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Poster

Functionally Constrained Algorithm Solves Convex Simple Bilevel Problem

Huaqing Zhang · Lesi Chen · Jing Xu · Jingzhao Zhang

West Ballroom A-D #6002
[ ]
[ Paper [ Slides [ Poster [ OpenReview
Wed 11 Dec 11 a.m. PST — 2 p.m. PST

Abstract:

This paper studies simple bilevel problems, where a convex upper-level function is minimized over the optimal solutions of a convex lower-level problem. We first show the fundamental difficulty of simple bilevel problems, that the approximate optimal value of such problems is not obtainable by first-order zero-respecting algorithms. Then we follow recent works to pursue the weak approximate solutions. For this goal, we propose a novel method by reformulating them into functionally constrained problems. Our method achieves near-optimal rates for both smooth and nonsmooth problems. To the best of our knowledge, this is the first near-optimal algorithm that works under standard assumptions of smoothness or Lipschitz continuity for the objective functions.

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