Hybrid Stochastic-Deterministic Minibatch Proximal Gradient: Less-Than-Single-Pass Optimization with Nearly Optimal Generalization

Jul 12, 2020

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Stochastic variance-reduced gradient (SVRG) algorithms have been shown to work favorably in solving large-scale learning problems. Despite the remarkable success, the stochastic gradient complexity of SVRG-type algorithms usually scales linearly with data size and thus could still be expensive for huge data. To address this deficiency, we propose a hybrid stochastic-deterministic minibatch proximal gradient (HSDMPG) algorithm for strongly-convex problems that enjoys provably improved data-size-independent complexity guarantees. More precisely, for quadratic loss F() of n components, we prove that HSDMPG can attain an ϵ-optimization-error E[F(θ)-F(θ^*)] ≤ϵ within 𝒪(κ^1.5/ϵ^0.25log^1.5(1/ϵ) ∧(κ√(n)log^2(1/ϵ) +κ^3/n^1.5ϵ)) stochastic gradient evaluations, where κ is condition number. For generic strongly convex loss functions, we prove a nearly identical complexity bound though at the cost of slightly increased logarithmic factors. For large-scale learning problems, our complexity bounds are superior to those of the prior state-of-the-art SVRG algorithms with or without dependence on data size. Particularly, in the case of ϵ=𝒪(1/√(n)) which is at the order of intrinsic excess error bound of a learning model and thus sufficient for generalization, the stochastic gradient complexity bounds of HSDMPG for quadratic and generic loss functions are respectively 𝒪 (n^0.875log^1.5(n)) and 𝒪 (n^0.875log^2.25(n)), which to our best knowledge, for the first time achieve optimal generalization in less than a single pass over data. Extensive numerical results demonstrate the computational advantages of our algorithm over the prior ones.

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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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