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A Stochastic Linearized Augmented Lagrangian Method for Decentralized Bilevel Optimization
Songtao Lu · Siliang Zeng · Xiaodong Cui · Mark Squillante · Lior Horesh · Brian Kingsbury · Jia Liu · Mingyi Hong

Thu Dec 01 02:00 PM -- 04:00 PM (PST) @ Hall J #402

Bilevel optimization has been shown to be a powerful framework for formulating multi-task machine learning problems, e.g., reinforcement learning (RL) and meta-learning, where the decision variables are coupled in both levels of the minimization problems. In practice, the learning tasks would be located at different computing resource environments, and thus there is a need for deploying a decentralized training framework to implement multi-agent and multi-task learning. We develop a stochastic linearized augmented Lagrangian method (SLAM) for solving general nonconvex bilevel optimization problems over a graph, where both upper and lower optimization variables are able to achieve a consensus. We also establish that the theoretical convergence rate of the proposed SLAM to the Karush-Kuhn-Tucker (KKT) points of this class of problems is on the same order as the one achieved by the classical distributed stochastic gradient descent for only single-level nonconvex minimization problems. Numerical results tested on multi-agent RL problems showcase the superiority of SLAM compared with the benchmarks.

Author Information

Songtao Lu (IBM Thomas J. Watson Research Center)
Siliang Zeng (University of Minnesota, Twin Cities)
Xiaodong Cui (IBM T. J. Watson Research Center)
Mark Squillante (IBM Research)
Lior Horesh (IBM Research)
Brian Kingsbury (IBM)
Jia Liu (The Ohio State University)
Jia Liu

Jia (Kevin) Liu is an Assistant Professor in the Dept. of Electrical and Computer Engineering at The Ohio State University and an Amazon Visiting Academics (AVA). He received his Ph.D. degree from the Dept. of Electrical and Computer Engineering at Virginia Tech in 2010. From Aug. 2017 to Aug. 2020, he was an Assistant Professor in the Dept. of Computer Science at Iowa State University. His research areas include theoretical machine learning, stochastic network optimization and control, and performance analysis for data analytics infrastructure and cyber-physical systems. Dr. Liu is a senior member of IEEE and a member of ACM. He has received numerous awards at top venues, including IEEE INFOCOM'19 Best Paper Award, IEEE INFOCOM'16 Best Paper Award, IEEE INFOCOM'13 Best Paper Runner-up Award, IEEE INFOCOM'11 Best Paper Runner-up Award, IEEE ICC'08 Best Paper Award, and honors of long/spotlight presentations at ICML, NeurIPS, and ICLR. He is an NSF CAREER Award recipient in 2020 and a winner of the Google Faculty Research Award in 2020. He received the LAS Award for Early Achievement in Research at Iowa State University in 2020, and the Bell Labs President Gold Award. His research is supported by NSF, AFOSR, AFRL, and ONR.

Mingyi Hong (University of Minnesota)

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