Large language models (LLMs) have demonstrated emergent in-context learning (ICL) capabilities across a range of tasks, including zero-shot time-series forecasting. We show that text-trained foundation models can accurately extrapolate spatiotemporal dynamics from discretized partial differential equation (PDE) solutions without fine-tuning or natural language prompting. Predictive accuracy improves with longer temporal contexts but degrades at finer spatial discretizations. In multi-step rollouts, where the model recursively predicts future spatial states over multiple time steps, errors grow algebraically with the time horizon, reminiscent of global error accumulation in classical finite-difference solvers. We interpret these trends as in-context neural scaling laws, where prediction quality varies predictably with both context length and output length. To better understand how LLMs are able to internally process PDE solutions so as to accurately roll them out, we analyze token-level output distributions and uncover a consistent three-stage ICL progression: beginning with syntactic pattern imitation, transitioning through an exploratory high-entropy phase, and culminating in confident, numerically grounded predictions.

Existing benchmarks in e-commerce primarily focus on basic user intents, such as finding or purchasing products. However, real-world users often pursue more complex goals, such as applying vouchers, managing budgets, and finding multi-products seller. To bridge this gap, we propose ShoppingBench, a novel end-to-end shopping benchmark designed to encompass increasingly challenging levels of grounded intent. Specifically, we propose a scalable framework to simulate user instructions based on various intents derived from sampled real-world products. To facilitate consistent and reliable evaluations, we provide a large-scale shopping sandbox that serves as an interactive simulated environment, incorporating over 2.5 million real-world products. Experimental results demonstrate that even state-of-the-art language agents (such as GPT-4.1) achieve absolute success rates under 50% on our benchmark tasks, highlighting the significant challenges posed by our ShoppingBench. In addition, we propose a trajectory distillation strategy and leverage supervised fine-tuning, along with reinforcement learning on synthetic trajectories, to distill the capabilities of a large language agent into a smaller one. As a result, our trained agent achieves competitive performance compared to GPT-4.1.

Quantum Boltzmann machines (QBMs) are generative models with potential advantages in quantum machine learning, yet their training is fundamentally limited by the barren plateau problem, where gradients vanish exponentially with system size. We introduce a quantum version of the em algorithm, an information-geometric generalization of the classical Expectation-Maximization method, which circumvents gradient-based optimization on non-convex functions. Implemented on a semi-quantum restricted Boltzmann machine (sqRBM) -- a hybrid architecture with quantum effects confined to the hidden layer -- our method achieves stable learning and outperforms gradient descent on multiple benchmark datasets. These results establish a structured and scalable alternative to gradient-based training in QML, offering a pathway to mitigate barren plateaus and enhance quantum generative modeling.

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.

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.

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.

The growing prevalence of artificial intelligence (AI) in various applications underscores the need for agents that can successfully navigate and adapt to an ever-changing, open-ended world. A key challenge is ensuring these AI agents are robust, excelling not only in familiar settings observed during training but also effectively generalising to previously unseen and varied scenarios. In this thesis, we harness methodologies from open-endedness and multi-agent learning to train and evaluate robust AI agents capable of generalising to novel environments, out-of-distribution inputs, and interactions with other co-player agents. We begin by introducing MiniHack, a sandbox framework for creating diverse environments through procedural content generation. Based on the game of NetHack, MiniHack enables the construction of new tasks for reinforcement learning (RL) agents with a focus on generalisation. We then present Maestro, a novel approach for generating adversarial curricula that progressively enhance the robustness and generality of RL agents in two-player zero-sum games. We further probe robustness in multi-agent domains, utilising quality-diversity methods to systematically identify vulnerabilities in state-of-the-art, pre-trained RL policies within the complex video game football domain, characterised by intertwined cooperative and competitive dynamics. Finally, we extend our exploration of robustness to the domain of LLMs. Here, our focus is on diagnosing and enhancing the robustness of LLMs against adversarial prompts, employing evolutionary search to generate a diverse range of effective inputs that aim to elicit undesirable outputs from an LLM. This work collectively paves the way for future advancements in AI robustness, enabling the development of agents that not only adapt to an ever-evolving world but also thrive in the face of unforeseen challenges and interactions.