Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond

• URL: http://arxiv.org/abs/2110.00455v1
• Date: Fri, 1 Oct 2021 14:41:17 GMT
• Title: Towards Gradient-based Bilevel Optimization with Non-convex Followers and Beyond
• Authors: Risheng Liu, Yaohua Liu, Shangzhi Zeng, Jin Zhang
• Abstract summary: Bi-LevelLOcation (BLO) has received extensive attentions from both learning and vision communities. We propose a new class of BLOs, named Auxiliaryization and Pessimy Truncated Gradient (IAPTT-GM) In particular, by introducing an auxiliary as to guide the optimization dynamics and designing a trunrun operation, we construct a reliable approximate version of the original BLO LLC.
• Score: 37.89147034158937
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In recent years, Bi-Level Optimization (BLO) techniques have received extensive attentions from both learning and vision communities. A variety of BLO models in complex and practical tasks are of non-convex follower structure in nature (a.k.a., without Lower-Level Convexity, LLC for short). However, this challenging class of BLOs is lack of developments on both efficient solution strategies and solid theoretical guarantees. In this work, we propose a new algorithmic framework, named Initialization Auxiliary and Pessimistic Trajectory Truncated Gradient Method (IAPTT-GM), to partially address the above issues. In particular, by introducing an auxiliary as initialization to guide the optimization dynamics and designing a pessimistic trajectory truncation operation, we construct a reliable approximate version of the original BLO in the absence of LLC hypothesis. Our theoretical investigations establish the convergence of solutions returned by IAPTT-GM towards those of the original BLO without LLC. As an additional bonus, we also theoretically justify the quality of our IAPTT-GM embedded with Nesterov's accelerated dynamics under LLC. The experimental results confirm both the convergence of our algorithm without LLC, and the theoretical findings under LLC.

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