No-Regret Dynamics in the Fenchel Game: A Unified Framework for Algorithmic Convex Optimization

11/22/2021
by   Jun-Kun Wang, et al.
0

We develop an algorithmic framework for solving convex optimization problems using no-regret game dynamics. By converting the problem of minimizing a convex function into an auxiliary problem of solving a min-max game in a sequential fashion, we can consider a range of strategies for each of the two-players who must select their actions one after the other. A common choice for these strategies are so-called no-regret learning algorithms, and we describe a number of such and prove bounds on their regret. We then show that many classical first-order methods for convex optimization – including average-iterate gradient descent, the Frank-Wolfe algorithm, the Heavy Ball algorithm, and Nesterov's acceleration methods – can be interpreted as special cases of our framework as long as each player makes the correct choice of no-regret strategy. Proving convergence rates in this framework becomes very straightforward, as they follow from plugging in the appropriate known regret bounds. Our framework also gives rise to a number of new first-order methods for special cases of convex optimization that were not previously known.

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

03/26/2022

Robust No-Regret Learning in Min-Max Stackelberg Games

The behavior of no-regret learning algorithms is well understood in two-...
12/08/2019

Additive Schwarz Methods for Convex Optimization as Gradient Methods

This paper gives a unified convergence analysis of additive Schwarz meth...
06/21/2018

Online Saddle Point Problem with Applications to Constrained Online Convex Optimization

We study an online saddle point problem where at each iteration a pair o...
12/31/2020

Optimizing Optimizers: Regret-optimal gradient descent algorithms

The need for fast and robust optimization algorithms are of critical imp...
09/06/2015

Deep Online Convex Optimization by Putting Forecaster to Sleep

Methods from convex optimization such as accelerated gradient descent ar...
01/25/2021

Extragradient and Extrapolation Methods with Generalized Bregman Distances for Saddle Point Problems

In this work, we introduce two algorithmic frameworks, named Bregman ext...
04/07/2016

Deep Online Convex Optimization with Gated Games

Methods from convex optimization are widely used as building blocks for ...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.