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We design and analyze a novel accelerated gradient-based algorithm for aclass of bilevel optimization problems. These problems have variousapplications arising from machine learning and image processing, where optimalsolutions of the two levels are interdependent. That is, achieving the optimalsolution of an upper-level problem depends on the solution set of a lower-leveloptimization problem. We significantly improve existing iteration complexity to$\mathcal{O}(\epsilon^{-0.5})$ for both suboptimality and infeasibility errormetrics, where $\epsilon>0$ denotes an arbitrary scalar. In addition, contraryto existing methods that require solving the optimization problem sequentially(initially solving an optimization problem to approximate the solution of thelower-level problem followed by a second algorithm), our algorithm concurrentlysolves the optimization problem. To the best of our knowledge, the proposedalgorithm has the fastest known iteration complexity, which matches the optimalcomplexity for single-level optimization. We conduct numerical experiments onsparse linear regression problems to demonstrate the efficacy of our approach.

Achieving optimal complexity guarantees for a class of bilevel convex optimization problems