Multi-block Min-max Bilevel Optimization with Applications in Multi-task Deep AUC Maximization
This work addresses computational bottlenecks in multi-task learning for applications like medical diagnosis, though it is incremental as it builds on existing optimization frameworks.
The paper tackles the high computational cost of multi-block min-max bilevel optimization by proposing a single-loop randomized stochastic algorithm that updates only a constant number of blocks per iteration, achieving an optimal sample complexity of O(1/ε^4) for finding an ε-stationary point. It demonstrates effectiveness in multi-task deep AUC maximization with experiments on problems involving hundreds of tasks.
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 $O(1/ε^4)$ for finding an $ε$-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.