We study policy optimization for online episodic tabular Markov decision processes with unknown transition kernels, aiming for best-of-both-worlds guarantees together with data-dependent regret bounds. Recent work (Dann et al., 2023; Li et al., 2026) has shown that policy optimization can adapt to both adversarial and stochastic losses with first-order, second-order, and path-length bounds, but only under known transitions, leaving open whether such data-dependent guarantees are achievable by policy optimization when the transition kernel is unknown. We resolve this by developing a new algorithm based on optimistic follow-the-regularized-leader that attains these guarantees under unknown transitions. The key ingredient is a new design of optimistic $Q$-function estimators together with a data-dependent transition bonus that controls estimator bias through the loss-prediction error. Our analysis further identifies an unavoidable transition-dependent complexity term that captures the intrinsic cost of estimating the transition kernel. As a result, we obtain first-order, second-order, and path-length bounds with the transition-dependent complexity term while simultaneously achieving gap-dependent $\mathrm{polylog}(T)$ regret in the stochastic regime.

Multi-agent reinforcement learning (MARL), as a thriving field, explores how multiple agents independently make decisions in a shared dynamic environment. Due to environmental uncertainties, policies in MARL must remain robust to tackle the sim-to-real gap. We focus on robust two-player zero-sum Markov games (TZMGs) in offline settings, specifically on tabular robust TZMGs (RTZMGs). We propose a model-based algorithm (RTZ-VI-LCB) for offline RTZMGs, which is optimistic robust value iteration combined with a data-driven Bernstein-style penalty term for robust value estimation. By accounting for distribution shifts in the historical dataset, the proposed algorithm establishes near-optimal sample complexity guarantees under partial coverage and environmental uncertainty. An information-theoretic lower bound is developed to confirm the tightness of our algorithm's sample complexity, which is optimal regarding both state and action spaces. To the best of our knowledge, RTZ-VI-LCB is the first to attain this optimality, sets a new benchmark for offline RTZMGs, and is validated experimentally.

Diffusion and flow matching models have significantly advanced media generation, yet their design space is well-explored, somewhat limiting further improvements. Concurrently, autoregressive (AR) models, particularly those generating continuous tokens, have emerged as a promising direction for unifying text and media generation. This paper introduces Transition Matching (TM), a novel discrete-time, continuous-state generative paradigm that unifies and advances both diffusion/flow models and continuous AR generation. TM decomposes complex generation tasks into simpler Markov transitions, allowing for expressive non-deterministic probability transition kernels and arbitrary non-continuous supervision processes, thereby unlocking new flexible design avenues. We explore these choices through three TM variants: (i) Difference Transition Matching (DTM), which generalizes flow matching to discrete-time by directly learning transition probabilities, yielding state-of-the-art image quality and text adherence as well as improved sampling efficiency.

Diffusion bridge models and stochastic interpolants enable high-quality imageto-image (I2I) translation by creating paths between distributions in pixel space. However, recent diffusion bridge models excel in image translation but suffer from restricted design flexibility and complicated hyperparameter tuning, whereas Stochastic Interpolants offer greater flexibility but lack essential refinements. We show that these complementary strengths can be unified by interpreting all existing methods within a single SI-based framework. In this work, we unify and expand the space of bridge models by extending Stochastic Interpolants (SIs) with preconditioning, endpoint conditioning, and an optimized sampling algorithm. These enhancements expand the design space of diffusion bridge models, leading to state-of-the-art performance in both image quality and sampling efficiency across diverse I2I tasks. Furthermore, we identify and address a previously overlooked issue of low sample diversity under fixed conditions. We introduce a quantitative analysis for output diversity and demonstrate how we can modify the base distribution for further improvements. Code is available at https://github.com/szhan311/ECSI.

We propose a new approach to unbiased estimation of the gradients of the stationary means associated with parametrized families of Markov chains. Our estimators are particularly efficient when the Markov chains have slow mixing rate. Our approach does not require a specific parametrization except for an oracle to evaluate the transition density and its gradient at a given data point without any additional knowledge about the density function itself. It makes our estimator suitable for parametrizations associated with neural networks. The estimator can potentially achieve large improvement in terms of efficiency. Numerical experiments confirm the good performance predicted by the theory.

