In this paper, for Markov decision processes (MDPs) with unbounded state spaces we present refined upper bounds presented in [Kara et. al. JMLR'23] on finite model approximation errors via optimizing the quantizers used for finite model approximations. We also consider implications on quantizer design for quantized Q-learning and empirical model learning, and the performance of policies obtained via Q-learning where the quantized state is treated as the state itself. We highlight the distinctions between planning, where approximating MDPs can be independently designed, and learning (either via Q-learning or empirical model learning), where approximating MDPs are restricted to be defined by invariant measures of Markov chains under exploration policies, leading to significant subtleties on quantizer design performance, even though asymptotic near optimality can be established under both setups. In particular, under Lyapunov growth conditions, we obtain explicit upper bounds which decay to zero as the number of bins approaches infinity

Causal discovery aims to learn causal relationships between variables from targeted data, making it a fundamental task in machine learning. However, causal discovery algorithms often rely on unverifiable causal assumptions, which are usually difficult to satisfy in real-world data, thereby limiting the broad application of causal discovery in practical scenarios. Inspired by these considerations, this work extensively benchmarks the empirical performance of various mainstream causal discovery algorithms, which assume i.i.d. data, under eight model assumption violations. Our experimental results show that differentiable causal discovery methods exhibit robustness under the metrics of Structural Hamming Distance and Structural Intervention Distance of the inferred graphs in commonly used challenging scenarios, except for scale variation. We also provide the theoretical explanations for the performance of differentiable causal discovery methods. Finally, our work aims to comprehensively benchmark the performance of recent differentiable causal discovery methods under model assumption violations, and provide the standard for reasonable evaluation of causal discovery, as well as to further promote its application in real-world scenarios.

Recent progress in reasoning with large language models (LLMs), such as DeepSeek-R1, demonstrates impressive capabilities in domains like mathematics and coding, by exhibiting complex cognitive behaviors such as verification, goal decomposition, and self-reflection. However, it is unclear what behavior is effective and what behavior is missing for long-horizon AI agents tasks. In this work, we propose Dyna-Think, a thinking framework that integrates planning with an internal world model with reasoning and acting to enhance AI agent performance. To enable Dyna-Think, we propose Dyna-Think Imitation Learning (DIT) and Dyna-Think Dyna Training (DDT). To initialize a policy with Dyna-Think, DIT reconstructs the thinking process of R1 to focus on performing world model simulation relevant to the proposed (and planned) action, and trains the policy using this reconstructed data. To enhance Dyna-Think, DDT uses a two-stage training process to first improve the agent's world modeling ability via objectives such as state prediction or critique generation, and then improve the agent's action via policy training. We evaluate our methods on OSWorld and WindowsAgentArena, and demonstrate that Dyna-Think improves the agent's in-domain and out-of-domain performance, achieving similar best-of-n performance compared to R1 while generating 2x less tokens on average. Our extensive empirical studies reveal that 1) using critique generation for world model training is effective to improve policy performance; and 2) AI agents with better performance correlate with better world modeling abilities. We believe our results suggest a promising research direction to integrate world model simulation into AI agents to enhance their reasoning, planning, and acting capabilities.

Missing data in online reinforcement learning (RL) poses challenges compared to missing data in standard tabular data or in offline policy learning. The need to impute and act at each time step means that imputation cannot be put off until enough data exist to produce stable imputation models. It also means future data collection and learning depend on previous imputations. This paper proposes fully online imputation ensembles. We find that maintaining multiple imputation pathways may help balance the need to capture uncertainty under missingness and the need for efficiency in online settings. We consider multiple approaches for incorporating these pathways into learning and action selection. Using a Grid World experiment with various types of missingness, we provide preliminary evidence that multiple imputation pathways may be a useful framework for constructing simple and efficient online missing data RL methods.

PAC generalization bounds on the risk, when expressed in terms of the expected loss, are often insufficient to capture imbalances between subgroups in the data. To overcome this limitation, we introduce a new family of risk measures, called constrained f-entropic risk measures, which enable finer control over distributional shifts and subgroup imbalances via f-divergences, and include the Conditional Value at Risk (CVaR), a well-known risk measure. We derive both classical and disintegrated PAC-Bayesian generalization bounds for this family of risks, providing the first disintegratedPAC-Bayesian guarantees beyond standard risks. Building on this theory, we design a self-bounding algorithm that minimizes our bounds directly, yielding models with guarantees at the subgroup level. Finally, we empirically demonstrate the usefulness of our approach.

Derivative-free Bayesian inversion is an important task in many science and engineering applications, particularly when computing the forward model derivative is computationally and practically challenging. In this paper, we introduce Blade, which can produce accurate and well-calibrated posteriors for Bayesian inversion using an ensemble of interacting particles. Blade leverages powerful data-driven priors based on diffusion models, and can handle nonlinear forward models that permit only black-box access (i.e., derivative-free). Theoretically, we establish a non-asymptotic convergence analysis to characterize the effects of forward model and prior estimation errors. Empirically, Blade achieves superior performance compared to existing derivative-free Bayesian inversion methods on various inverse problems, including challenging highly nonlinear fluid dynamics.

