficient convergence and decision-making.

Contribution

The paper presents FOIM, the first algorithm achieving polynomial-time learning in factored MDPs with optimistic initialization and greedy policy updates.

Findings

FOIM converges to the fixed point of approximate value iteration.

The number of non-near-optimal steps is polynomially bounded.

Per-step computational costs are polynomial.

Abstract

In this paper we propose an algorithm for polynomial-time reinforcement learning in factored Markov decision processes (FMDPs). The factored optimistic initial model (FOIM) algorithm, maintains an empirical model of the FMDP in a conventional way, and always follows a greedy policy with respect to its model. The only trick of the algorithm is that the model is initialized optimistically. We prove that with suitable initialization (i) FOIM converges to the fixed point of approximate value iteration (AVI); (ii) the number of steps when the agent makes non-near-optimal decisions (with respect to the solution of AVI) is polynomial in all relevant quantities; (iii) the per-step costs of the algorithm are also polynomial. To our best knowledge, FOIM is the first algorithm with these properties. This extended version contains the rigorous proofs of the main theorem. A version of this paper appeared in ICML'09.