Logarithmic Regret for Online Control

Jul 12, 2020



We consider the problem of online control in a known linear dynamical system subject to adversarial noise. Existing regret bounds for this setting scale as √(T) unless strong stochastic assumptions are imposed on the noise. We give the first algorithm with logarithmic regret for arbitrary adversarial noise sequences, provided that the state and control costs are given by fixed quadratic functions. We propose a novel analysis that combines a new variant of the performance difference lemma with techniques from optimal control, allowing us to reduce online control to online prediction with delayed feedback. Unlike prior work, which leverages the so-called online convex optimization with memory framework, our analysis does not need to bound movement costs of the iterates, leading to logarithmic regret. Our performance difference lemma-based analysis may be of broader interest beyond linear control.



About ICML 2020

The International Conference on Machine Learning (ICML) is the premier gathering of professionals dedicated to the advancement of the branch of artificial intelligence known as machine learning. ICML is globally renowned for presenting and publishing cutting-edge research on all aspects of machine learning used in closely related areas like artificial intelligence, statistics and data science, as well as important application areas such as machine vision, computational biology, speech recognition, and robotics. ICML is one of the fastest growing artificial intelligence conferences in the world. Participants at ICML span a wide range of backgrounds, from academic and industrial researchers, to entrepreneurs and engineers, to graduate students and postdocs.

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