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.

Online reinforcement learning (RL) typically requires online interaction data to learn a policy for a target task, but collecting such data can be high-stakes. This prompts interest in leveraging historical data to improve sample efficiency. The historical data may come from outdated or related source environments with different dynamics. It remains unclear how to effectively use such data in the target task to provably enhance learning and sample efficiency. To address this, we propose a hybrid transfer RL (HTRL) setting, where an agent learns in a target environment while accessing offline data from a source environment with shifted dynamics. We show that -- without information on the dynamics shift -- general shifted-dynamics data, even with subtle shifts, does not reduce sample complexity in the target environment. However, focusing on HTRL with prior information on the degree of the dynamics shift, we design HySRL, a transfer algorithm that outperforms pure online RL with problem-dependent sample complexity guarantees. Finally, our experimental results demonstrate that HySRL surpasses the state-of-the-art pure online RL baseline.

Practitioners often aim to infer an unobserved population trajectory using sample snapshots at multiple time points. E.g. given single-cell sequencing data, scientists would like to learn how gene expression changes over a cell’s life cycle. But sequencing any cell destroys that cell. So we can access data for any particular cell only at a single time point, but we have data across many cells. The deep learning community has recently explored using Schrödinger bridges (SBs) and their extensions in similar settings. However, existing methods either (1) interpolate between just two time points or (2) require a single fixed reference dynamic (often set to Brownian motion within SB). But learning piecewise from adjacent time points can fail to capture long-term dependencies. And practitioners are typically able to specify a model class for the reference dynamic but not the exact values of the parameters within it. So we propose a new method that (1) learns the unobserved trajectories from sample snapshots across multiple time points and (2) requires specification only of a class of reference dynamics, not a single fixed one. We demonstrate the advantages of our method on simulated and real data.

This paper studies a non-stationary kernelized bandit (KB) problem, also called time-varying Bayesian optimization, where one seeks to minimize the regret under an unknown reward function that varies over time. In particular, we focus on a near-optimal algorithm whose regret upper bound matches the regret lower bound. For this goal, we show the first algorithm-independent regret lower bound for non-stationary KB with squared exponential and Mat\'ern kernels, which reveals that an existing optimization-based KB algorithm with slight modification is near-optimal. However, this existing algorithm suffers from feasibility issues due to its huge computational cost.Therefore, we propose a novel near-optimal algorithm called restarting phased elimination with random permutation (R-PERP), which bypasses the huge computational cost. A technical key point is the simple permutation procedures of query candidates, which enable us to derive a novel tighter confidence bound tailored to the non-stationary problems.

We study the sample complexity of pure exploration in an online learning problem with a feedback graph. This graph dictates the feedback available to the learner, covering scenarios between full-information, pure bandit feedback, and settings with no feedback on the chosen action. While variants of this problem have been investigated for regret minimization, no prior work has addressed the pure exploration setting, which is the focus of our study. We derive an instance-specific lower bound on the sample complexity of learning the best action with fixed confidence, even when the feedback graph is unknown and stochastic, and present unidentifiability results for Bernoulli rewards. Additionally, our findings reveal how the sample complexity scales with key graph-dependent quantities. Lastly, we introduce TaS-FG (Track and Stop for Feedback Graphs), an asymptotically optimal algorithm, and demonstrate its efficiency across different graph configurations.