In self-supervised reinforcement learning (RL), one of the key challenges is learning a diverse set of skills to prepare agents for unknown future tasks. Despite impressive advances, scalability and evaluation remain prevalent issues. Regarding scalability, the search for meaningful skills can be obscured by high-dimensional feature spaces, where relevant features may vary across downstream task domains. For evaluating skill diversity, defining what constitutes "diversity" typically requires a hard commitment to a specific notion of what it means for skills to be diverse, potentially leading to inconsistencies in how skill diversity is understood, making results across different approaches hard to compare, and leaving many forms of diversity unexplored. To address these issues, we adopt a measure of sample diversity that translates ideas from ecology to machine learning -- the Vendi Score -- allowing the user to specify and evaluate any desired form of diversity. We demonstrate how this metric facilitates skill evaluation and introduce VendiRL, a unified framework for learning diversely diverse sets of skills. Given distinct similarity functions, VendiRL motivates distinct forms of diversity, which could support skill-diversity pretraining in new and richly interactive environments where optimising for various forms of diversity may be desirable.

Research on applications of reinforcement learning (RL) to large language models has mostly been focused on single-turn problems, such as mathematical reasoning or single-shot code generation. While these problems can be viewed as token-level multi-turn Markov decision processes (MDPs), this view corresponds to a degenerate case of multi-turn interaction where the environment provides no feedback. This contrasts with many real-world domains, such as software engineering (SWE), which require rich multi-turn interactions with a stateful environment that responds to each action with a non-trivial observation. To bridge this gap, we demonstrate the successful application of RL to this general regime. Our methodology begins with rejection fine-tuning (RFT) using execution feedback to train a policy to follow instructions and formatting effectively, followed by a synchronous RL pipeline using DAPO for iterative improvement. Applying this pipeline to Qwen2.5-72B-Instruct, we increase its Pass@1 on the SWE-bench Verified benchmark from 11% to 39%, substantially improving upon the 20% RFT baseline. On the May and June splits of SWE-rebench, the resulting agent achieves Pass@1 of 35% and 31% respectively, competitive with even larger models such as DeepSeek-V3-0324 or Qwen3-235B-A22B, demonstrating that our methodology offers a practical approach for training capable agents for multi-turn interactive tasks using open-weight models.

We introduce Reliable Policy Iteration (RPI) and Conservative RPI (CRPI), variants of Policy Iteration (PI) and Conservative PI (CPI), that retain tabular guarantees under function approximation. RPI uses a novel Bellman-constrained optimization for policy evaluation. We show that RPI restores the textbook \textit{monotonicity} of value estimates and that these estimates provably \textit{lower-bound} the true return; moreover, their limit partially satisfies the \textit{unprojected} Bellman equation. CRPI shares RPI's evaluation, but updates policies conservatively by maximizing a new performance-difference \textit{lower bound} that explicitly accounts for function-approximation-induced errors. CRPI inherits RPI's guarantees and, crucially, admits per-step improvement bounds. In initial simulations, RPI and CRPI outperform PI and its variants. Our work addresses a foundational gap in RL: popular algorithms such as TRPO and PPO derive from tabular CPI yet are deployed with function approximation, where CPI's guarantees often fail-leading to divergence, oscillations, or convergence to suboptimal policies. By restoring PI/CPI-style guarantees for \textit{arbitrary} function classes, RPI and CRPI provide a principled basis for next-generation RL.

Timely delivery of delay-sensitive information over dynamic, heterogeneous networks is increasingly essential for a range of interactive applications, such as industrial automation, self-driving vehicles, and augmented reality. However, most existing network control solutions target only average delay performance, falling short of providing strict End-to-End (E2E) peak latency guarantees. This paper addresses the challenge of reliably delivering packets within application-imposed deadlines by leveraging recent advancements in Multi-Agent Deep Reinforcement Learning (MA-DRL). After introducing the Delay-Constrained Maximum-Throughput (DCMT) dynamic network control problem, and highlighting the limitations of current solutions, we present a novel MA-DRL network control framework that leverages a centralized routing and distributed scheduling architecture. The proposed framework leverages critical networking domain knowledge for the design of effective MA-DRL strategies based on the Multi-Agent Deep Deterministic Policy Gradient (MADDPG) technique, where centralized routing and distributed scheduling agents dynamically assign paths and schedule packet transmissions according to packet lifetimes, thereby maximizing on-time packet delivery. The generality of the proposed framework allows integrating both data-driven \blue{Deep Reinforcement Learning (DRL)} agents and traditional rule-based policies in order to strike the right balance between performance and learning complexity. Our results confirm the superiority of the proposed framework with respect to traditional stochastic optimization-based approaches and provide key insights into the role and interplay between data-driven DRL agents and new rule-based policies for both efficient and high-performance control of latency-critical services.