We introduce a Markov Chain Monte Carlo (MCMC) algorithm that dramatically accelerates the simulation of quantum many-body systems, a grand challenge in computational science. State-of-the-art methods for these problems are severely limited by $O(N^3)$ computational complexity. Our method avoids this bottleneck, achieving near-linear $O(N \log N)$ scaling per sweep. Our approach samples a joint probability measure over two coupled variable sets: (1) particle trajectories of the fundamental fermions, and (2) auxiliary variables that decouple fermion interactions. The key innovation is a novel transition kernel for particle trajectories formulated in the Fourier domain, revealing the transition probability as a convolution that enables massive acceleration via the Fast Fourier Transform (FFT). The auxiliary variables admit closed-form, factorized conditional distributions, enabling efficient exact Gibbs sampling update. We validate our algorithm on benchmark quantum physics problems, accurately reproducing known theoretical results and matching traditional $O(N^3)$ algorithms on $32\times 32$ lattice simulations at a fraction of the wall-clock time, empirically demonstrating $N \log N$ scaling. By reformulating a long-standing physics simulation problem in machine learning language, our work provides a powerful tool for large-scale probabilistic inference and opens avenues for physics-inspired generative models.

We study the problem of minimizing non-convex functionals on the space of probability measures, regularized by the relative entropy (KL divergence) with respect to a fixed reference measure, as well as the corresponding problem of solving entropy-regularized non-convex-non-concave min-max problems. We utilize the Best Response flow (also known in the literature as the fictitious play flow) and study how its convergence is influenced by the relation between the degree of non-convexity of the functional under consideration, the regularization parameter and the tail behaviour of the reference measure. In particular, we demonstrate how to choose the regularizer, given the non-convex functional, so that the Best Response operator becomes a contraction with respect to the $L^1$-Wasserstein distance, which ensures the existence of its unique fixed point that is then shown to be the unique global minimizer for our optimization problem. This extends recent results where the Best Response flow was applied to solve convex optimization problems regularized by the relative entropy with respect to arbitrary reference measures, and with arbitrary values of the regularization parameter. Our results explain precisely how the assumption of convexity can be relaxed, at the expense of making a specific choice of the regularizer. Additionally, we demonstrate how these results can be applied in reinforcement learning in the context of policy optimization for Markov Decision Processes and Markov games with softmax parametrized policies in the mean-field regime.

Standard imitation learning (IL) methods have achieved considerable success in robotics, yet often rely on the Markov assumption, which falters in long-horizon tasks where history is crucial for resolving perceptual ambiguity. This limitation stems not only from a conceptual gap but also from a fundamental computational barrier: prevailing architectures like Transformers are often constrained by quadratic complexity, rendering the processing of long, high-dimensional observation sequences infeasible. To overcome this dual challenge, we introduce Mamba Temporal Imitation Learning (MTIL). Our approach represents a new paradigm for robotic learning, which we frame as a practical synthesis of World Model and Dynamical System concepts. By leveraging the linear-time recurrent dynamics of State Space Models (SSMs), MTIL learns an implicit, action-oriented world model that efficiently encodes the entire trajectory history into a compressed, evolving state. This allows the policy to be conditioned on a comprehensive temporal context, transcending the confines of Markovian approaches. Through extensive experiments on simulated benchmarks (ACT, Robomimic, LIBERO) and on challenging real-world tasks, MTIL demonstrates superior performance against SOTA methods like ACT and Diffusion Policy, particularly in resolving long-term temporal ambiguities. Our findings not only affirm the necessity of full temporal context but also validate MTIL as a powerful and a computationally feasible approach for learning long-horizon, non-Markovian behaviors from high-dimensional observations.

Stochastic games have become a prevalent framework for studying long-term multi-agent interactions, especially in the context of multi-agent reinforcement learning. In this work, we comprehensively investigate the concept of constant-memory strategies in stochastic games. We first establish some results on best responses and Nash equilibria for behavioral constant-memory strategies, followed by a discussion on the computational hardness of best responding to mixed constant-memory strategies. Those theoretic insights are later verified on several sequential decision-making testbeds, including the $\textit{Iterated Prisoner's Dilemma}$, the $\textit{Iterated Traveler's Dilemma}$, and the $\textit{Pursuit}$ domain. This work aims to enhance the understanding of theoretical issues in single-agent planning under multi-agent systems, and uncover the connection between decision models in single-agent and multi-agent contexts. The code is available at $\texttt{https://github.com/Fernadoo/Const-Mem.}$

The increasing number of satellites and orbital debris has made space congestion a critical issue, threatening satellite safety and sustainability. Challenges such as collision avoidance, station-keeping, and orbital maneuvering require advanced techniques to handle dynamic uncertainties and multi-agent interactions. Reinforcement learning (RL) has shown promise in this domain, enabling adaptive, autonomous policies for space operations; however, many existing RL frameworks rely on custom-built environments developed from scratch, which often use simplified models and require significant time to implement and validate the orbital dynamics, limiting their ability to fully capture real-world complexities. To address this, we introduce OrbitZoo, a versatile multi-agent RL environment built on a high-fidelity industry standard library, that enables realistic data generation, supports scenarios like collision avoidance and cooperative maneuvers, and ensures robust and accurate orbital dynamics. The environment is validated against a real satellite constellation, Starlink, achieving a Mean Absolute Percentage Error (MAPE) of 0.16% compared to real-world data. This validation ensures reliability for generating high-fidelity simulations and enabling autonomous and independent satellite operations.

