arXiv research

New algorithm expands FTRL framework with improved worst-case regret bounds.

Establishes geometric convergence of iterative optimization algorithms.

New algorithm reduces regret and constraint violation in online convex optimization with complex constraints.

Paper develops efficient algorithms for robust optimization across multiple groups.

A new framework optimizes model transfer across domains with labeled data.

Improved algorithms for convex-concave min-max optimization and monotone variational inequalities.

We consider variational inequalities coming from monotone operators, a setting that includes convex minimization and convex-concave saddle-point problems. We assume an access to potentially noisy unbiased values of the monotone operators and assess convergence through a compatible gap function which corresponds to the …

In this paper we propose a primal-dual proximal extragradient algorithm to solve the generalized Dantzig selector (GDS) estimation problem, based on a new convex-concave saddle-point (SP) reformulation. Our new formulation makes it possible to adopt recent developments in saddle-point optimization, to achieve the optim…

Sample efficiency is critical in solving real-world reinforcement learning problems, where agent-environment interactions can be costly. Imitation learning from expert advice has proved to be an effective strategy for reducing the number of interactions required to train a policy. Online imitation learning, which inter…

This monograph presents the main complexity theorems in convex optimization and their corresponding algorithms. Starting from the fundamental theory of black-box optimization, the material progresses towards recent advances in structural optimization and stochastic optimization. Our presentation of black-box optimizati…

We study the iteration complexity of the optimistic gradient descent-ascent (OGDA) method and the extra-gradient (EG) method for finding a saddle point of a convex-concave unconstrained min-max problem. To do so, we first show that both OGDA and EG can be interpreted as approximate variants of the proximal point method…

This paper studies first order methods for solving smooth minimax optimization problems $\min_x \max_y g(x,y)$ where $g(\cdot,\cdot)$ is smooth and $g(x,\cdot)$ is concave for each $x$. In terms of $g(\cdot,y)$, we consider two settings -- strongly convex and nonconvex -- and improve upon the best known rates in both. …

Develops a gradient flow for Muon optimizer, a method for optimization.