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Updated: Jun 11, 2025

Design and Application of a Fault Detection Method Based on Adaptive Filters and Rotational Speed Estimation for an Electro-Hydrostatic Actuator
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Online Bilevel Optimization: Regret Analysis of Online Alternating Gradient Methods.

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This study introduces online bilevel optimization for time-varying problems. It extends single-level regret bounds and develops a new gradient method to bound bilevel regret effectively.

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Area of Science:

  • Optimization Theory
  • Machine Learning
  • Operations Research

Background:

  • Online optimization deals with sequential decision-making where data arrives over time.
  • Bilevel optimization involves nested optimization problems, common in hierarchical decision-making.
  • Existing regret bounds are primarily for single-level online optimization.

Purpose of the Study:

  • To introduce and analyze an online bilevel optimization framework for time-varying problems.
  • To extend existing regret analysis from single-level to bilevel online optimization.
  • To develop and evaluate a novel algorithm for this setting.

Main Methods:

  • Definition of new bilevel regret notions tailored for the online setting.
  • Development of an online alternating time-averaged gradient method.
  • Analysis of regret bounds leveraging problem smoothness and path-length properties.

Main Results:

  • Extension of regret bounds from single-level to bilevel online optimization.
  • Introduction of a novel online alternating gradient method.
  • Regret bounds are established in terms of the path-length of inner and outer minimizers.

Conclusions:

  • The proposed methods effectively handle time-varying bilevel optimization problems.
  • The new bilevel regret bounds provide theoretical guarantees for the developed algorithm.
  • This work opens avenues for applying online bilevel optimization in dynamic, hierarchical systems.