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

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.

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.

Autonomous vehicles have shown promising potential to be a groundbreaking technology for improving the safety of road users. For these vehicles, as well as many other safety-critical robotic technologies, to be deployed in real-world applications, we require algorithms that can generalize well to unseen scenarios and data. Model-based reinforcement learning algorithms (MBRL) have demonstrated state-of-the-art performance and data efficiency across a diverse set of domains. However, these algorithms have also shown susceptibility to changes in the environment and its transition dynamics. In this work, we explore the performance and generalization capabilities of MBRL algorithms for autonomous driving, specifically in the simulated autonomous racing environment, Roboracer (formerly F1Tenth). We frame the head-to-head racing task as a learning problem using contextual Markov decision processes and parameterize the driving behavior of the adversaries using the context of the episode, thereby also parameterizing the transition and reward dynamics. We benchmark the behavior of MBRL algorithms in this environment and propose a novel context-aware extension of the existing literature, cMask. We demonstrate that context-aware MBRL algorithms generalize better to out-of-distribution adversary behaviors relative to context-free approaches. We also demonstrate that cMask displays strong generalization capabilities, as well as further performance improvement relative to other context-aware MBRL approaches when racing against adversaries with in-distribution behaviors.

While large language models (LLMs) are increasingly used as automated heuristic designers for vehicle routing problems (VRPs), current state-of-the-art methods predominantly rely on prompting massive, general-purpose models like GPT-4. This work challenges that paradigm by demonstrating that a smaller, specialized LLM, when meticulously fine-tuned, can generate components that surpass expert-crafted heuristics within advanced solvers. We propose RFTHGS, a novel Reinforcement learning (RL) framework for Fine-Tuning a small LLM to generate high-performance crossover operators for the Hybrid Genetic Search (HGS) solver, applied to the Capacitated VRP (CVRP). Our method employs a multi-tiered, curriculum-based reward function that progressively guides the LLM to master generating first compilable, then executable, and finally, superior-performing operators that exceed human expert designs. This is coupled with an operator caching mechanism that discourages plagiarism and promotes diversity during training. Comprehensive experiments show that our fine-tuned LLM produces crossover operators which significantly outperform the expert-designed ones in HGS. The performance advantage remains consistent, generalizing from small-scale instances to large-scale problems with up to 1000 nodes. Furthermore, RFTHGS exceeds the performance of leading neuro-combinatorial baselines, prompt-based methods, and commercial LLMs such as GPT-4o and GPT-4o-mini.

Priors are vital for planning under partial observability, yet difficult to obtain in practice. We present a sampling-based pipeline that leverages large-scale pretrained generative models to produce probabilistic priors capturing environmental uncertainty and spatio-semantic relationships in a zero-shot manner. Conditioned on partial observations, the pipeline recovers complete RGB-D point cloud samples with occupancy and target semantics, formulated to be directly useful in configuration-space planning. We establish a Matterport3D benchmark of rooms partially visible through doorways, where a robot must navigate to an unobserved target object. Effective priors for this setting must represent both occupancy and target-location uncertainty in unobserved regions. Experiments show that our approach recovers commonsense spatial semantics consistent with ground truth, yielding diverse, clean 3D point clouds usable in motion planning, highlight the promise of generative models as a rich source of priors for robotic planning.