We introduce theoretically grounded Continuous Semi-Quantum Boltzmann Machines (CSQBMs) that supports continuous-action reinforcement learning. By combining exponential-family priors over visible units with quantum Boltzmann distributions over hidden units, CSQBMs yield a hybrid quantum-classical model that reduces qubit requirements while retaining strong expressiveness. Crucially, gradients with respect to continuous variables can be computed analytically, enabling direct integration into Actor-Critic algorithms. Building on this, we propose a continuous Q-learning framework that replaces global maximization by efficient sampling from the CSQBM distribution, thereby overcoming instability issues in continuous control.

Building Behavioral Foundation Models (BFMs) for humanoid robots has the potential to unify diverse control tasks under a single, promptable generalist policy. However, existing approaches are either exclusively deployed on simulated humanoid characters, or specialized to specific tasks such as tracking. We propose BFM-Zero, a framework that learns an effective shared latent representation that embeds motions, goals, and rewards into a common space, enabling a single policy to be prompted for multiple downstream tasks without retraining. This well-structured latent space in BFM-Zero enables versatile and robust whole-body skills on a Unitree G1 humanoid in the real world, via diverse inference methods, including zero-shot motion tracking, goal reaching, and reward optimization, and few-shot optimization-based adaptation. Unlike prior on-policy reinforcement learning (RL) frameworks, BFM-Zero builds upon recent advancements in unsupervised RL and Forward-Backward (FB) models, which offer an objective-centric, explainable, and smooth latent representation of whole-body motions. We further extend BFM-Zero with critical reward shaping, domain randomization, and history-dependent asymmetric learning to bridge the sim-to-real gap. Those key design choices are quantitatively ablated in simulation. A first-of-its-kind model, BFM-Zero establishes a step toward scalable, promptable behavioral foundation models for whole-body humanoid control.

Humanoid soccer poses a representative challenge for embodied intelligence, requiring robots to operate within a tightly coupled perception-action loop. However, existing systems typically rely on decoupled modules, resulting in delayed responses and incoherent behaviors in dynamic environments, while real-world perceptual limitations further exacerbate these issues. In this work, we present a unified reinforcement learning-based controller that enables humanoid robots to acquire reactive soccer skills through the direct integration of visual perception and motion control. Our approach extends Adversarial Motion Priors to perceptual settings in real-world dynamic environments, bridging motion imitation and visually grounded dynamic control. We introduce an encoder-decoder architecture combined with a virtual perception system that models real-world visual characteristics, allowing the policy to recover privileged states from imperfect observations and establish active coordination between perception and action. The resulting controller demonstrates strong reactivity, consistently executing coherent and robust soccer behaviors across various scenarios, including real RoboCup matches.

We address the problem of quickest change detection in Markov processes with unknown transition kernels. The key idea is to learn the conditional score $\nabla_{\mathbf{y}} \log p(\mathbf{y}|\mathbf{x})$ directly from sample pairs $( \mathbf{x},\mathbf{y})$, where both $\mathbf{x}$ and $\mathbf{y}$ are high-dimensional data generated by the same transition kernel. In this way, we avoid explicit likelihood evaluation and provide a practical way to learn the transition dynamics. Based on this estimation, we develop a score-based CUSUM procedure that uses conditional Hyvarinen score differences to detect changes in the kernel. To ensure bounded increments, we propose a truncated version of the statistic. With Hoeffding's inequality for uniformly ergodic Markov processes, we prove exponential lower bounds on the mean time to false alarm. We also prove asymptotic upper bounds on detection delay. These results give both theoretical guarantees and practical feasibility for score-based detection in high-dimensional Markov models.

Low-rank structure is a common implicit assumption in many modern reinforcement learning (RL) algorithms. For instance, reward-free and goal-conditioned RL methods often presume that the successor measure admits a low-rank representation. In this work, we challenge this assumption by first remarking that the successor measure itself is not approximately low-rank. Instead, we demonstrate that a low-rank structure naturally emerges in the shifted successor measure, which captures the system dynamics after bypassing a few initial transitions. We provide finite-sample performance guarantees for the entry-wise estimation of a low-rank approximation of the shifted successor measure from sampled entries. Our analysis reveals that both the approximation and estimation errors are primarily governed by a newly introduced quantitity: the spectral recoverability of the corresponding matrix. To bound this parameter, we derive a new class of functional inequalities for Markov chains that we call Type II Poincaré inequalities and from which we can quantify the amount of shift needed for effective low-rank approximation and estimation. This analysis shows in particular that the required shift depends on decay of the high-order singular values of the shifted successor measure and is hence typically small in practice. Additionally, we establish a connection between the necessary shift and the local mixing properties of the underlying dynamical system, which provides a natural way of selecting the shift. Finally, we validate our theoretical findings with experiments, and demonstrate that shifting the successor measure indeed leads to improved performance in goal-conditioned RL.

