Principled Reinforcement Learning with Human Feedback from Pairwise or $K$-wise Comparisons (2301.11270v5)

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. 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.

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

The paper provides a comprehensive theoretical framework for Reinforcement Learning with Human Feedback (RLHF), a method used to align machine learning systems with human interests by leveraging human feedback to inform policy training in reinforcement learning scenarios. The authors focus on scenarios where feedback is obtained through either pairwise or $K$-wise comparisons of actions, utilizing models such as Bradley-Terry-Luce (BTL) and Plackett-Luce (PL).

Key Contributions

1. Convergence of Maximum Likelihood Estimator (MLE): The paper establishes that when the true reward function follows a linear parameterization, MLE converges under both the BTL and PL models. Such convergence supports the widespread empirical success observed in RLHF applications, including in powerful LLMs like InstructGPT and ChatGPT.
2. Limitations of MLE for Policy Training: While MLE proves effective for estimating the reward model, the authors identify its shortcomings when training a policy based solely on MLE. They propose a pessimistic variant of MLE that accounts for coverage deficiencies, providing superior policy performance by incorporating conservative assumptions about underrepresented action data in the training set.
3. Theoretical Insights into RLHF Algorithms: The research draws parallels between RLHF and max-entropy Inverse Reinforcement Learning (IRL), offering the first known sample complexity bounds for max-entropy IRL. The paper contributes theoretical foundations that explain empirical observations and guide further algorithm development.
4. Comparison and Efficiency of Estimators: Upon comparing the true MLE and its variant that splits $K$-wise comparisons into pairwise comparisons, they note that both methods converge but true MLE holds an asymptotic efficiency advantage. This suggests a more favorable variance profile, assuring more reliable performance with increased sample sizes.

Numerical Results and Theoretical Implications

Prominent results include the demonstration that pessimistic MLE retains near-optimal sub-optimality bounds even in scenarios where traditional MLE fails. Such findings underline the necessity for enhanced coverage assumptions or conservative adaptations in reward learning settings within RLHF.

The research emphasizes the favorable estimation properties of the MLE, alongside M-estimators used in modern RLHF frameworks like InstructGPT, confirming empirical observations in AI applications. By quantifying bounds on semi-normed parameter estimation errors, the paper provides a robust analytical tool for evaluating RLHF approaches under human feedback constraints.

Implications for Future Research

The work offers critical insights into RL with structured human interaction, proposing methods that bridge conventional RL approaches and newer paradigms necessitating human-in-the-loop coordination. Future research could expand upon this framework by dynamically integrating the evolving parameterizations in non-linear reward functions or studying the implications of different behavioral models (beyond BTL and PL).

Additionally, exploring the interface between pre-trained models and RLHF in a continuously learning environment can address the gap between empirical success and theoretical underpinning. This paper lays the groundwork for such investigations by showcasing how RLHF can be effectively modeled and utilized to guide decision-making processes in collaborative human-machine learning environments.

In conclusion, this paper fortifies the RLHF theoretical landscape, providing essential groundwork for understanding and improving the integration of human feedback in reinforcement learning paradigms. Such understanding is critical as AI systems increasingly find themselves embedded in environments demanding sophisticated alignment with human values.