English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

While traditional distributionally robust optimization (DRO) aims to minimizethe maximal risk over a set of distributions, Agarwal and Zhang (2022) recentlyproposed a variant that replaces risk with excess risk. Compared to DRO, thenew formulation -- minimax excess risk optimization (MERO) has the advantage ofsuppressing the effect of heterogeneous noise in different distributions.However, the choice of excess risk leads to a very challenging minimaxoptimization problem, and currently there exists only an inefficient algorithmfor empirical MERO. In this paper, we develop efficient stochasticapproximation approaches which directly target MERO. Specifically, we leveragetechniques from stochastic convex optimization to estimate the minimal risk ofevery distribution, and solve MERO as a stochastic convex-concave optimization(SCCO) problem with biased gradients. The presence of bias makes existingtheoretical guarantees of SCCO inapplicable, and fortunately, we demonstratethat the bias, caused by the estimation error of the minimal risk, isunder-control. Thus, MERO can still be optimized with a nearly optimalconvergence rate. Moreover, we investigate a practical scenario where thequantity of samples drawn from each distribution may differ, and propose astochastic approach that delivers distribution-dependent convergence rates.

Efficient Stochastic Approximation of Minimax Excess Risk Optimization