arXiv:2607. 18652v3 Announce Type: replace-cross Abstract: We establish improved lower bounds on the minimax expected regret of stochastic bandit convex optimization for $1$-Lipschitz functions on the $d$-dimensional Euclidean ball.
By Nived Rajaraman, Yanjun Han
arXiv:2608. 25182v1 Announce Type: cross Abstract: In this paper, we study alternating regret in online convex optimization (OCO), motivated by the success of alternating learning dynamics in two-player games.
By Mengxiao Zhang
arXiv:2110. 03950v3 Announce Type: replace-cross Abstract: We study the problem of finding approximate first-order stationary points in optimization problems of the form $\min_{x \in X} \max_{y \in Y} f(x,y)$, where the sets $X,Y$ are convex and $Y$ is compact.
By Dmitrii M. Ostrovskii, Babak Barazandeh, Meisam Razaviyayn
arXiv:2609. 21880v1 Announce Type: cross Abstract: We study the optimization of convex objectives with $(L,\kappa-1)$-H\"older-continuous gradients in $\ell_q$ over $R B_p^d$, $1<\kappa\le 2$.
By David Mart\'inez-Rubio, Brian Bullins, Crist\'obal Guzm\'an, Mathieu Molina
arXiv:2609. 04578v1 Announce Type: cross Abstract: We study stochastic gradient descent with random reshuffling for finite sums \[ F(x)=\frac1n\sum_{i=1}^n f_i(x).
By Jiaxiang Li
The paper introduces a new convergence framework for solving distributionally robust optimization problems formulated as nonconvex, nonconcave minimax problems over a Euclidean space and a Riemannian manifold. It defines a "basin saddle point"—a locally defined Nash equilibrium—and proves that a Riemannian gradient ascent–descent algorithm converges to such points under a local Łojasiewicz growth condition. The authors apply this theory to a statistical risk DRO problem over Gaussian measures, deriving explicit convergence rates and constants in terms of data dimension, loss moments, and reference covariance.
By Rishabh Dixit, Pranav Upadrashta, Alex Cloninger