Generative AI systems are increasingly assisting and acting on behalf of end users in practical settings, from digital shopping assistants to next-generation autonomous cars. In this context, safety is no longer about blocking harmful content, but about preempting downstream hazards like financial or physical harm. Yet, most AI guardrails continue to rely on output classification based on labeled datasets and human-specified criteria,making them brittle to new hazardous situations. Even when unsafe conditions are flagged, this detection offers no path to recovery: typically, the AI system simply refuses to act--which is not always a safe choice. In this work, we argue that agentic AI safety is fundamentally a sequential decision problem: harmful outcomes arise from the AI system's continually evolving interactions and their downstream consequences on the world. We formalize this through the lens of safety-critical control theory, but within the AI model's latent representation of the world. This enables us to build predictive guardrails that (i) monitor an AI system's outputs (actions) in real time and (ii) proactively correct risky outputs to safe ones, all in a model-agnostic manner so the same guardrail can be wrapped around any AI model. We also offer a practical training recipe for computing such guardrails at scale via safety-critical reinforcement learning. Our experiments in simulated driving and e-commerce settings demonstrate that control-theoretic guardrails can reliably steer LLM agents clear of catastrophic outcomes (from collisions to bankruptcy) while preserving task performance, offering a principled dynamic alternative to today's flag-and-block guardrails.

Although average gain optimality is a commonly adopted performance measure in Markov Decision Processes (MDPs), it is often too asymptotic. Further incorporating measures of immediate losses leads to the hierarchy of bias optimalities, all the way up to Blackwell optimality. In this paper, we investigate the problem of identifying policies of such optimality orders. To that end, for each order, we construct a learning algorithm with vanishing probability of error. Furthermore, we characterize the class of MDPs for which identification algorithms can stop in finite time. That class corresponds to the MDPs with a unique Bellman optimal policy, and does not depend on the optimality order considered. Lastly, we provide a tractable stopping rule that when coupled to our learning algorithm triggers in finite time whenever it is possible to do so.

Multi-Agent Deep Reinforcement Learning (MADRL) has shown potential for cooperative and competitive tasks such as autonomous driving and strategic gaming. However, models trained by MADRL are vulnerable to adversarial perturbations on states and actions. Therefore, it is essential to investigate the robustness of MADRL models from an attack perspective. Existing studies focus on either state-only attacks or action-only attacks, but do not consider how to effectively joint them. Simply combining state and action perturbations such as randomly perturbing states and actions does not exploit their potential synergistic effects. In this paper, we propose the State-Action Joint Attack (SAJA) framework that has a good synergistic effects. SAJA consists of two important phases: (1) In the state attack phase, a multi-step gradient ascent method utilizes both the actor network and the critic network to compute an adversarial state, and (2) in the action attack phase, based on the perturbed state, a second gradient ascent uses the critic network to craft the final adversarial action. Additionally, a heuristic regularizer measuring the distance between the perturbed actions and the original clean ones is added into the loss function to enhance the effectiveness of the critic's guidance. We evaluate SAJA in the Multi-Agent Particle Environment (MPE), demonstrating that (1) it outperforms and is more stealthy than state-only or action-only attacks, and (2) existing state or action defense methods cannot defend its attacks.

A fundamental limitation of current AI agents is their inability to learn complex skills on the fly at test time, often behaving like "clever but clueless interns" in novel environments. This severely limits their practical utility. To systematically measure and drive progress on this challenge, we first introduce the Jericho Test-Time Learning (J-TTL) benchmark. J-TTL is a new evaluation setup where an agent must play the same game for several consecutive episodes, attempting to improve its performance from one episode to the next. On J-TTL, we find that existing adaptation methods like reflection, memory, or reinforcement learning struggle. To address the challenges posed by our benchmark, we present EvoTest, an evolutionary test-time learning framework that improves an agent without any fine-tuning or gradients-by evolving the entire agentic system after every episode. EvoTest has two roles: the Actor Agent, which plays the game, and the Evolver Agent, which analyzes the episode transcript to propose a revised configuration for the next run. This configuration rewrites the prompt, updates memory by logging effective state-action choices, tunes hyperparameters, and learns the tool-use routines. On our J-TTL benchmark, EvoTest consistently increases performance, outperforming not only reflection and memory-only baselines but also more complex online fine-tuning methods. Notably, our method is the only one capable of winning two games (Detective and Library), while all baselines fail to win any.

We compare Ising ({-1,+1}) and QUBO ({0,1}) encodings for Boltzmann machine learning under a controlled protocol that fixes the model, sampler, and step size. Exploiting the identity that the Fisher information matrix (FIM) equals the covariance of sufficient statistics, we visualize empirical moments from model samples and reveal systematic, representation-dependent differences. QUBO induces larger cross terms between first- and second-order statistics, creating more small-eigenvalue directions in the FIM and lowering spectral entropy. This ill-conditioning explains slower convergence under stochastic gradient descent (SGD). In contrast, natural gradient descent (NGD)-which rescales updates by the FIM metric-achieves similar convergence across encodings due to reparameterization invariance. Practically, for SGD-based training, the Ising encoding provides more isotropic curvature and faster convergence; for QUBO, centering/scaling or NGD-style preconditioning mitigates curvature pathologies. These results clarify how representation shapes information geometry and finite-time learning dynamics in Boltzmann machines and yield actionable guidelines for variable encoding and preprocessing.