Exploration-Driven Policy Optimization in RLHF: Theoretical Insights on Efficient Data Utilization

TL;DR

This paper offers a theoretical analysis of a policy optimization-based RLHF algorithm, explaining why limited human feedback can suffice for effective learning, through novel elliptical potential analysis and performance bounds.

Contribution

It introduces a new theoretical framework for policy-based RLHF, providing performance bounds and analysis for algorithms with low feedback query complexity.

Findings

Performance bounds for PO-RLHF with low query complexity

Novel elliptical potential analysis for reward estimation error

Algorithms analyzed for linear and neural function approximation

Abstract

Reinforcement Learning from Human Feedback (RLHF) has achieved impressive empirical successes while relying on a small amount of human feedback. However, there is limited theoretical justification for this phenomenon. Additionally, most recent studies focus on value-based algorithms despite the recent empirical successes of policy-based algorithms. In this work, we consider an RLHF algorithm based on policy optimization (PO-RLHF). The algorithm is based on the popular Policy Cover-Policy Gradient (PC-PG) algorithm, which assumes knowledge of the reward function. In PO-RLHF, knowledge of the reward function is not assumed, and the algorithm uses trajectory-based comparison feedback to infer the reward function. We provide performance bounds for PO-RLHF with low query complexity, which provides insight into why a small amount of human feedback may be sufficient to achieve good performance with RLHF. A key novelty is a trajectory-level elliptical potential analysis, which bounds the reward estimation error when comparison feedback (rather than numerical reward observation) is given. We provide and analyze algorithms PG-RLHF and NN-PG-RLHF for two settings: linear and neural function approximation, respectively.