Occupancy Information Ratio: Infinite-Horizon, Information-Directed, Parameterized Policy Search

TL;DR

This paper introduces the occupancy information ratio (OIR), a novel objective for infinite-horizon reinforcement learning that balances policy cost and state occupancy entropy, enabling scalable model-free policy search with proven convergence properties.

Contribution

The work formulates the OIR as a new RL objective, develops a theoretical foundation with a policy gradient theorem, and proposes algorithms with convergence guarantees, demonstrating practical benefits in sparse-reward environments.

Findings

OIR-based methods outperform vanilla RL in sparse rewards.

Finite-time convergence to global optimality for REINFORCE-style algorithms.

Asymptotic convergence of actor-critic methods to near-global optima.

Abstract

In this work, we propose an information-directed objective for infinite-horizon reinforcement learning (RL), called the occupancy information ratio (OIR), inspired by the information ratio objectives used in previous information-directed sampling schemes for multi-armed bandits and Markov decision processes as well as recent advances in general utility RL. The OIR, comprised of a ratio between the average cost of a policy and the entropy of its induced state occupancy measure, enjoys rich underlying structure and presents an objective to which scalable, model-free policy search methods naturally apply. Specifically, we show by leveraging connections between quasiconcave optimization and the linear programming theory for Markov decision processes that the OIR problem can be transformed and solved via concave programming methods when the underlying model is known. Since model knowledge is typically lacking in practice, we lay the foundations for model-free OIR policy search methods by establishing a corresponding policy gradient theorem. Building on this result, we subsequently derive REINFORCE- and actor-critic-style algorithms for solving the OIR problem in policy parameter space. Crucially, exploiting the powerful hidden quasiconcavity property implied by the concave programming transformation of the OIR problem, we establish finite-time convergence of the REINFORCE-style scheme to global optimality and asymptotic convergence of the actor-critic-style scheme to (near) global optimality under suitable conditions. Finally, we experimentally illustrate the utility of OIR-based methods over vanilla methods in sparse-reward settings, supporting the OIR as an alternative to existing RL objectives.