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Title: An Accelerated Gradient Method for Convex Smooth Simple Bilevel Optimization
In this paper, we focus on simple bilevel optimization problems, where we minimize a convex smooth objective function over the optimal solution set of another convex smooth constrained optimization problem. We present a novel bilevel optimization method that locally approximates the solution set of the lower-level problem using a cutting plane approach and employs an accelerated gradient-based update to reduce the upper-level objective function over the approximated solution set. We measure the performance of our method in terms of suboptimality and infeasibility errors and provide non-asymptotic convergence guarantees for both error criteria. Specifically, when the feasible set is compact, we show that our method requires at most (max{1/ϵf‾‾√,1/ϵg}) iterations to find a solution that is ϵf-suboptimal and ϵg-infeasible. Moreover, under the additional assumption that the lower-level objective satisfies the r-th Hölderian error bound, we show that our method achieves an iteration complexity of (max{ϵ−2r−12rf,ϵ−2r−12rg}), which matches the optimal complexity of single-level convex constrained optimization when r=1.  more » « less
Award ID(s):
2505865
PAR ID:
10631864
Author(s) / Creator(s):
; ; ;
Publisher / Repository:
https://doi.org/10.48550/arXiv.2402.08097
Date Published:
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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