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.
arXiv:2511. 22331v2 Announce Type: replace-cross Abstract: Bilevel optimization minimizes an objective function, defined by an upper-level problem whose feasible region is the solution of a lower-level problem.
arXiv:2601. 21243v3 Announce Type: replace-cross Abstract: We consider max-min and min-max problems with objective functions that are possibly non-smooth, submodular with respect to the minimiser and concave with respect to the maximiser.
arXiv:2609. 17973v1 Announce Type: cross Abstract: We introduce a new single-loop algorithmic framework for smooth nonconvex--concave minimax optimization.
arXiv:2608. 08463v1 Announce Type: cross Abstract: We study second- and higher-order methods for solving smooth monotone variational inequalities (MVI).
arXiv:2405. 00914v4 Announce Type: replace-cross Abstract: We present in this paper novel accelerated fully first-order methods in \emph{Bilevel Optimization} (BLO).
arXiv:2610. 12328v1 Announce Type: new Abstract: We consider stochastic nonsmooth nonconvex composite optimization, which includes several important problems such as constrained optimization and the regularized training of neural networks.
arXiv:2609. 20687v1 Announce Type: cross Abstract: We study first-order black-box convex optimization over an $\ell_p$-ball for objectives Lipschitz in the $\ell_q$-norm, solving in the affirmative the nonsmooth version of the COLT open question (Guz15b) on whether the geometry of a smaller feasible set ($p < q$) can improve convergence rates in convex optimization, and matching prior lower bounds up to logarithmic factors.
arXiv:2609. 30501v1 Announce Type: new Abstract: Although bilevel optimization (BLO) has emerged as a powerful framework for addressing many complex and nested machine learning problems in recent years, most existing studies are confined to the lower-level strongly convex (LLSC) or lower-level generally convex (LLGC) settings (i.
arXiv:2610. 00545v1 Announce Type: new Abstract: We study adversarial online maximization of nonnegative, non-monotone DR-submodular functions over compact convex down-closed sets.
arXiv:2608. 05460v1 Announce Type: cross Abstract: This work introduces a proximal stochastic subgradient method for minimizing the sum of an expected cost, whose integrand is potentially nonsmooth and nonconvex, and a lower semicontinuous, prox-bounded function.
arXiv:2606. 14640v1 Announce Type: new Abstract: We study Online Convex Optimization (OCO) over a convex set $K\subseteq \mathbb R^d$, where in each round $t$ the learner selects $x_t\in K$ and then observes a convex loss $f_t:K\to[0,1]$, with the goal of minimizing regret to the best fixed decision in hindsight.
arXiv:2610.01662v1 Announce Type: cross Abstract: We establish complexity lower bounds for stochastic first-order algorithms in nonconvex--concave minimax optimization, allowing algorithms to use var...