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Contextual Online Uncertainty-Aware Preference Learning for Human Feedback

Nan Lu, Ethan X. Fang, Junwei Lu

TL;DR

This work tackles online RLHF under a contextual Bradley-Terry-Luce model where comparisons yield pairwise preferences rather than explicit rewards. It introduces a two-stage Ranking Bandit algorithm that uses an $oldsymbol{ ext{$oldsymbol{ ext{ε}}$-greedy}}$ exploration phase followed by a pure exploitation phase, and develops estimation and inference for item attributes from dependent online data via matrix martingale methods. Theoretical results establish near-optimal regret $R(T)=O(( ext{log}T/T)^{1/2})$, convergence rates for the estimators, and asymptotic normality of debiased estimators to enable uncertainty quantification. Empirical studies show superior performance of RB over baselines in simulations and demonstrate its applicability to ranking large language models using MMLU anatomy data, providing a practical tool for uncertainty-aware model selection and alignment in RLHF.

Abstract

Reinforcement Learning from Human Feedback (RLHF) has become a pivotal paradigm in artificial intelligence to align large models with human preferences. In this paper, we propose a novel statistical framework to simultaneously conduct the online decision-making and statistical inference on the optimal model using human preference data based on dynamic contextual information. Our approach introduces an efficient decision strategy that achieves both the optimal regret bound and the asymptotic distribution of the estimators. A key challenge in RLHF is handling the dependent online human preference outcomes with dynamic contexts. To address this, in the methodological aspect, we propose a two-stage algorithm starting with $ε$-greedy followed by exploitations; in the theoretical aspect, we tailor anti-concentration inequalities and matrix martingale concentration techniques to derive the uniform estimation rate and asymptotic normality of the estimators using dependent samples from both stages. Extensive simulation results demonstrate that our method outperforms state-of-the-art strategies. We apply the proposed framework to analyze the human preference data for ranking large language models on the Massive Multitask Language Understanding dataset, yielding insightful results on the performance of different large language models for medical anatomy knowledge.

Contextual Online Uncertainty-Aware Preference Learning for Human Feedback

TL;DR

This work tackles online RLHF under a contextual Bradley-Terry-Luce model where comparisons yield pairwise preferences rather than explicit rewards. It introduces a two-stage Ranking Bandit algorithm that uses an oldsymbol{ ext{ε}} exploration phase followed by a pure exploitation phase, and develops estimation and inference for item attributes from dependent online data via matrix martingale methods. Theoretical results establish near-optimal regret , convergence rates for the estimators, and asymptotic normality of debiased estimators to enable uncertainty quantification. Empirical studies show superior performance of RB over baselines in simulations and demonstrate its applicability to ranking large language models using MMLU anatomy data, providing a practical tool for uncertainty-aware model selection and alignment in RLHF.

Abstract

Reinforcement Learning from Human Feedback (RLHF) has become a pivotal paradigm in artificial intelligence to align large models with human preferences. In this paper, we propose a novel statistical framework to simultaneously conduct the online decision-making and statistical inference on the optimal model using human preference data based on dynamic contextual information. Our approach introduces an efficient decision strategy that achieves both the optimal regret bound and the asymptotic distribution of the estimators. A key challenge in RLHF is handling the dependent online human preference outcomes with dynamic contexts. To address this, in the methodological aspect, we propose a two-stage algorithm starting with -greedy followed by exploitations; in the theoretical aspect, we tailor anti-concentration inequalities and matrix martingale concentration techniques to derive the uniform estimation rate and asymptotic normality of the estimators using dependent samples from both stages. Extensive simulation results demonstrate that our method outperforms state-of-the-art strategies. We apply the proposed framework to analyze the human preference data for ranking large language models on the Massive Multitask Language Understanding dataset, yielding insightful results on the performance of different large language models for medical anatomy knowledge.
Paper Structure (37 sections, 25 theorems, 179 equations, 5 figures, 1 algorithm)

This paper contains 37 sections, 25 theorems, 179 equations, 5 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Major Contributions
  3. Related Research
  4. Contextual Bradley-Terry-Luce Model
  5. Two-Stage Ranking Bandit Method
  6. Theoretical Results
  7. Statistical Rates
  8. Regret Analysis
  9. Asymptotic Normality
  10. Numerical Studies
  11. Applications to Language Model Ranking
  12. Conclusion
  13. Proof of Theorem \ref{['thm:2rate']}
  14. Proof of Theorem \ref{['thm:BT']}
  15. Analysis of the Hessian Matrix
  16. ...and 22 more sections

Key Result

Theorem 4.5

Suppose that Assumption ass:Sigx holds. For the estimator $\widehat{\bm{\theta}}(t)$ defined in (opt1), if $\gamma$ is large enough such that $\bm{\theta}^*\in\widetilde{\Theta}$, there exists a constant $c > 0$ such that for any $t\in[(cn^2p\log T)^{1/(1-\alpha)},T_0]$ and $np>c\log n$, we have holds with probability $1-O(\max\{T^{-3},n^{-10}\})$.

Figures (5)

  • Figure 1: (a) and (b) show the regret and estimation error for Setting A, while (c) and (d) show the regret and estimation error for Setting B.
  • Figure 2: Coverage probability estimation under Setting A.
  • Figure 3: Coverage probability estimation under Setting B.
  • Figure 4: (a) and (b) show the regret and estimation error for the LLM ranking.
  • Figure 5: Changes in the ranking of LLMs over time.

Theorems & Definitions (28)

  • Theorem 4.5: $\epsilon$-Greedy stage rate
  • Remark 4.6
  • Theorem 4.7: Exploitation stage rate
  • Remark 4.8
  • Theorem 4.9
  • Remark 4.10
  • Theorem 4.11
  • Lemma A.1
  • Lemma A.2
  • Lemma A.3
  • ...and 18 more