In this paper, we prove the first Bayesian regret bounds for Thompson Sampling in reinforcement learning in a multitude of settings. We simplify the learning problem using a discrete set of surrogate environments, and present a refined analysis of the information ratio using posterior consistency. This leads to an upper bound of order eO(H p dl1T) in the time inhomogeneous reinforcement learning problem where H is the episode length and dl1 is the Kolmogorov l1 dimension of the space of environments. We then find concrete bounds of dl1 in a variety of settings, such as tabular, linear and finite mixtures, and discuss how how our results are either the first of their kind or improve the state-of-the-art.

As large language models (LLMs) transition from chat interfaces to integral components of stochastic pipelines and systems approaching general intelligence, the ability to faithfully sample from specified probability distributions has become a functional requirement rather than a theoretical curiosity. We present the first large-scale, statistically powered audit of native probabilistic sampling in frontier LLMs, benchmarking 11 models across 15 distributions. To disentangle failure modes, we employ a dual-protocol design: Batch Generation, where a model produces $N{=}1000$ samples within one response, and Independent Requests, comprising $N{=}1000$ stateless calls. We observe a sharp protocol asymmetry: batch generation achieves only modest statistical validity, with a 7% median pass rate, while independent requests collapse almost entirely, with 10 of 11 models passing none of the distributions. Beyond this asymmetry, we reveal that sampling fidelity degrades monotonically with distributional complexity and aggravates as the sampling horizon $N$ increases. Finally, we demonstrate how the propagation of these failures into downstream real-world application tasks introduces systematic biases: models fail to enforce uniform answer-position constraints in Multiple Choice Question generation and systematically violate demographic targets in attribute-constrained text-to-image prompt synthesis. These findings indicate that current LLMs lack a functional internal sampler, necessitating external tools for applications requiring statistical guarantees.

Domain generalization (DG) aims to transfer the learning task from a single or multiple source domains to unseen target domains. To extract and leverage the information which exhibits sufficient generalization ability, we propose a simple yet effective approach of Adversarial Teacher-Student Representation Learning, with the goal of deriving the domain generalizable representations via generating and exploring out-of-source data distributions. Our proposed framework advances Teacher-Student learning in an adversarial learning manner, which alternates between knowledge-distillation based representation learning and novel-domain data augmentation.

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We consider the problem of teaching via demonstrations in sequential decisionmaking settings. In particular, we study how to design a personalized curriculum over demonstrations to speed up the learner's convergence. We provide a unified curriculum strategy for two popular learner models: Maximum Causal Entropy Inverse Reinforcement Learning (MaxEnt-IRL) and Cross-Entropy Behavioral Cloning (CrossEnt-BC). Our unified strategy induces a ranking over demonstrations based on a notion of difficulty scores computed w.r.t. the teacher's optimal policy and the learner's current policy. Compared to the state of the art, our strategy doesn't require access to the learner's internal dynamics and still enjoys similar convergence guarantees under mild technical conditions. Furthermore, we adapt our curriculum strategy to the setting where no teacher agent is present using task-specific difficulty scores. Experiments on a synthetic car driving environment and navigation-based environments demonstrate the effectiveness of our curriculum strategy.