This paper investigates infinite-horizon average reward Constrained Markov Decision Processes (CMDPs) with general parametrization. We propose a Primal-Dual Natural Actor-Critic algorithm that adeptly manages constraints while ensuring a high convergence rate. In particular, our algorithm achieves global convergence and constraint violation rates of $\tilde{\mathcal{O}}(1/\sqrt{T})$ over a horizon of length $T$ when the mixing time, $τ_{\mathrm{mix}}$, is known to the learner. In absence of knowledge of $τ_{\mathrm{mix}}$, the achievable rates change to $\tilde{\mathcal{O}}(1/T^{0.5-ε})$ provided that $T \geq \tilde{\mathcal{O}}\left(τ_{\mathrm{mix}}^{2/ε}\right)$. Our results match the theoretical lower bound for Markov Decision Processes and establish a new benchmark in the theoretical exploration of average reward CMDPs.

A large amount of work has been done in Multi-Agent Systems (MAS) for modeling and solving problems with multiple interacting agents. However, most LLMs are pretrained independently and not specifically optimized for coordination. For example, existing LLM fine-tuning frameworks rely on individual rewards, which require complex reward designs for each agent to encourage collaboration. To address this challenge, we model LLM collaboration as a cooperative Multi-Agent Reinforcement Learning (MARL) problem. We develop a multi-agent, multi-turn algorithm, Multi-Agent Group Relative Policy Optimization (MAGRPO), to solve it, building on current RL approaches for LLMs as well as MARL techniques. Our experiments on LLM writing and coding collaboration demonstrate that fine-tuning multiple LLMs with MAGRPO enables agents to generate high-quality responses efficiently through effective cooperation. Our approach opens the door to using MARL methods for LLM collaboration and highlights the associated challenges.

Since the 1990s, considerable empirical work has been carried out to train statistical models, such as neural networks (NNs), as learned heuristics for combinatorial optimization (CO) problems. When successful, such an approach eliminates the need for experts to design heuristics per problem type. Due to their structure, many hard CO problems are amenable to treatment through reinforcement learning (RL). Indeed, we find a wealth of literature training NNs using value-based, policy gradient, or actor-critic approaches, with promising results, both in terms of empirical optimality gaps and inference runtimes. Nevertheless, there has been a paucity of theoretical work undergirding the use of RL for CO problems. To this end, we introduce a unified framework to model CO problems through Markov decision processes (MDPs) and solve them using RL techniques. We provide easy-to-test assumptions under which CO problems can be formulated as equivalent undiscounted MDPs that provide optimal solutions to the original CO problems. Moreover, we establish conditions under which value-based RL techniques converge to approximate solutions of the CO problem with a guarantee on the associated optimality gap. Our convergence analysis provides: (1) a sufficient rate of increase in batch size and projected gradient descent steps at each RL iteration; (2) the resulting optimality gap in terms of problem parameters and targeted RL accuracy; and (3) the importance of a choice of state-space embedding. Together, our analysis illuminates the success (and limitations) of the celebrated deep Q-learning algorithm in this problem context.

In recent years, mixture cure models have gained increasing popularity in survival analysis as an alternative to the Cox proportional hazards model, particularly in settings where a subset of patients is considered cured. The proportional hazards mixture cure model is especially advantageous when the presence of a cured fraction can be reasonably assumed, providing a more accurate representation of long-term survival dynamics. In this study, we propose a novel hierarchical Bayesian framework for the semiparametric mixture cure model, which accommodates both the inclusion and exclusion of a frailty component, allowing for greater flexibility in capturing unobserved heterogeneity among patients. Samples from the posterior distribution are obtained using a Markov chain Monte Carlo method, leveraging a hierarchical structure inspired by Bayesian Lasso. Comprehensive simulation studies are conducted across diverse scenarios to evaluate the performance and robustness of the proposed models. Bayesian model comparison and assessment are performed using various criteria. Finally, the proposed approaches are applied to two well-known datasets in the cure model literature: the E1690 melanoma trial and a colon cancer clinical trial.

This paper proposes a novel diffusion-based posterior sampling method within a plug-and-play (PnP) framework. Our approach constructs a probability transport from an easy-to-sample terminal distribution to the target posterior, using a warm-start strategy to initialize the particles. To approximate the posterior score, we develop a Monte Carlo estimator in which particles are generated using Langevin dynamics, avoiding the heuristic approximations commonly used in prior work. The score governing the Langevin dynamics is learned from data, enabling the model to capture rich structural features of the underlying prior distribution. On the theoretical side, we provide non-asymptotic error bounds, showing that the method converges even for complex, multi-modal target posterior distributions. These bounds explicitly quantify the errors arising from posterior score estimation, the warm-start initialization, and the posterior sampling procedure. Our analysis further clarifies how the prior score-matching error and the condition number of the Bayesian inverse problem influence overall performance. Finally, we present numerical experiments demonstrating the effectiveness of the proposed method across a range of inverse problems.

