Multi-block Min-max Bilevel Optimization with Applications in Multi-task Deep AUC Maximization

• URL: http://arxiv.org/abs/2206.00260v1
• Date: Wed, 1 Jun 2022 06:42:36 GMT
• Title: Multi-block Min-max Bilevel Optimization with Applications in Multi-task Deep AUC Maximization
• Authors: Quanqi Hu, Yongjian Zhong, Tianbao Yang
• Abstract summary: We present a single-loop algorithm to tackle a multiblock min-max bilevel optimization problem. We show that our algorithm can be used to tackle problems with hundreds of tasks.
• Score: 36.743632418094
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we study multi-block min-max bilevel optimization problems, where the upper level is non-convex strongly-concave minimax objective and the lower level is a strongly convex objective, and there are multiple blocks of dual variables and lower level problems. Due to the intertwined multi-block min-max bilevel structure, the computational cost at each iteration could be prohibitively high, especially with a large number of blocks. To tackle this challenge, we present a single-loop randomized stochastic algorithm, which requires updates for only a constant number of blocks at each iteration. Under some mild assumptions on the problem, we establish its sample complexity of $\mathcal{O}(1/\epsilon^4)$ for finding an $\epsilon$-stationary point. This matches the optimal complexity for solving stochastic nonconvex optimization under a general unbiased stochastic oracle model. Moreover, we provide two applications of the proposed method in multi-task deep AUC (area under ROC curve) maximization and multi-task deep partial AUC maximization. Experimental results validate our theory and demonstrate the effectiveness of our method on problems with hundreds of tasks.

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