We analyze the generalization gap (gap between the training and test errors) when training a potentially over-parametrized model using a Markovian stochastic training algorithm, initialized from some distribution θ0 p0. We focus on Langevin dynamics with a positive temperature β 1, i.e. gradient descent on a training loss Lwith infinitesimal step size, perturbed with β 1-variances Gaussian noise, and lightly regularized or bounded. There, we bound the generalization gap, at any time during training, by p (βEL(θ0)+ln(1/δ))/N with probability 1 δ over the dataset, where N is the sample size, and EL(θ0) = O(1)with standard initialization scaling. In contrast to previous guarantees, we have no dependence on either training time or reliance on mixing, nor a dependence on dimensionality, gradient norms, or any other properties of the loss or model. This guarantee follows from a general analysis of any Markov process-based training that has a Gibbs-style stationary distribution. The proof is surprisingly simple, once we observe that the marginal distribution divergence from initialization remains bounded, as implied by a generalized second law of thermodynamics.

In this paper, we consider fully decentralized cooperative multi-agent reinforcement learning, where each agent has access only to the states, its local actions, and the shared rewards. The absence of information about other agents' actions typically leads to the non-stationarity problem during per-agent value function updates, and the relative overgeneralization issue during value function estimation. However, existing works fail to address both issues simultaneously, as they lack the capability to model the agents' joint policy in a fully decentralized setting. To overcome this limitation, we propose a simple yet effective method named Return-Aware Context (RAC). RAC formalizes the dynamically changing task, as locally perceived by each agent, as a contextual Markov Decision Process (MDP), and addresses both nonstationarity and relative overgeneralization through return-aware context modeling. Specifically, the contextual MDP attributes the non-stationary local dynamics of each agent to switches between contexts, each corresponding to a distinct joint policy.

This work presents the first finite-time analysis of average-reward Q-learning with an asynchronous implementation. A key feature of the algorithm we study is the use of adaptive stepsizes that act as local clocks for each state-action pair. We show that the mean-square error of this Q-learning algorithm, measured in the span seminorm, converges at a rate of O(1/k). To establish this result, we demonstrate that adaptive stepsizes are necessary: without them, the algorithm fails to converge to the correct target. Moreover, adaptive stepsizes can be viewed as a form of implicit importance sampling that counteracts the effect of asynchronous updates. Technically, the use of adaptive stepsizes causes each Q-learning update to depend on the full sample history, introducing strong correlations and making the algorithm a non-Markovian stochastic approximation (SA) scheme. Our approach to overcoming this challenge involves (1) a time-inhomogeneous Markovian reformulation of non-Markovian SA, and (2) a combination of almost-sure time-varying bounds, conditioning arguments, and Markov chain concentration inequalities to break the strong correlations between the adaptive stepsizes and the iterates.

Reinforcement Learning (RL) is a continuously growing field that has the potential to revolutionize many areas of artificial intelligence. However, despite its promise, RL research is often hindered by the lack of standardization in the environment and algorithmic implementations. This makes it difficult for researchers to compare and build upon each other's work, slowing progress in the field. Gymnasium is an open-source library that provides a standardized API for RL environments, aiming to tackle this issue, with over 18 million installations. Gymnasium's main feature is a set of abstractions that allow for wide interoperability between environments and training algorithms, making it easier for researchers to develop and test new environments and/or RL algorithms. In addition, Gymnasium provides a collection of built-in easy-to-use environments, tools for easily customizing environments, and tools to ensure the reproducibility and robustness of RL research. Through this unified framework, Gymnasium significantly streamlines the process of developing and testing RL algorithms, enabling researchers to focus on innovation and less on implementation details. By providing a standardized platform for RL research, Gymnasium helps to drive forward the field of reinforcement learning and unlock its full potential.

Training Reinforcement Learning (RL) controllers in simulation offers costefficiency and safety advantages. However, the resultant policies often suffer significant performance degradation during real-world deployment due to the reality gap. Previous works like System Identification (Sys-Id) have attempted to bridge this discrepancy by improving simulator fidelity, but encounter challenges including the collapse of high-dimensional parameter identification, low identification accuracy, and unstable convergence dynamics. To address these challenges, we propose a novel Sys-Id framework that combines Diffusion Evolution with Adversarial Learning (DEAL) to iteratively infer physical parameters with limited real-world data, which makes the state transitions between simulation and reality as similar as possible. Specifically, our method iteratively refines physical parameters through a dual mechanism: a discriminator network evaluates the similarity of state transitions between parameterized simulations and target environment as fitness guidance, while diffusion evolution adaptively modulates noise prediction and denoising processes to optimize parameter distributions.

