Corruption-Robust Offline Two-Player Zero-Sum Markov Games

We study data corruption robustness in offline two-player zero-sum Markov games. Given a dataset of realized trajectories of two players, an adversary is allowed to modify an $\epsilon$-fraction of it. The learner's goal is to identify an approximate Nash Equilibrium policy pair from the corrupted data. We consider this problem in linear Markov games under different degrees of data coverage and corruption. We start by providing an information-theoretic lower bound on the suboptimality gap of any learner. Next, we propose robust versions of the Pessimistic Minimax Value Iteration algorithm, both under coverage on the corrupted data and under coverage only on the clean data, and show that they achieve (near)-optimal suboptimality gap bounds with respect to $\epsilon$. We note that we are the first to provide such a characterization of the problem of learning approximate Nash Equilibrium policies in offline two-player zero-sum Markov games under data corruption.

Reward Model Learning vs. Direct Policy Optimization: A Comparative Analysis of Learning from Human Preferences

In this paper, we take a step towards a deeper understanding of learning from human preferences by systematically comparing the paradigm of reinforcement learning from human feedback (RLHF) with the recently proposed paradigm of direct preference optimization (DPO). We focus our attention on the class of loglinear policy parametrization and linear reward functions. In order to compare the two paradigms, we first derive minimax statistical bounds on the suboptimality gap induced by both RLHF and DPO, assuming access to an oracle that exactly solves the optimization problems. We provide a detailed discussion on the relative comparison between the two paradigms, simultaneously taking into account the sample size, policy and reward class dimensions, and the regularization temperature. Moreover, we extend our analysis to the approximate optimization setting and derive exponentially decaying convergence rates for both RLHF and DPO. Next, we analyze the setting where the ground-truth reward is not realizable and find that, while RLHF incurs a constant additional error, DPO retains its asymptotically decaying gap by just tuning the temperature accordingly. Finally, we extend our comparison to the Markov decision process setting, where we generalize our results with exact optimization. To the best of our knowledge, we are the first to provide such a comparative analysis for RLHF and DPO.

Corruption Robust Offline Reinforcement Learning with Human Feedback

We study data corruption robustness for reinforcement learning with human feedback (RLHF) in an offline setting. Given an offline dataset of pairs of trajectories along with feedback about human preferences, an $\varepsilon$-fraction of the pairs is corrupted (e.g., feedback flipped or trajectory features manipulated), capturing an adversarial attack or noisy human preferences. We aim to design algorithms that identify a near-optimal policy from the corrupted data, with provable guarantees. Existing theoretical works have separately studied the settings of corruption robust RL (learning from scalar rewards directly under corruption) and offline RLHF (learning from human feedback without corruption); however, they are inapplicable to our problem of dealing with corrupted data in offline RLHF setting. To this end, we design novel corruption robust offline RLHF methods under various assumptions on the coverage of the data-generating distributions. At a high level, our methodology robustifies an offline RLHF framework by first learning a reward model along with confidence sets and then learning a pessimistic optimal policy over the confidence set. Our key insight is that learning optimal policy can be done by leveraging an offline corruption-robust RL oracle in different ways (e.g., zero-order oracle or first-order oracle), depending on the data coverage assumptions. To our knowledge, ours is the first work that provides provable corruption robust offline RLHF methods.