Two pressing topics in the theory of deep learning are the interpretation of feature learning mechanisms and the determination of implicit bias of networks in the rich regime. Current theories of rich feature learning, often appear in the form of high-dimensional non-linear equations, which require computationally intensive numerical solutions. Given the many details that go into defining a deep learning problem, this complexity is a significant and often unavoidable challenge. Here, we propose a powerful heuristic route for predicting the data and width scales at which various patterns of feature learning emerge. This form of scale analysis is considerably simpler than exact theories and reproduces the scaling exponents of various known results. In addition, we make novel predictions on complex toy architectures, such as three-layer non-linear networks and attention heads, thus extending the scope of first-principle theories of deep learning.

Preliminary mission design of low-thrust spacecraft trajectories in the Circular Restricted Three-Body Problem is a global search characterized by a complex objective landscape and numerous local minima. Formulating the problem as sampling from an unnormalized distribution supported on neighborhoods of locally optimal solutions, provides the opportunity to deploy Markov chain Monte Carlo methods and generative machine learning. In this work, we extend our previous self-supervised diffusion model fine-tuning framework to employ gradient-informed Markov chain Monte Carlo. We compare two algorithms - the Metropolis-Adjusted Langevin Algorithm and Hamiltonian Monte Carlo - both initialized from a distribution learned by a diffusion model. Derivatives of an objective function that balances fuel consumption, time of flight and constraint violations are computed analytically using state transition matrices. We show that incorporating the gradient drift term accelerates mixing and improves convergence of the Markov chain for a multi-revolution transfer in the Saturn-Titan system. Among the evaluated methods, MALA provides the best trade-off between performance and computational cost. Starting from samples generated by a baseline diffusion model trained on a related transfer, MALA explicitly targets Pareto-optimal solutions. Compared to a random walk Metropolis algorithm, it increases the feasibility rate from 17.34% to 63.01% and produces a denser, more diverse coverage of the Pareto front. By fine-tuning a diffusion model on the generated samples and associated reward values with reward-weighted likelihood maximization, we learn the global solution structure of the problem and eliminate the need for a tedious separate data generation phase.

Recent advances in Multimodal Large Language Models (MLLMs) have enabled their use as intelligent agents for smartphone operation. However, existing methods depend on the Android Debug Bridge (ADB) for data transmission and action execution, limiting their applicability to Android devices. In this work, we introduce the novel Embodied Smartphone Operation (ESO) task and present See-Control, a framework that enables smartphone operation via direct physical interaction with a low-DoF robotic arm, offering a platform-agnostic solution. See-Control comprises three key components: (1) an ESO benchmark with 155 tasks and corresponding evaluation metrics; (2) an MLLM-based embodied agent that generates robotic control commands without requiring ADB or system back-end access; and (3) a richly annotated dataset of operation episodes, offering valuable resources for future research. By bridging the gap between digital agents and the physical world, See-Control provides a concrete step toward enabling home robots to perform smartphone-dependent tasks in realistic environments.

Understanding how humans respond to uncertainty is critical for designing safe and effective physical human-robot interaction (pHRI), as physically working with robots introduces multiple sources of uncertainty, including trust, comfort, and perceived safety. Conventional pHRI control frameworks typically build on optimal control theory, which assumes that human actions minimize a cost function; however, human behavior under uncertainty often departs from such optimal patterns. To address this gap, additional understanding of human behavior under uncertainty is needed. This pilot study implemented a physically coupled target-reaching task in which the robot delivered assistance or disturbances with systematically varied probabilities (10\% to 90\%). Analysis of participants' force inputs and decision-making strategies revealed two distinct behavioral clusters: a "trade-off" group that modulated their physical responses according to disturbance likelihood, and an "always-compensate" group characterized by strong risk aversion irrespective of probability. These findings provide empirical evidence that human decision-making in pHRI is highly individualized and that the perception of probability can differ to its true value. Accordingly, the study highlights the need for more interpretable behavioral models, such as cumulative prospect theory (CPT), to more accurately capture these behaviors and inform the design of future adaptive robot controllers.

The deployment of Unmanned Aerial Vehicle (UAV) swarms as dynamic communication relays is critical for next-generation tactical networks. However, operating in contested environments requires solving a complex trade-off, including maximizing system throughput while ensuring collision avoidance and resilience against adversarial jamming. Existing heuristic-based approaches often struggle to find effective solutions due to the dynamic and multi-objective nature of this problem. This paper formulates this challenge as a cooperative Multi-Agent Reinforcement Learning (MARL) problem, solved using the Centralized Training with Decentralized Execution (CTDE) framework. Our approach employs a centralized critic that uses global state information to guide decentralized actors which operate using only local observations. Simulation results show that our proposed framework significantly outperforms heuristic baselines, increasing the total system throughput by approximately 50% while simultaneously achieving a near-zero collision rate. A key finding is that the agents develop an emergent anti-jamming strategy without explicit programming. They learn to intelligently position themselves to balance the trade-off between mitigating interference from jammers and maintaining effective communication links with ground users.