Universal Average-Case Optimality of Polyak Momentum

Jul 12, 2020



We consider the average-case runtime analysis of algorithms for minimizing quadratic objectives. In this setting, and contrary to the more classical worst-case analysis, non-asymptotic convergence rates and optimal algorithms depend on the full spectrum of the Hessian through its expected spectral distribution. Under mild assumptions, we show that these optimal methods converge asymptotically towards Polyak momentum independently of the expected spectral density. This makes Polyak momentum universally (i.e., independent of the spectral distribution) asymptotically average-case optimal.



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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