The sharpest known high probability generalization bounds for uniformly stable algorithms (Feldman, Vondrák, NeurIPS 2018, COLT, 2019), (Bousquet, Klochkov, Zhivotovskiy, COLT, 2020) contain a generally inevitable sampling error term of order Θ(1/ n). When applied to excess risk bounds, this leads to suboptimal results in several standard stochastic convex optimization problems. We show that if the so-called Bernstein condition is satisfied, the term Θ(1/ n) can be avoided, and high probability excess risk bounds of order up to O(1/n) are possible via uniform stability. Using this result, we show a high probability excess risk bound with the rate O(log n/n) for strongly convex and Lipschitz losses valid for any empirical risk minimization method.

A worker checks the radiation level inside the control room of reactor No 4, where the Chornobyl disaster happened in 1986. A worker checks the radiation level inside the control room of reactor No 4, where the Chornobyl disaster happened in 1986. In February 2025, a cheap Russian drone tore through Chornobyl's confinement shelter. Workers warn the site of the world's worst nuclear accident is not safe yet The dosimeter clipped to your chest ticks faster the moment you step off the designated path inside the Chornobyl nuclear power plant. Step back, and it slows again - an invisible line between clean ground and contamination.

Nonnegative (linear) least square problems are a fundamental class of problems that is well-studied in statistical learning and for which solvers have been implemented in many of the standard programming languages used within the machine learning community. The existing off-the-shelf solvers view the non-negativity constraint in these problems as an obstacle and, compared to unconstrained least squares, perform additional effort to address it. However, in many of the typical applications, the data itself is nonnegative as well, and we show that the nonnegativity in this case makes the problem easier. In particular, while the worst-case dimension-independent oracle complexity for unconstrained least squares problems necessarily scales with one of the data matrix constants (typically the spectral norm) and these problems are solved to additive error, we show that nonnegative least squares problems with nonnegative data are solvable to multiplicative error and with complexity independent of any matrix constants. The algorithm we introduce is accelerated and based on a primal-dual perspective. We further show how to provably obtain linear convergence using adaptive restart coupled with our method and demonstrate its effectiveness on large-scale data via numerical experiments.

'Animals are traumatised too': Pet rescuers under fire in Ukraine On a morning in February, animal shelter staff were getting changed for their shift when a Russian drone slammed into the centre of their compound in the frontline Ukrainian city of Zaporizhzhia. The steel door at the entrance probably saved their lives. More than a dozen animals sheltering at Give a Paw, Friend were not so lucky. It was terrifying, to put it mildly, says the group's head Iryna Didur. Residents rushed to help clean up the rubble and catch the animals that had escaped in terror.

Recent years have seen embodied visual navigation advance in two distinct directions: (i) in equipping the AI agent to follow natural language instructions, and (ii) in making the navigable world multimodal, e.g., audio-visual navigation. However, the real world is not only multimodal, but also often complex, and thus in spite of these advances, agents still need to understand the uncertainty in their actions and seek instructions to navigate.

Theorem, 4.2 - Optimizing Neural Nets.SupposeJ (', )is 1s-stronglysmoothinl1 norm. Let n bethe Sinkhornplanbetweenˆµand ˆ atregularization , andletD: = diam (X).