Principled Reinforcement Learning with Human Feedback from Pairwise or $K$-wise Comparisons
This work provides foundational theoretical insights for RLHF, impacting algorithm design in AI alignment and reinforcement learning, though it is incremental in building on existing empirical successes like InstructGPT.
The paper tackles the theoretical analysis of Reinforcement Learning with Human Feedback (RLHF), showing that maximum likelihood estimator (MLE) converges for linear reward functions under common models but fails in policy training, while a pessimistic MLE improves performance under coverage assumptions, and it unifies RLHF with max-entropy Inverse Reinforcement Learning, providing the first sample complexity bound for the latter.
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. Furthermore, our results unify the problem of RLHF and max-entropy Inverse Reinforcement Learning (IRL), and provide the first sample complexity bound for max-entropy IRL.