Standard diffusion models for graph generation typically rely on uniform time-stepping, an approach that overlooks the non-homogeneous dynamics of distributional evolution on complex manifolds. In this paper, we present an information-geometric framework that reinterprets the diffusion sampling trajectory as a parametric curve on a Riemannian manifold. Our key observation is that the Fisher-Rao metric provides a principled measure of the intrinsic distance. By analyzing this metric, we derive the Drift Variation Score (DVS), a geometry-aware indicator that quantifies the instantaneous rate of distributional change. Unlike prior heuristic-based adaptive samplers, our DVS solver enforces a constant informational speed on the statistical manifold, automatically maintaining a uniform rate of distributional change along the sampling trajectory. This equal arc-length strategy ensures that each discretization step contributes equally to the information speed. Theoretical analysis verifies that DVS characterizes the local stiffness of the sampling dynamics in the Fisher-Rao sense. Experimental results on molecule and social network generation show that DVS significantly improves structural fidelity and sampling efficiency. Code is at https://github.com/kunzhan/DVS

Robust reinforcement learning (RL) is to find a policy that optimizes the worstcase performance over an uncertainty set of MDPs. In this paper, we focus on model-free robust RL, where the uncertainty set is defined to be centering at a misspecified MDP that generates a single sample trajectory sequentially, and is assumed to be unknown. We develop a sample-based approach to estimate the unknown uncertainty set, and design robust Q-learning algorithm (tabular case) and robust TDC algorithm (function approximation setting), which can be implemented in an online and incremental fashion. For the robust Q-learning algorithm, we prove that it converges to the optimal robust Q function, and for the robust TDC algorithm, we prove that it converges asymptotically to some stationary points. Unlike the results in [Roy et al., 2017], our algorithms do not need any additional conditions on the discount factor to guarantee the convergence. We further characterize the finite-time error bounds of the two algorithms, and show that both the robust Qlearning and robust TDC algorithms converge as fast as their vanilla counterparts (within a constant factor). Our numerical experiments further demonstrate the robustness of our algorithms. Our approach can be readily extended to robustify many other algorithms, e.g., TD, SARSA, and other GTD algorithms.

We study distributionally robust offline reinforcement learning (RL), which seeks to find an optimal robust policy purely from an offline dataset that can perform well in perturbed environments. We propose a generic algorithm framework Doubly Pessimistic Model-based Policy Optimization (P2MPO) for robust offline RL, which features a novel combination of a flexible model estimation subroutine and a doubly pessimistic policy optimization step. Here the double pessimism principle is crucial to overcome the distribution shift incurred by i) the mismatch between behavior policy and the family of target policies; and ii) the perturbation of the nominal model. Under certain accuracy assumptions on the model estimation subroutine, we show that P2MPOis provably sample-efficient with robust partial coverage data, which means that the offline dataset has good coverage of the distributions induced by the optimal robust policy and perturbed models around the nominal model. By tailoring specific model estimation subroutines for concrete examples including tabular Robust Markov Decision Process (RMDP), factored RMDP, and RMDP with kernel and neural function approximations, we show that P2MPO enjoys a eO(n 1/2) convergence rate, where nis the number of trajectories in the offline dataset. Notably, these models, except for the tabular case, are first identified and proven tractable by this paper. To the best of our knowledge, we first propose a general learning principle -- double pessimism -- for robust offline RL and show that it is provably efficient in the context of general function approximations.

Incorporating causality into reinforcement learning methods increases the interpretability of artificial636 intelligence, which helps humans understand the underlying mechanism of algorithms and check637 the source of failures. However, the learned causal transition model may contain human-readable638 private information about the environment, which could raise privacy issues. To mitigate this potential639 negative societal impact, the causal transition model needs to be encrypted and only accessible to640 algorithms and trustworthy users.641 In this section, besides the most related formulation, robust RL introduced in Sec 3.3, we also643 introduce some other related RL problem formulations partially shown in Figure 3. Then, we limit644 our discussion to mainly two lines of work that are related to ours: (1) promoting robustness in RL;645 (2) concerning the spurious correlation issues in RL.646 B.1 Related RL formulations647 Robustness to noisy state: POMDPs and SA-MDPs.