Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods.

Davoud Ataee Tarzanagh, Parvin Nazari, Bojian Hou, Li Shen, Laura Balzano
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Abstract

This paper introduces an online bilevel optimization setting in which a sequence of time-varying bilevel problems is revealed one after the other. We extend the known regret bounds for single-level online algorithms to the bilevel setting. Specifically, we provide new notions of bilevel regret, develop an online alternating time-averaged gradient method that is capable of leveraging smoothness, and give regret bounds in terms of the path-length of the inner and outer minimizer sequences.

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在线双级优化:在线梯度交替法的遗憾分析
本文介绍了一种在线双层优化设置,在这种设置中,一连串时变双层问题相继揭示。我们将已知的单级在线算法的遗憾边界扩展到双级设置。具体来说,我们提供了双级遗憾的新概念,开发了一种能够利用平滑性的在线交替时间平均梯度法,并给出了内外部最小化序列的路径长度的遗憾边界。
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