无需已知偏好函数,通过符号估计实现稳定强化学习。
Sign-SZPO: Provable Preference-based Reinforcement Learning with an Unknown Link Function
- 仅用价值差的符号构造更新方向,不依赖具体偏好函数形式。
- 理论证明在多项式迭代次数内收敛至稳定策略。
- 对偏好函数误设具有鲁棒性,适合真实人类偏好场景。
偏好反馈驱动的强化学习中,链接函数刻画了双轨迹偏好与回报之间的关系,是关键组件。现有方法普遍假设该函数已知(如基于Bradley-Terry模型的逻辑函数),但这一假设在复杂人类偏好下过于受限。本文研究链接函数未知情形下的偏好强化学习,提出新型零阶策略优化算法Sign-SZPO。不同于传统零阶方法需利用已知链接函数估计价值差并构造梯度,Sign-SZPO仅估计价值差的符号,并据此构建与真实策略梯度正相关的参数更新方向,无需精确知道链接函数。在温和条件下,Sign-SZPO可保证以多项式速率收敛至平稳策略。实验表明,该方法在链接函数误设情况下仍具优异鲁棒性。
原文摘要 · Abstract (English)
The link function, which characterizes the relationship between the preference for two trajectories and their returns, is a crucial component in designing RL algorithms that learn from preference feedback. Most existing methods, both theoretical and empirical, assume that the link function is known (often a logistic function based on the Bradley-Terry model), which is arguably restrictive given the complex nature of preferences, especially those of humans. To avoid mis-specification, this paper studies preference-based RL with an unknown link function and proposes a novel zeroth-order policy optimization algorithm called Sign-SZPO. Unlike typical zeroth-order methods, which rely on the known link function to estimate the value function differences and form a gradient estimator, Sign-SZPO only estimates the sign of the value function difference. It then constructs a parameter update direction that is positively correlated with the true policy gradient, eliminating the need to know the link function exactly. Under mild conditions, Sign-SZPO provably converges to a stationary policy with a polynomial rate in the number of policy iterations and trajectories per iteration. Empirical evaluations further demonstrate the robustness of Sign-SZPO under link function mis-specifications.
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