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Proximal Compositional Optimization for Distributionally Robust Learning
Prashant Khanduri · Chengyin Li · RAFI IBN SULTAN · Yao Qiang · Joerg Kliewer · Dongxiao Zhu
Event URL: https://openreview.net/forum?id=a7pK9UK4kB »
Recently, compositional optimization (CO) has gained popularity because of its applications in distributionally robust optimization (DRO) and many other machine learning problems. Often (non-smooth) regularization terms are added to an objective to impose some structure and/or improve the generalization performance of the learned model. However, when it comes to CO, there is a lack of efficient algorithms that can solve regularized CO problems. Moreover, current state-of-the-art methods to solve such problems rely on the computation of large batch gradients (depending on the solution accuracy) not feasible for most practical settings. To address these challenges, in this work, we consider a certain regularized version of the CO problem that often arises in DRO formulations and develop a proximal algorithm for solving the problem. We perform a Moreau envelope-based analysis and establish that without the need to compute large batch gradients \anamec~achieves $\mathcal{O}(\epsilon^{-2})$ sample complexity, that matches the vanilla SGD guarantees for solving non-CO problems. We corroborate our theoretical findings with empirical studies on large-scale DRO problems.

Author Information

Prashant Khanduri (Wayne State University)
Chengyin Li (Wayne State University)
RAFI IBN SULTAN (Wayne State University)
Yao Qiang (Wayne State University)
Joerg Kliewer (New Jersey Institute of Technology)
Dongxiao Zhu (Wayne State University)

Dongxiao Zhu is currently an Associate Professor at Department of Computer Science, Wayne State University. He received the B.S. from Shandong University (1996), the M.S. from Peking University (1999) and the Ph.D. from University of Michigan (2006). Dongxiao Zhu's recent research interests are in Machine Learning and Applications in health informatics, natural language processing, medical imaging and other data science domains. Dr. Zhu is the Director of Machine Learning and Predictive Analytics (MLPA) Lab and the Director of Computer Science Graduate Program at Wayne State University. He has published over 70 peer-reviewed publications and numerous book chapters and he served on several editorial boards of scientific journals. Dr. Zhu's research has been supported by NIH, NSF and private agencies and he has served on multiple NIH and NSF grant review panels. Dr. Zhu has advised numerous students at undergraduate, graduate and postdoctoral levels and his teaching interest lies in programming language, data structures and algorithms, machine learning and data science.

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