Aligning AI systems with human preferences typically suffers from the infamous *reward hacking* problem, where optimization of an imperfect reward model leads to undesired behaviors. In this paper, we investigate reward hacking in offline preference optimization, which aims to improve an initial model using a preference dataset. We identify two types of reward hacking stemming from statistical fluctuations in the dataset: Type I Reward Hacking due to subpar choices appearing more favorable, and Type II Reward Hacking due to decent choices appearing less desirable. We prove that many (mainstream or theoretical) preference optimization methods suffer from both types of reward hacking. To mitigate Type I Reward Hacking, we propose POWER, a new preference optimization method that combines Guiasu's weighted entropy with a robust reward maximization objective. POWER enjoys finite-sample guarantees under general function approximation, competing with the best covered policy in the data. To mitigate Type II Reward Hacking, we analyze the learning dynamics of preference optimization and develop a novel technique that dynamically updates preference labels toward certain "stationary labels", resulting in diminishing gradients for untrustworthy samples. Empirically, POWER with dynamic labels (DL) consistently outperforms state-of-the-art methods on alignment benchmarks, achieving improvements of up to **13.0** points on AlpacaEval 2 and **11.5** points on Arena-Hard over DPO, while also improving or maintaining performance on downstream tasks such as mathematical reasoning. Strong theoretical guarantees and empirical results demonstrate the promise of POWER-DL in mitigating reward hacking.

We propose A-Crab (Actor-Critic Regularized by Average Bellman error), a new practical algorithm for offline reinforcement learning (RL) in complex environments with insufficient data coverage. Our algorithm combines the marginalized importance sampling framework with the actor-critic paradigm, where the critic returns evaluations of the actor (policy) that are pessimistic relative to the offline data and have a small average (importance-weighted) Bellman error. Compared to existing methods, our algorithm simultaneously offers a number of advantages: (1) It achieves the optimal statistical rate of $1/\sqrt{N}$---where $N$ is the size of offline dataset---in converging to the best policy covered in the offline dataset, even when combined with general function approximators. (2) It relies on a weaker \textit{average} notion of policy coverage (compared to the $\ell_\infty$ single-policy concentrability) that exploits the structure of policy visitations. (3) It outperforms the data-collection behavior policy over a wide range of specific hyperparameters. We provide both theoretical analysis and experimental results to validate the effectiveness of our proposed algorithm. The code is available at https://github.com/zhuhl98/ACrab.

Offline reinforcement learning (RL) algorithms seek to learn an optimal policy from a fixed dataset without active data collection. Based on the composition of the offline dataset, two main methods are used: imitation learning which is suitable for expert datasets, and vanilla offline RL which often requires uniform coverage datasets. From a practical standpoint, datasets often deviate from these two extremes and the exact data composition is usually unknown. To bridge this gap, we present a new offline RL framework, called single-policy concentrability, that smoothly interpolates between the two extremes of data composition, hence unifying imitation learning and vanilla offline RL. Under this new framework, we ask: can one develop an algorithm that achieves a minimax optimal rate adaptive to unknown data composition? To address this question, we consider a lower confidence bound (LCB) algorithm developed based on pessimism in the face of uncertainty in offline RL. We study finite-sample properties of LCB as well as information-theoretic limits in multi-armed bandits, contextual bandits, and Markov decision processes (MDPs). Our analysis reveals surprising facts about optimality rates. In particular, in both contextual bandits and RL, LCB achieves a fast convergence rate for nearly-expert datasets, analogous to the one achieved by imitation learning, contrary to the slow rate achieved in offline RL. In contextual bandits, we prove that LCB is adaptively optimal for the entire data composition range, achieving a smooth transition from imitation learning to offline RL. We further show that LCB is almost adaptively optimal in MDPs.

Offline (or batch) reinforcement learning (RL) algorithms seek to learn an optimal policy from a fixed dataset without active data collection. Based on the composition of the offline dataset, two main methods are used: imitation learning which is suitable for expert datasets, and vanilla offline RL which often requires uniform coverage datasets. From a practical standpoint, datasets often deviate from these two extremes and the exact data composition is usually unknown. To bridge this gap, we present a new offline RL framework that smoothly interpolates between the two extremes of data composition, hence unifying imitation learning and vanilla offline RL. The new framework is centered around a weak version of the concentrability coefficient that measures the deviation of the behavior policy from the expert policy alone. Under this new framework, we ask: can one develop an algorithm that achieves a minimax optimal rate adaptive to unknown data composition? To address this question, we consider a lower confidence bound (LCB) algorithm developed based on pessimism in the face of uncertainty in offline RL. We study finite-sample properties of LCB as well as information-theoretic limits in multi-armed bandits, contextual bandits, and Markov decision processes (MDPs). Our analysis reveals surprising facts about optimality rates. In particular, in both contextual bandits and RL, LCB achieves a faster rate of $1/N$ for nearly-expert datasets compared to the usual rate of $1/\sqrt{N}$ in offline RL, where $N$ is the batch dataset sample size. In contextual bandits with at least two contexts, we prove that LCB is adaptively optimal for the entire data composition range, achieving a smooth transition from imitation learning to offline RL. We further show that LCB is almost adaptively optimal in MDPs.

In online reinforcement learning (RL), efficient exploration remains particularly challenging in high-dimensional environments with sparse rewards. In low-dimensional environments, where tabular parameterization is possible, count-based upper confidence bound (UCB) exploration methods achieve minimax near-optimal rates. However, it remains unclear how to efficiently implement UCB in realistic RL tasks that involve non-linear function approximation. To address this, we propose a new exploration approach via maximizing the deviation of the occupancy of the next policy from the explored regions. We add this term as an adaptive regularizer to the standard RL objective to balance exploration vs. exploitation. We pair the new objective with a provably convergent algorithm, giving rise to a new intrinsic reward that adjusts existing bonuses. The proposed intrinsic reward is easy to implement and combine with other existing RL algorithms to conduct exploration. As a proof of concept, we evaluate the new intrinsic reward on tabular examples across a variety of model-based and model-free algorithms, showing improvements over count-only exploration strategies. When tested on navigation and locomotion tasks from MiniGrid and DeepMind Control Suite benchmarks, our approach significantly improves sample efficiency over state-of-the-art methods.

We present an efficient and practical (polynomial time) algorithm for online prediction in unknown and partially observed linear dynamical systems (LDS) under stochastic noise. When the system parameters are known, the optimal linear predictor is the Kalman filter. However, in unknown systems, the performance of existing predictive models is poor in important classes of LDS that are only marginally stable and exhibit long-term forecast memory. We tackle this problem by bounding the generalized Kolmogorov width of the Kalman filter coefficient set. This motivates the design of an algorithm, which we call spectral LDS improper predictor (SLIP), based on conducting a tight convex relaxation of the Kalman predictive model via spectral methods. We provide a finite-sample analysis, showing that our algorithm competes with the Kalman filter in hindsight with only logarithmic regret. Our regret analysis relies on Mendelson’s small-ball method, providing sharp error bounds without concentration, boundedness, or exponential forgetting assumptions. Empirical evaluations demonstrate that SLIP outperforms state-of-the-art methods in LDS prediction. Our theoretical and experimental results shed light on the conditions required for efficient probably approximately correct (PAC) learning of the Kalman filter from partially observed data.