Luigi Mangione has admitted to killing UnitedHealthcare CEO Brian Thompson after pleading guilty to federal charges of interstate stalking resulting in death. I shot Mr Thompson in Manhattan and he died, the 28-year-old admitted in Manhattan federal court on Friday. Thompson, a 50-year-old father of two, was shot from behind on 4 December, 2024 as he walked into a hotel in midtown Manhattan. Following the plea hearing, his family issued a statement calling it an important step toward justice for Brian and for our family. Mangione faces a maximum sentence of life in prison.

'I shot Mr Thompson'- What it was like inside court as Mangione pleaded guilty To play this video you need to enable JavaScript in your browser. After more than a year-and-a-half of intense spectacle and legal wrangling, Luigi Mangione appeared in a federal courtroom in New York on Friday as rumours swirled that he may plead guilty. The 28-year-old, accused of shooting dead UnitedHealthcare chief executive Brian Thompson on a Manhattan street in December 2024, arrived wearing a beige prison uniform with a white T-shirt underneath. His feet were shackled and he held his hands behind his back, although US marshals had not handcuffed him. A crowd of press, supporters of Mangione, observers, and a handful of court staff members who had won a lottery to attend gathered in the packed courtroom.

For years now, executives at companies that are pouring hundreds of billions of dollars a year into developing various artificial intelligence tools have insisted that the technology will ultimately mean people will spend less of their time working. An engineering director at Google said four years ago that AI would deliver a four-day work week by 2025, external . Earlier this year, and just one year after that engineering director's prediction, OpenAI took up the challenge, in a manner of speaking. It formally urged companies to start testing out a four-day work week (with no change in pay), claiming that AI will soon be able to speed up so much human labour that the corporate world should prepare itself. However, a former OpenAI technical employee who left the company last year told the BBC the firm never actually trialled the four-day work week it suggested others should try while they were there.

Since WIRED reported on Meta's NameTag face recognition system, company executives have made confusing and conflicting remarks about its very existence. Does a software feature exist if its code has been deployed to the devices of millions of people but they can't use it yet? Not if you work at Meta . The company's executives have spent the last few weeks making this semantic argument about NameTag, the in-development face-recognition system that Meta built for its smart glasses . The inevitable result is confusion, but that's easy enough to clear up.

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Efficient online decision-making in contextual bandits is challenging, as methods without informative priors often suffer from computational or statistical inefficiencies. In this work, we leverage pre-trained diffusion models as expressive priors to capture complex action dependencies and develop a practical algorithm that efficiently approximates posteriors under such priors, enabling both fast updates and sampling. Empirical results demonstrate the effectiveness and versatility of our approach across diverse contextual bandit settings.

Recent advances in generative artificial intelligence (GenAI) models have enabled the generation of personalized content that adapts to up-to-date user context. While personalized decision systems are often modeled using bandit formulations, the integration of GenAI introduces new structure into otherwise classical sequential learning problems. In GenAI-powered interventions, the agent selects a query, but the environment experiences a stochastic response drawn from the generative model. Standard bandit methods do not explicitly account for this structure, where actions influence rewards only through stochastic, observed treatments. We introduce generator-mediated bandit-Thompson sampling (GAMBITTS), a bandit approach designed for this action/treatment split, using mobile health interventions with large language model-generated text as a motivating case study. GAMBITTS explicitly models both the treatment and reward generation processes, using information in the delivered treatment to accelerate policy learning relative to standard methods. We establish regret bounds for GAMBITTS by decomposing sources of uncertainty in treatment and reward, identifying conditions where it achieves stronger guarantees than standard bandit approaches. In simulation studies, GAMBITTS consistently outperforms conventional algorithms by leveraging observed treatments to more accurately estimate expected rewards.

We propose an extension of Thompson sampling to optimization problems over function spaces where the objective is a known functional of an unknown operator's output. We assume that queries to the operator (such as running a high-fidelity simulator or physical experiment) are costly, while functional evaluations on the operator's output are inexpensive. Our algorithm employs a sample-then-optimize approach using neural operator surrogates. This strategy avoids explicit uncertainty quantification by treating trained neural operators as approximate samples from a Gaussian process (GP) posterior. We derive regret bounds and theoretical results connecting neural operators with GPs in infinite-dimensional settings.

Variance-dependent regret bounds have received increasing attention in recent studies on contextual bandits. However, most of these studies are focused on upper confidence bound (UCB)-based bandit algorithms, while sampling based bandit algorithms such as Thompson sampling are still understudied. The only exception is the `LinVDTS` algorithm (Xu et al., 2023), which is limited to linear reward function and its regret bound is not optimal with respect to the model dimension. In this paper, we present `FGTSVA`, a variance-aware Thompson Sampling algorithm for contextual bandits with general reward function with optimal regret bound. At the core of our analysis is an extension of the decoupling coefficient, a technique commonly used in the analysis of Feel-good Thompson sampling (FGTS) that reflects the complexity of the model space.

The Bayesian paradigm offers principled tools for sequential decision-making under uncertainty, but its reliance on a probabilistic model for all parameters can hinder the incorporation of complex structural constraints. We introduce a minimalist Bayesian framework that places a prior only on the location of the optimum, while eliminating nuisance parameters through profile likelihood. This yields a generalized posterior that naturally accommodates structural constraints. As a direct instantiation, we develop MINimalist Thompson Sampling (MINTS). For multi-armed bandits with mean constraints, we establish near-optimal non-asymptotic regret guarantees and sharp almost-sure asymptotic regret characterizations. In particular, MINTS attains the classical Lai--Robbins constant in the unstructured setting and automatically adapts to unimodal structure, achieving the sharp constant determined only by the immediate neighbors of the optimal arm.