We study online convex optimisation on ℓp-balls in Rd for p > 2. While always sub-linear, the optimal regret exhibits a shift between the high-dimensional setting (d > T), when the dimension d is greater than the time horizon T and the low-dimensional setting (d T). We show that Follow-the-Regularised-Leader (FTRL) with time-varying regularisation which is adaptive to the dimension regime is anytime optimal for all dimension regimes. Motivated by this, we ask whether it is possible to obtain anytime optimality of FTRL with fixed non-adaptive regularisation. Our main result establishes that for separable regularisers, adaptivity in the regulariser is necessary, and that any fixed regulariser will be sub-optimal in one of the two dimension regimes. Finally, we provide lower bounds which rule out sublinear regret bounds for the linear bandit problem in sufficiently high-dimension for all ℓp-balls with p 1.

The law of supply and demand asserts that in a perfectly competitive market, the price of a good adjusts to a market clearing price. In a market clearing price p the number of sellers willing to sell the good at p equals the number of sellers willing to buy the good at price p . In this work, we provide a mathematical foundation on the law of supply and demand through the lens of online learning. Specifically, we demonstrate that if each seller employs a no-swap regret algorithm to set their individual selling price--aiming to maximize its individual revenue--the collective pricing dynamics converge to the market-clearing price p . Our findings offer a novel perspective on the law of supply and demand, framing it as the emergent outcome of an adaptive learning processes among sellers.

Online reinforcement learning (RL) with complex function approximations such as transformers and deep neural networks plays a significant role in the modern practice of artificial intelligence. Despite its popularity and importance, balancing the fundamental trade-off between exploration and exploitation remains a longstanding challenge; in particular, we are still in lack of efficient and practical schemes that are backed by theoretical performance guarantees. Motivated by recent developments in exploration via optimistic regularization, this paper provides an interpretation of the principle of optimism through the lens of primal-dual optimization. From this fresh perspective, we set forth a new value-incentivized actor-critic (VAC) method, which optimizes a single easy-to-optimize objective integrating exploration and exploitation -- it promotes state-action and policy estimates that are both consistent with collected data transitions and result in higher value functions. Theoretically, the proposed VAC method has near-optimal regret guarantees under linear Markov decision processes (MDPs) in both finite-horizon and infinite-horizon settings, which can be extended to the general function approximation setting under appropriate assumptions.

The evolution of the human brain has led to the development of complex synaptic plasticity, enabling dynamic adaptation to a constantly evolving world.

Causal discovery for dynamical systems poses a major challenge in fields where active interventions are infeasible. Most methods used to investigate these systems and their associated benchmarks are tailored to deterministic, low-dimensional and weakly nonlinear time-series data. To address these limitations, we present CausalDynamics, a large-scale benchmark and extensible data generation framework to advance the structural discovery of dynamical causal models. Our benchmark consists of true causal graphs derived from thousands of both linearly and nonlinearly coupled ordinary and stochastic differential equations as well as two idealized climate models. We perform a comprehensive evaluation of state-of-the-art causal discovery algorithms for graph reconstruction on systems with noisy, confounded, and lagged dynamics. CausalDynamics consists of a plug-and-play, build-yourown coupling workflow that enables the construction of a hierarchy of physical systems. We anticipate that our framework will facilitate the development of robust causal discovery algorithms that are broadly applicable across domains while addressing their unique challenges. We provide a user-friendly implementation and documentation on https://kausable.github.io/CausalDynamics.

Ultrasound (US) is a widely used medical imaging modality due to its real-time capabilities, non-invasive nature, and cost-effectiveness. Robotic ultrasound can further enhance its utility by reducing operator dependence and improving access to complex anatomical regions. For this, while deep reinforcement learning (DRL) and imitation learning (IL) have shown potential for autonomous navigation, their use in complex surgical tasks such as anatomy reconstruction and surgical guidance remains limited -- largely due to the lack of realistic and efficient simulation environments tailored to these tasks. We introduce SonoGym, a scalable simulation platform for complex robotic ultrasound tasks that enables parallel simulation across tens to hundreds of environments. Our framework supports realistic and real-time simulation of US data from CT-derived 3D models of the anatomy through both a physics-based and a generative modeling approach.

Industrial anomaly segmentation relies heavily on pixel-level annotations, yet real-world anomalies are often scarce, diverse, and costly to label. Segmentationoriented industrial anomaly synthesis (SIAS) has emerged as a promising alternative; however, existing methods struggle to balance sampling efficiency and generation quality. Moreover, most approaches treat all spatial regions uniformly, overlooking the distinct statistical differences between anomaly and background areas. This uniform treatment hinders the synthesis of controllable, structure-specific anomalies tailored for segmentation tasks. In this paper, we propose FAST, a foreground-aware diffusion framework featuring two novel modules: the AnomalyInformed Accelerated Sampling (AIAS) and the Foreground-Aware Reconstruction Module (FARM). AIAS is a training-free sampling algorithm specifically designed for segmentation-oriented industrial anomaly synthesis, which accelerates the reverse process through coarse-to-fine aggregation and enables the synthesis of state-of-the-art segmentation-oriented anomalies in as few as 10 steps. Meanwhile, FARM adaptively adjusts the anomaly-aware noise within the masked foreground regions at each sampling step, preserving localized anomaly signals throughout the denoising trajectory. Extensive experiments on multiple industrial benchmarks demonstrate that FAST consistently outperforms existing anomaly synthesis methods in downstream segmentation tasks.

Police in Poland are investigating the execution-style murder of a Russian artist and vocal critic of President Vladimir Putin. Polish prosecutors said Robert K, known as the artist Semyon Skrepetsky, was shot dead on Monday morning in the Polish city of Biała Podlaska, about 40km (25 miles) from the Belarusian border. The 44-year-old was shot five times in the head, chest and back in a car park in the city, located about 600m from the Belarusian consulate. He was known for his caricatures of politicians, including Putin, Belarusian leader Alexander Lukashenko and Chechen leader Ramzan Kadyrov. Marcin Kozak, spokesman for the District Prosecutor's Office in Lublin, said the artist was approached by an unidentified gunman who fired two shots at him.

Distinguishing visually similar objects by their motion remains a critical challenge in computer vision. Although supervised trackers show promise, contemporary self-supervised trackers struggle when visual cues become ambiguous, limiting their scalability and generalization without extensive labeled data. We find that pretrained video diffusion models inherently learn motion representations suitable for tracking without task-specific training. This ability arises because their denoising process isolates motion in early, high-noise stages, distinct from later appearance refinement. Capitalizing on this discovery, our self-supervised tracker significantly improves performance in distinguishing visually similar objects, an underexplored failure point for existing methods. Our method achieves up to a 6-point improvement over recent self-supervised approaches on established benchmarks and our newly introduced tests focused on tracking visually similar items. Visualizations confirm that these diffusion-derived motion representations enable robust tracking of even identical objects across challenging viewpoint changes and deformations.

While vision-language-action models (VLAs) have shown promising robotic behaviors across a diverse set of manipulation tasks, they achieve limited success rates when deployed on novel tasks out of the box. To allow these policies to safely interact with their environments, we need a failure detector that gives a timely alert such that the robot can stop, backtrack, or ask for help. However, existing failure detectors are trained and tested only on one or a few specific tasks, while generalist VLAs require the detector to generalize and detect failures also in unseen tasks and novel environments. In this paper, we introduce the multitask failure detection problem and propose SAFE, a failure detector for generalist robot policies such as VLAs. We analyze the VLA feature space and find that VLAs have sufficient highlevel knowledge about task success and failure, which is generic across different tasks.