The exponential growth of Low Earth Orbit (LEO) satellites has revolutionised Earth Observation (EO) missions, addressing challenges in climate monitoring, disaster management, and more. However, autonomous coordination in multi-satellite systems remains a fundamental challenge. Traditional optimisation approaches struggle to handle the real-time decision-making demands of dynamic EO missions, necessitating the use of Reinforcement Learning (RL) and Multi-Agent Reinforcement Learning (MARL). In this paper, we investigate RL-based autonomous EO mission planning by modelling single-satellite operations and extending to multi-satellite constellations using MARL frameworks. We address key challenges, including energy and data storage limitations, uncertainties in satellite observations, and the complexities of decentralised coordination under partial observability. By leveraging a near-realistic satellite simulation environment, we evaluate the training stability and performance of state-of-the-art MARL algorithms, including PPO, IPPO, MAPPO, and HAPPO. Our results demonstrate that MARL can effectively balance imaging and resource management while addressing non-stationarity and reward interdependency in multi-satellite coordination. The insights gained from this study provide a foundation for autonomous satellite operations, offering practical guidelines for improving policy learning in decentralised EO missions.

This paper addresses a motion planning problem to achieve spatio-temporal-logical tasks, expressed by syntactically co-safe linear temporal logic specifications (scLTL\next), in uncertain environments. Here, the uncertainty is modeled as some probabilistic knowledge on the semantic labels of the environment. For example, the task is "first go to region 1, then go to region 2"; however, the exact locations of regions 1 and 2 are not known a priori, instead a probabilistic belief is available. We propose a novel automata-theoretic approach, where a special product automaton is constructed to capture the uncertainty related to semantic labels, and a reward function is designed for each edge of this product automaton. The proposed algorithm utilizes value iteration for online replanning. We show some theoretical results and present some simulations/experiments to demonstrate the efficacy of the proposed approach.

Large language models (LLMs) achieve strong performance across benchmarks--from knowledge quizzes and math reasoning to web-agent tasks--but these tests occur in static settings, lacking real dynamics and uncertainty. Consequently, they evaluate isolated reasoning or problem-solving rather than decision-making under uncertainty. To address this, we introduce LiveTradeBench, a live trading environment for evaluating LLM agents in realistic and evolving markets. LiveTradeBench follows three design principles: (i) Live data streaming of market prices and news, eliminating dependence on offline backtesting and preventing information leakage while capturing real-time uncertainty; (ii) a portfolio-management abstraction that extends control from single-asset actions to multi-asset allocation, integrating risk management and cross-asset reasoning; and (iii) multi-market evaluation across structurally distinct environments--U.S. stocks and Polymarket prediction markets--differing in volatility, liquidity, and information flow. At each step, an agent observes prices, news, and its portfolio, then outputs percentage allocations that balance risk and return. Using LiveTradeBench, we run 50-day live evaluations of 21 LLMs across families. Results show that (1) high LMArena scores do not imply superior trading outcomes; (2) models display distinct portfolio styles reflecting risk appetite and reasoning dynamics; and (3) some LLMs effectively leverage live signals to adapt decisions. These findings expose a gap between static evaluation and real-world competence, motivating benchmarks that test sequential decision making and consistency under live uncertainty.

Abstract-- Multi-legged robots offer enhanced stability to navigate complex terrains with their multiple legs interacting with the environment. However, how to effectively coordinate the multiple legs in a larger action exploration space to generate natural and robust movements is a key issue. In this paper, we introduce a motion prior-based approach, successfully applying deep reinforcement learning algorithms to a real hexapod robot. We generate a dataset of optimized motion priors, and train an adversarial discriminator based on the priors to guide the hexapod robot to learn natural gaits. The learned policy is then successfully transferred to a real hexapod robot, and demonstrate natural gait patterns and remarkable robustness without visual information in complex terrains. This is the first time that a reinforcement learning controller has been used to achieve complex terrain walking on a real hexapod robot.

The analysis and control of stochastic dynamical systems rely on probabilistic models such as (continuous-space) Markov decision processes, but large or continuous state spaces make exact analysis intractable and call for principled quantitative abstraction. This work develops a unified theory of such abstraction by integrating category theory, coalgebra, quantitative logic, and optimal transport, centred on a canonical $\varepsilon$-quotient of the behavioral pseudo-metric with a universal property: among all abstractions that collapse behavioral differences below $\varepsilon$, it is the most detailed, and every other abstraction achieving the same discounted value-loss guarantee factors uniquely through it. Categorically, a quotient functor $Q_\varepsilon$ from a category of probabilistic systems to a category of metric specifications admits, via the Special Adjoint Functor Theorem, a right adjoint $R_\varepsilon$, yielding an adjunction $Q_\varepsilon \dashv R_\varepsilon$ that formalizes a duality between abstraction and realization; logically, a quantitative modal $μ$-calculus with separate reward and transition modalities is shown, for a broad class of systems, to be expressively complete for the behavioral pseudo-metric, with a countable fully abstract fragment suitable for computation. The theory is developed coalgebraically over Polish spaces and the Giry monad and validated on finite-state models using optimal-transport solvers, with experiments corroborating the predicted contraction properties and structural stability and aligning with the theoretical value-loss bounds, thereby providing a rigorous foundation for quantitative state abstraction and representation learning in probabilistic domains.