Jul 12, 2020
We develop a framework for designing optimal optimization methods in terms of their average-case runtime. This yields a new class of methods that achieve acceleration through a model of the Hessian's expected spectral density. We develop explicit algorithms for the uniform, Marchenko-Pastur and exponential distribution. These methods are momentum-based gradient algorithms whose hyper-parameters can be estimated cheaply using only the norm and the trace of the Hessian, in stark contrast with classical accelerated methods like Nesterov acceleration and Polyak momentum that require knowledge of the Hessian's largest and smallest singular value. Empirical results on quadratic, logistic regression and neural network show the proposed methods always match and in many cases significantly improve upon classical accelerated methods.
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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