Principled Reinforcement Learning with Human Feedback from Pairwise or $K$-wise Comparisons

Abstract

We provide a theoretical framework for Reinforcement Learning with Human Feedback (RLHF). Our analysis shows that when the true reward function is linear, the widely used maximum likelihood estimator (MLE) converges under both the Bradley-Terry-Luce (BTL) model and the Plackett-Luce (PL) model. However, we show that when training a policy based on the learned reward model, MLE fails while a pessimistic MLE provides policies with improved performance under certain coverage assumptions. Additionally, we demonstrate that under the PL model, the true MLE and an alternative MLE that splits the K-wise comparison into pairwise comparisons both converge. Moreover, the true MLE is asymptotically more efficient. Our results validate the empirical success of existing RLHF algorithms in InstructGPT and provide new insights for algorithm design. We also unify the problem of RLHF and max-entropy Inverse Reinforcement Learning (IRL), and provide the first sample complexity bound for max-entropy IRL.

A Comprehensive Survey of AI-Generated Content (AIGC): A History of Generative AI from GAN to ChatGPT

“…The AI feedback focuses on controlling the outputs to be less harmful by explaining its objections to dangerous queries. Moreover, recently a preliminary theoretical analysis of the RLAIF [51] justifies the empirical success of RLHF and provides new insights for specialized RLHF algorithm design for language models.…”