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

Yihan Du, Anna Winnicki, Gal Dalal, Shie Mannor, R. Srikant

TL;DR

The paper provides theoretical guarantees for policy-gradient RLHF by introducing PO-RLHF, which combines exploration-driven data collection with human-preference-based reward learning under both linear and neural function-approximation regimes. A key novelty is a trajectory-level elliptical potential analysis that bounds reward estimation error when comparisons, rather than numeric rewards, are observed. The authors formulate provably efficient algorithms (PG-RLHF and NN-PG-RLHF), derive sample-and-query-complexity bounds, and demonstrate near-optimal performance with relatively few human queries in experiments. The work offers mechanistic insights into why RLHF can be data-efficient in practice and guides how to design reward-learning and exploration phases in policy optimization under human feedback.

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.

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

TL;DR

The paper provides theoretical guarantees for policy-gradient RLHF by introducing PO-RLHF, which combines exploration-driven data collection with human-preference-based reward learning under both linear and neural function-approximation regimes. A key novelty is a trajectory-level elliptical potential analysis that bounds reward estimation error when comparisons, rather than numeric rewards, are observed. The authors formulate provably efficient algorithms (PG-RLHF and NN-PG-RLHF), derive sample-and-query-complexity bounds, and demonstrate near-optimal performance with relatively few human queries in experiments. The work offers mechanistic insights into why RLHF can be data-efficient in practice and guides how to design reward-learning and exploration phases in policy optimization under human feedback.

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.
Paper Structure (40 sections, 35 theorems, 229 equations, 2 figures, 1 table, 6 algorithms)

This paper contains 40 sections, 35 theorems, 229 equations, 2 figures, 1 table, 6 algorithms.

Table of Contents

  1. Introduction
  2. Related Work
  3. Formulation
  4. Linear Function Approximation
  5. Neural Function Approximation
  6. Baseline Policy
  7. PO-RLHF with Linear Function Approximation
  8. Algorithm $\mathtt{PG\hbox{-}RLHF}$
  9. Theoretical Guarantee of Algorithm $\mathtt{PG\hbox{-}RLHF}$
  10. Insight into the Practical Efficiency of RLHF
  11. PO-RLHF with Neural Function Approximation
  12. Algorithm $\mathtt{NN\hbox{-}PG\hbox{-}RLHF}$
  13. Experiments
  14. Conclusion
  15. Details of the Experimental Environment
  16. ...and 25 more sections

Key Result

Theorem 4.2

With probability at least $1-\delta$, the output policy of algorithm $\mathtt{PG\hbox{-}RLHF}$ satisfies Furthermore, by tuning parameters as in Eq. eq:set_parameter_linear in Appendix apx:main_thm_proof_linear, we can guarantee with $\tilde{O}( \textup{Poly}(W_Q, W_{\mu}, \zeta_{\textup{HF}}, d, (1-\gamma)^{-1} , \varepsilon^{-1} , c_{\textup{base}}^{-1}, c_{\textup{MLE}}^{-1} ) )$ samples. Her

Figures (2)

  • Figure 1: Experimental results of algorithms $\mathtt{PG\hbox{-}RLHF}$ and PC-PG.
  • Figure 2: The Bidirectional Lock environment.

Theorems & Definitions (63)

  • Theorem 4.2
  • Theorem 5.2
  • Lemma 4.1
  • proof
  • Lemma 4.2: Lemma C.1 in agarwal2020pc
  • Lemma 4.3: Lemma C.2 in agarwal2020pc
  • Lemma 4.4: Lemma C.3 in agarwal2020pc
  • Lemma 4.5: Performance Difference Lemma on $\mathcal{M}^n$
  • proof
  • Lemma 4.6: Regret for Natural Policy Gradient
  • ...and 53 more