In this monograph, I introduce the basic concepts of Online Learning through a modern view
of Online Convex Optimization. Here, online learning refers to the framework of regret …

Most existing results about last-iterate convergence of learning dynamics are limited to two-
player zero-sum games, and only apply under rigid assumptions about what dynamics the …

Given a separation oracle for a convex set K⊂ ℝ n that is contained in a box of radius R, the
goal is to either compute a point in K or prove that K does not contain a ball of radius є. We …

The main focus of this paper is on the problem of maximizing the Nash social welfare (NSW).
In particular, given a collection of indivisible goods that needs to be allocated to a set of …

We present a strikingly simple proof that two rules are sufficient to automate gradient
descent: 1) don't increase the stepsize too fast and 2) don't overstep the local curvature. No …

We consider the problem of minimizing the sum of two convex functions: one is differentiable
and relatively smooth with respect to a reference convex function, and the other can be …

Many problems in machine learning can be formulated as optimizing a convex functional
over a vector space of measures. This paper studies the convergence of the mirror descent …

We investigate the convergence of stochastic mirror descent (SMD) under interpolation in
relatively smooth and smooth convex optimization. In relatively smooth convex optimization …

Abstract We study Proportional Response Dynamics (PRD) in linear Fisher markets, where
participants act asynchronously. We model this scenario as a sequential process in which at …

In the literature on game-theoretic equilibrium finding, focus has mainly been on solving a
single game in isolation. In practice, however, strategic interactions--ranging from routing …