A Simple and Unified Method for Gradient-Variation Regret

Key points

• It has been studied in both non-stationary online learning, which aims to minimize dynamic regret against time-varying comparator sequences, and universal online learning, which seeks to adapt to unknown loss curvature.1
• Prior work obtained gradient-variation bounds using different techniques tailored to each setting.1
• We propose a simple and unified method based on surrogate losses with a quadratic penalty on decision movement, yielding gradient-variation bounds in both settings.1
• For universal online learning, it yields a simple algorithm that matches the optimal universal regret bounds of Yan et al. (2024) while relaxing the extended smoothness assumption.1

Sources (1)

• [1]A Simple and Unified Method for Gradient-Variation Regret
  arXiv (AI, ML, NLP, CV, robotics, multi-agent) · Oct 19, 02:19 PM

  Gradient-variation online learning has attracted increasing attention for its connections to game theory and optimization.

  It has been studied in both non-stationary online learning, which aims to minimize dynamic regret against time-varying comparator sequences, and universal online learning, which seeks to adapt to unknown loss curvature.

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