In this brief note, we considers the problem of learning with dynamic-optimizing principal-agent setting, in which the agents are allowed to have global perspectives about the learning process, i.e., the ability to view things according to their relative importances or in their true relations based-on some aggregated information shared by the principal. Whereas, the principal, which is exerting an influence on the learning process of the agents in the aggregation, is primarily tasked to solve a high-level optimization problem posed as an empirical-likelihood estimator under conditional moment restrictions model that also accounts information about the agents' predictive performances on out-of-samples as well as a set of private datasets available only to the principal (e.g., see [1], [2], [3], [4] and [5] for further discussions on empirical likelihood methods with moment restrictions). Here, we provide a coherent mathematical argument which is necessary for characterizing the learning process behind this abstract dynamic-optimizing principal-agent learning framework. Note that, due to the inherent feedbacks behavior among the agents, the proposed learning framework remarkably offers some advantages in terms of stability and consistency, despite that both the principal and the agents do not necessarily need to have any knowledge of the sample distributions or the quality of each others datasets. Finally, it is worth remarking that such a learning framework can provide new insights in the context of collaborative learning problem with global perspectives that exploits the principal-agent setting (e.g., see [6], [7], [8] or [9] for related discussions), although we acknowledge that there are a number of conceptual and theoretical problems, such as small sample properties, still need to be addressed.

Multi-group classification arises in many prediction and decision-making problems, including applications in epidemiology, genomics, finance, and image recognition. Although classification methods have advanced considerably, much of the literature focuses on binary problems, and available extensions often provide limited flexibility for multi-group settings. Recent work has extended linear discriminant analysis to multiple groups, but more general methods are still needed to handle complex structures such as nonlinear decision boundaries and group-specific covariance patterns. We develop Multi-Group Quadratic Discriminant Analysis (MGQDA), a method for multi-group classification built on quadratic discriminant analysis. MGQDA projects high-dimensional predictors onto a lower-dimensional subspace, which enables accurate classification while capturing nonlinearity and heterogeneity in group-specific covariance structures. We derive theoretical guarantees, including variable selection consistency, to support the reliability of the procedure. In simulations and a gene-expression application, MGQDA achieves competitive or improved predictive performance compared with existing methods while selecting group-specific informative variables, indicating its practical value for high-dimensional multi-group classification problems. Supplementary materials for this article are available online.

Empirical models of demand for differentiated products rely on low-dimensional product representations to capture substitution patterns. These representations are increasingly proxied by applying ML methods to high-dimensional, unstructured data, including product descriptions and images. When proxies fail to capture the true dimensions of differentiation that drive substitution, standard workflows will deliver biased counterfactuals and invalid inference. We develop a practical toolkit that corrects this bias and ensures valid inference for a broad class of counterfactuals. Our approach applies to market-level and/or individual data, requires minimal additional computation, is efficient, delivers simple formulas for standard errors, and accommodates data-dependent proxies, including embeddings from fine-tuned ML models. It can also be used with standard quantitative attributes when mismeasurement is a concern. In addition, we propose diagnostics to assess the adequacy of the proxy construction and dimension. The approach yields meaningful improvements in predicting counterfactual substitution in both simulations and an empirical application.

The use of neural networks trained on individual claims data has become increasingly popular in the actuarial reserving literature. We consider how to best input historical payment data in neural network models. Additionally, case estimates are also available in the format of a time series, and we extend our analysis to assessing their predictive power. In this paper, we compare a feed-forward neural network trained on summarised transactions to a recurrent neural network equipped to analyse a claim's entire payment history and/or case estimate development history. We draw conclusions from training and comparing the performance of the models on multiple, comparable highly complex datasets simulated from SPLICE (Avanzi, Taylor and Wang, 2023). We find evidence that case estimates will improve predictions significantly, but that equipping the neural network with memory only leads to meagre improvements. Although the case estimation process and quality will vary significantly between insurers, we provide a standardised methodology for assessing their value.

The Universal Commerce Protocol introduces three new major AI features meant to reduce friction when online shopping. To further push the limits of consumerism, Google has launched a new open standard for agentic commerce that's called Universal Commerce Protocol (UCP). In brief, it's a framework that combines the power of AI agents and online shopping platforms to help customers buy more things. Thanks to the introduction of UCP, Google is offering three new online shopping features. To start, Google's AI mode will have a new checkout feature that allows customers to buy eligible products from certain US retailers within Google Search.

Sophie Turner reveals intense 8-hour daily training for upcoming "Tomb Raider" film as Lara Croft. The "Game of Thrones" actress discusses her physical preparation since February 2025.

Science Archaeology 3D map of Easter Island takes you places visitors aren't allowed One of the world's most isolated islands is open to virtual tourists. Breakthroughs, discoveries, and DIY tips sent every weekday. Nestled in the South Pacific Ocean, some 6,000 people live on the most isolated, inhabited island in the world: Rapa Nui. Known to many as Easter Island, a name Dutch explorer Jacob Roggeveen coined after landing on the island on Easter Sunday 1722, Rapa Nui is roughly double the size of Disney World, or 63.2 square miles. And every year, some 100,000 people visit the remote island to see the famed 13-foot-tall moai statues or Easter Island heads .

Things to Do in L.A. Tap to enable a layout that focuses on the article. Voters are silhouetted near the American flag while casting ballots in the California special election at the Huntington Beach Central Library in Huntington Beach on Nov. 4. This is read by an automated voice. Please report any issues or inconsistencies here . A mysterious news site called the California Courier floods Facebook with conservative-leaning stories attacking Democrats.

Wing's drone deliveries are coming to 150 more Walmarts The service expansion will reach Walmart customers in Los Angeles, St. Louis, Cincinnati, Miami and other US metro areas. Don't be surprised if you see even more drones delivering groceries across the US since the Alphabet-owned Wing announced another service expansion with Walmart over the next year. The partnership said that drone delivery services will be available at 150 more Walmart locations in Los Angeles, St. Louis, Cincinnati, Miami and more metros that have yet to be announced. According to Wing, its top 25 percent of customers have ordered its delivery drones up to three times a week. To meet growing demand, Wing and Walmart said it will serve up to 40 million US customers and build up a network of 270 delivery locations by 2027.

Even the Empire State Building would eventually crumble. Breakthroughs, discoveries, and DIY tips sent every weekday. New York City is one of the noisiest cities in the world. With a population of eight and a half million people, the city is a nonstop symphony of car honks, yelling, and ambulance sirens. Now, imagine if all that noise and all those people suddenly disappeared overnight. Just how quickly would nature move into abandoned apartments? Well in a new episode of's podcast, we explore just that. So, yes, there's a reason cats love boxes and no, hot workout classes usually aren't better . If you have a question for us, send us a note .