Multi-block Min-max Bilevel Optimization with Applications in Multi-task Deep AUC Maximization. (arXiv:2206.00260v2 [math.OC] UPDATED)

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 …

applications arxiv auc math optimization