In single-cell perturbation prediction, a central task is to forecast the effects of perturbing a gene unseen in the training data. The efficacy of such predictions depends on two factors: (1) the similarity of the target gene to those covered in the training data, which informs model (epistemic) uncertainty, and (2) the quality of the corresponding training data, which reflects data (aleatoric) uncertainty. Both factors are critical for determining the reliability of a prediction, particularly as gene perturbation is an inherently stochastic biochemical process. In this paper, we propose PRESCRIBE (PREdicting Single-Cell Response wIth Bayesian Estimation), a multivariate deep evidential regression framework designed to measure both sources of uncertainty jointly. Our analysis demonstrates that PRESCRIBE effectively estimates a confidence score for each prediction, which strongly correlates with its empirical accuracy. This capability enables the filtering of untrustworthy results, and in our experiments, it achieves steady accuracy improvements of over 3% compared to comparable baselines.

Protein fitness optimization involves finding a protein sequence that maximizes desired quantitative properties in a combinatorially large design space of possible sequences. Recent advances in steering protein generative models (e.g., diffusion models and language models) with labeled data offer a promising approach. However, most previous studies have optimized surrogate rewards and/or utilized large amounts of labeled data for steering, making it unclear how well existing methods perform and compare to each other in real-world optimization campaigns where fitness is measured through low-throughput wet-lab assays. In this study, we explore fitness optimization using small amounts (hundreds) of labeled sequencefitness pairs and comprehensively evaluate strategies such as classifier guidance and posterior sampling for guiding generation from different discrete diffusion models of protein sequences. We also demonstrate how guidance can be integrated into adaptive sequence selection akin to Thompson sampling in Bayesian optimization, showing that plug-and-play guidance strategies offer advantages over alternatives such as reinforcement learning with protein language models. Overall, we provide practical insights into how to effectively steer modern generative models for next-generation protein fitness optimization.

Predictions in the form of sets of probability distributions, so-called credal sets, provide a suitable means to represent a learner's epistemic uncertainty. In this paper, we propose a theoretically grounded approach to credal prediction based on the statistical notion of relative likelihood: The target of prediction is the set of all (conditional) probability distributions produced by the collection of plausible models, namely those models whose relative likelihood exceeds a specified threshold. This threshold has an intuitive interpretation and allows for controlling the trade-off between correctness and precision of credal predictions. We tackle the problem of approximating credal sets defined in this way by means of suitably modified ensemble learning techniques. To validate our approach, we illustrate its effectiveness by experiments on benchmark datasets demonstrating superior uncertainty representation without compromising predictive performance. We also compare our method against several state-of-the-art baselines in credal prediction.

Noisy labels often compel models to overfit, especially in multi-label classification tasks. Existing methods for noisy multi-label learning (NML) primarily follow a discriminative paradigm, which relies on noise transition matrix estimation or small-loss strategies to correct noisy labels. However, they remain substantial optimization difficulties compared to noisy single-label learning. In this paper, we propose a Co-Occurrence-Aware Diffusion (CAD) model, which reformulates NML from a generative perspective. We treat features as conditions and multilabels as diffusion targets, optimizing the diffusion model for multi-label learning with theoretical guarantees. Benefiting from the diffusion model's strength in capturing multi-object semantics and structured label matrix representation, we can effectively learn the posterior mapping from features to true multi-labels. To mitigate the interference of noisy labels in the forward process, we guide generation using pseudo-clean labels reconstructed from the latent neighborhood space, replacing original point-wise estimates with neighborhood-based proxies. In the reverse process, we further incorporate label co-occurrence constraints to enhance the model's awareness of incorrect generation directions, thereby promoting robust optimization. Extensive experiments on both synthetic (Pascal-VOC, MS-COCO) and real-world (NUS-WIDE) noisy datasets demonstrate that our approach outperforms state-of-the-art methods.

However, these methods often suffer from a significant one-step bias, which may lead to convergence towards local optima and poor performance in complex or high-dimensional tasks. Recently, Black-Box Optimization (BBO) has achieved success across various scientific and engineering domains, particularly when function evaluations are costly and gradients are unavailable. Motivated by this, we propose the Reinforced EnergyBased Model for Bayesian Optimization (REBMBO), which integrates Gaussian Processes (GP) for local guidance with an Energy-Based Model (EBM) to capture global structural information. Notably, we define each Bayesian Optimization iteration as a Markov Decision Process (MDP) and use Proximal Policy Optimization (PPO) for adaptive multi-step lookahead, dynamically adjusting the depth and direction of exploration to effectively overcome the limitations of traditional BO methods. We conduct extensive experiments on synthetic and real-world benchmarks, confirming the superior performance of REBMBO.