The local functions at each node are assumed to be similar, due to statistical data similarity or otherwise. We establish lower complexity bounds for a fairly general class of algorithms solving the SPP. We show that a given suboptimality > 0 is achieved over master/workers networks in /µ log(1/") rounds of communications, where > 0 measures the degree of similarity of the local functions, µ is their strong convexity constant, and is the diameter of the network. The lower communication complexity bound over mesh networks reads 1/ p /µ log(1/"), where is the (normalized) eigengap of the gossip matrix used for the communication between neighbouring nodes. We then propose algorithms matching the lower bounds over either types of networks (up to log-factors). We assess the effectiveness of the proposed algorithms on a robust regression problem.

We study fair classification in the presence of an omniscient adversary that, given an η, is allowed to choose an arbitrary η-fraction of the training samples and arbitrarily perturb their protected attributes. The motivation comes from settings in which protected attributes can be incorrect due to strategic misreporting, malicious actors, or errors in imputation; and prior approaches that make stochastic or independence assumptions on errors may not satisfy their guarantees in this adversarial setting. Our main contribution is an optimization framework to learn fair classifiers in this adversarial setting that comes with provable guarantees on accuracy and fairness. Our framework works with multiple and non-binary protected attributes, is designed for the large class of linear-fractional fairness metrics, and can also handle perturbations besides protected attributes. We prove near-tightness of our framework's guarantees for natural hypothesis classes: no algorithm can have significantly better accuracy and any algorithm with better fairness must have lower accuracy. Empirically, we evaluate the classifiers produced by our framework for statistical rate on real-world and synthetic datasets for a family of adversaries.

The Met said corruption was the most consistent offence detected, with misconduct related to'abuse of the IT system that rosters shifts by police officers for personal or financial gain'. The Met said corruption was the most consistent offence detected, with misconduct related to'abuse of the IT system that rosters shifts by police officers for personal or financial gain'. Sat 25 Apr 2026 11.34 EDTFirst published on Sat 25 Apr 2026 11.31 EDT The Metropolitan police have launched investigations into hundreds of officers after using an AI tool built by the controversial tech company Palantir to root out rogue cops. The software was deployed by the Met over the course of a week, surveilling staff members using data the force has ready access to, unearthing rule-breaking ranging from work-from-home violations to suspected corruption and even criminal allegations such as rape. The Met said as a result of the software, evidence had been found tying a small number of officers to serious cases of misconduct and criminality, resulting in the arrest of three officers for offences including abuse of authority for sexual purposes, fraud, sexual assault, misconduct in public office and misuse of police systems.

Given a point set P M from a metric space (M,d)and numbers k,z N, the metric k-center problem with z outliers is to find a set C P of k points such that the maximum distance of all but at most z outlier points of P to their nearest center in C is minimized. We consider this problem in the fully dynamic model, i.e., under insertions and deletions of points, for the case that the metric space has a bounded doubling dimension dim. We utilize a hierarchical data structure to maintain the points and their neighborhoods, which enables us to efficiently find the clusters. In particular, our data structure can be queried at any time to generate a (3 + ε)-approximate solution for input values of k and z in worst-case query time ε O(dim)klognloglog, where is the ratio between the maximum and minimum distance between two points in P. Moreover, it allows insertion/deletion of a point in worst-case update time ε O(dim) lognlog . Our result achieves a significantly faster query time with respect to k and z than the current state-of-theart by Pellizzoni, Pietracaprina, and Pucci [18], which uses ε O(dim)(k+z)2 log query time to obtain a (3+ε)-approximate solution.