Nicolas Loizou, “Stochastic Iterative Methods for Smooth Games: Practical Variants and Convergence Guarantees”
“Stochastic Iterative Methods for Smooth Games: Practical Variants and Convergence Guarantees”
Nicolas Loizou, PhD
Assistant Professor
AMS and MINDS
Johns Hopkins University
Abstract: Two of the most prominent algorithms for solving unconstrained smooth games and variational inequalities problems (VIP) are the classical stochastic gradient descent-ascent (SGDA) and the recently introduced stochastic consensus optimization (SCO). SGDA is known to converge to a stationary point for specific classes of games, but current convergence analyses require a bounded variance assumption. SCO is used successfully for solving large-scale adversarial problems, but its convergence guarantees are limited to its deterministic variant. In the first part of the talk, we will introduce the expected co-coercivity condition, explain its benefits, and provide the first last-iterate convergence guarantees of SGDA and SCO under this condition for solving a class of stochastic variational inequality problems that are potentially non-monotone. In the second part of the talk, we will focus on more advanced extensions of the classical SGDA. We will propose a unified convergence analysis that covers a large variety of stochastic gradient descent-ascent methods, which so far have required different intuitions, have different applications and have been developed separately in various communities. A key to our unified framework is a parametric assumption on the stochastic estimates. Via our general theoretical framework, we either recover the sharpest known rates for the known special cases or tighten them. Moreover, to illustrate the flexibility of our approach we develop several new variants of SGDA such as a new variance-reduced method (L-SVRGDA), and new distributed methods with compression (QSGDA, DIANA-SGDA, VR-DIANA-SGDA). Although variants of the new methods are known for solving minimization problems, they were never considered or analyzed for solving min-max problems and VIPs. We will demonstrate the most important properties of the proposed methods through extensive numerical experiments.
Biography: Nicolas Loizou is an Assistant Professor in the Department of Applied Mathematics and Statistics and the Mathematical Institute for Data Science (MINDS), with a secondary appointment in the Department of Computer Science, at Johns Hopkins University. Prior to this, he was a Postdoctoral Research Fellow at Mila – Quebec Artificial Intelligence Institute and the Université de Montréal, from September 2019 to December 2021. He completed his Ph.D. studies in Optimization and Operational Research at the University of Edinburgh, School of Mathematics, in 2019.
His research interests include large-scale optimization, machine learning, randomized algorithms, distributed and decentralized algorithms, game theory, and deep learning. His current research focuses on the theory and applications of convex and non-convex optimization in large-scale machine learning and data science problems. He has received several awards and fellowships, including OR Society’s 2019 Doctoral Award (runner-up) for the ”Most Distinguished Body of Research leading to the Award of a Doctorate in the field of Operational Research”, the IVADO Postdoctoral Fellowship and COAP 2020 Best Paper Award.
In-person in KAVLI – Clark Hall, Room 316 or over Zoom
Join Zoom Meeting
https://wse.zoom.us/j/99304114570
Meeting ID: 993 0411 4570
One tap mobile
+13017158592,,99304114570# US (Washington DC) 13126266799,,99304114570#
+US (Chicago)
Dial by your location
+1 301 715 8592 US (Washington DC)
+1 312 626 6799 US (Chicago)
+1 646 558 8656 US (New York)
+1 669 900 6833 US (San Jose)
+1 253 215 8782 US (Tacoma)
+1 346 248 7799 US (Houston)
Meeting ID: 993 0411 4570
Find your local number: https://wse.zoom.us/u/acPT2svkU3
Join by SIP
Join by H.323
162.255.37.11 (US West)
162.255.36.11 (US East)
115.114.131.7 (India Mumbai)
115.114.115.7 (India Hyderabad)
213.19.144.110 (Amsterdam Netherlands)
213.244.140.110 (Germany)
103.122.166.55 (Australia Sydney)
103.122.167.55 (Australia Melbourne)
149.137.40.110 (Singapore)
64.211.144.160 (Brazil)
149.137.68.253 (Mexico)
69.174.57.160 (Canada Toronto)
65.39.152.160 (Canada Vancouver)
207.226.132.110 (Japan Tokyo)
149.137.24.110 (Japan Osaka)
Meeting ID: 993 0411 4570