A Loopless Distributed Algorithm for Personalized Bilevel Optimization

This paper studies a class of personalized distributed bilevel optimization problems over networks, where nodes aim at jointly optimizing the sum of outer-level objectives that depend on the solution of inner-level optimization problems. The existing algorithms for distributed bilevel optimization problems usually require extra computation loops for estimating hypergradients. To facilitate computational efficiency, we develop a loopless distributed algorithm that employs certain steps to approximate the optimal solution of innerlevel optimization problems, and track Hessian-inverse-vector products in a recursive manner. We prove that for stochastic nonconvex-strongly-convex problems, the proposed algorithm achieves the state of the art O(^-2) communication cost, while improving the computational cost by O(1og(1/)). Numerical experiments validate our theoretical findings.