A central problem in online learning and decision making--from bandits to reinforcement learning--is to understand what modeling assumptions lead to sampleefficient learning guarantees. We consider a general adversarial decision making framework that encompasses (structured) bandit problems with adversarial rewards and reinforcement learning problems with adversarial dynamics. Our main result is to show--via new upper and lower bounds--that the Decision-Estimation Coefficient, a complexity measure introduced by Foster et al. [17] in the stochastic counterpart to our setting, is necessary and sufficient to obtain low regret for adversarial decision making. However, compared to the stochastic setting, one must apply the Decision-Estimation Coefficient to the convex hull of the class of models (or, hypotheses) under consideration. This establishes that the price of accommodating adversarial rewards or dynamics is governed by the behavior of the model class under convexification, and recovers a number of existing results--both positive and negative. En route to obtaining these guarantees, we provide new structural results that connect the Decision-Estimation Coefficient to variants of other well-known complexity measures, including the Information Ratio of Russo and Van Roy [47] and the Exploration-by-Optimization objective of Lattimore and György [32].

To achieve autonomy in a priori unknown real-world scenarios, agents should be able to: i) act from high-dimensional sensory observations (e.g., images), ii) learn from past experience to adapt and improve, and iii) be capable of long horizon planning.

Offline multi-agent reinforcement learning (MARL) enables policy learning from fixed datasets, but is prone to coordination failure: agents trained on static, off-policy data converge to suboptimal joint behaviours because they cannot co-adapt as their policies change. We introduce CODA (Coordination via On-Policy Diffusion for Multi-Agent Reinforcement Learning), a diffusion-based multi-agent trajectory generator for data augmentation that samples conditioned on the current joint policy, producing synthetic experience which reflects the evolving behaviours of the agents, thereby providing a mechanism for co-adaptation. We find that previous diffusion-based augmentation approaches are insufficient for fostering multi-agent coordination because they produce static augmented datasets that do not evolve as the current joint policy changes during training; CODA resolves this by more closely simulating on-policy learning and is a meaningful step toward coordinated behaviours in the offline setting. CODA is algorithm-agnostic and can be layered onto both model-free and model-based offline reinforcement learning pipelines as an augmentation module. Empirically, CODA not only resolves canonical coordination pathologies in continuous polynomial games but also delivers strong results on the more complex MaMuJoCo continuous-control benchmarks.

Recent work has demonstrated the effectiveness of formulating decision making as supervised learning on offline-collected trajectories. Powerful sequence models, such as GPT or BERT, are often employed to encode the trajectories. However, the benefits of performing sequence modeling on trajectory data remain unclear. In this work, we investigate whether sequence modeling has the ability to condense trajectories into useful representations that enhance policy learning. We adopt a two-stage framework that first leverages sequence models to encode trajectory-level representations, and then learns a goal-conditioned policy employing the encoded representations as its input.