Recently there is a large amount of work devoted to the study of Markov chain stochastic gradient methods (MC-SGMs) which mainly focus on their convergence analysis for solving minimization problems. In this paper, we provide a comprehensive generalization analysis of MC-SGMs for both minimization and minimax problems through the lens of algorithmic stability in the framework of statistical learning theory. For empirical risk minimization (ERM) problems, we establish the optimal excess population risk bounds for both smooth and non-smooth cases by introducing on-average argument stability. For minimax problems, we develop a quantitative connection between on-average argument stability and generalization error which extends the existing results for uniform stability [38]. We further develop the first nearly optimal convergence rates for convex-concave problems both in expectation and with high probability, which, combined with our stability results, show that the optimal generalization bounds can be attained for both smooth and non-smooth cases. To the best of our knowledge, this is the first generalization analysis of SGMs when the gradients are sampled from a Markov process.

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].

The framework of feedback graphs is a generalization of sequential decisionmaking with bandit or full information feedback. In this work, we study an extension where the directed feedback graph is stochastic, following a distribution similar to the classical Erdős-Rényi model. Specifically, in each round every edge in the graph is either realized or not with a distinct probability for each edge.

We propose an analysis in fair learning that preserves the utility of the data while reducing prediction disparities under the criteria of group sufficiency. We focus on the scenario where the data contains multiple or even many subgroups, each with limited number of samples. As a result, we present a principled method for learning a fair predictor for all subgroups via formulating it as a bilevel objective. In the lower-level, the subgroup-specific predictors are learned through a small amount of data and the fair predictor. In the upper-level, the fair predictor is updated to be close to all subgroup specific predictors. We further prove that such a bilevel objective can effectively control the group sufficiency and generalization error. We evaluate the proposed framework on real-world datasets. Empirical evidence suggests the consistently improved fair predictions, as well as the comparable accuracy to the baselines.

We argue that current definitions of machine unlearning are underspecified for second-order optimizers. We compare first-order and second-order learners for their ability to handle the data deletion task with varying degrees of eigendecomposition to mimic the loss model memory. While both first and second-order methods realign with the ideal counterfactul in terms of performance and gradient, the second-order optimizer shows significant volatility in the optimizer state. This indicates residual information, supposedly deleted, that isn't detectable by first-order analysis. Various eigendecay treatments show that stability and information loss is regained only under controlled state pertubation where geometric information (or memory) is erased.

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.

Diffusion models are central to modern generative modeling, and understanding how they balance memorization and generalization is critical for reliable deployment. Recent work has shown that memorization in diffusion models is shaped by training dynamics, with generalization and memorization emerging at different stages of training. However, deployed diffusion models are often further distilled, introducing an additional training phase whose impact on memorization is not well understood. In this work, we analyze how distillation reshapes memorization behavior in diffusion models, taking consistency distillation as a representative framework. Empirically, we show that when applied to a teacher model that has memorized data, consistency distillation significantly reduces transferred memorization in the student while preserving, and sometimes improving, sample quality. To explain this behavior, we provide a theoretical analysis using a random feature neural network model [Bonnaire et al., 2025], showing that consistency distillation suppresses unstable feature directions associated with memorization while preserving stable, generalizable modes. Our findings suggest that distillation can serve not only as an acceleration tool, but also as a mechanism for improving the memorization-generalization trade-off.

We consider online learning problems under a partial observability model capturing situations where the information conveyed to the learner is between full information and bandit feedback. In the simplest variant, we assume that in addition to its own loss, the learner also gets to observe losses of some other actions. The revealed losses depend on the learner's action and a directed observation system chosen by the environment. For this setting, we propose the first algorithm that enjoys near-optimal regret guarantees without having to know the observation system before selecting its actions. Along similar lines, we also define a new partial information setting that models online combinatorial optimization problems where the feedback received by the learner is between semi-bandit and full feedback. As the predictions of our first algorithm cannot be always computed efficiently in this setting, we propose another algorithm with similar properties and with the benefit of always being computationally efficient, at the price of a slightly more complicated tuning mechanism. Both algorithms rely on a novel exploration strategy called implicit exploration, which is shown to be more efficient both computationally and information-theoretically than previously studied exploration strategies for the problem.