10 research outputs found
Acceleration non-linéaire d'algorithmes stochastiques
Extrapolation methods use the last few iterates of an optimization algorithm to produce a better estimate of the optimum. They were shown to achieve optimal convergence rates in a deterministic setting using simple gradient iterates. Here, we study extrapolation methods in a stochastic setting, where the iterates are produced by either a simple or an accelerated stochastic gradient algorithm. We first derive convergence bounds for arbitrary, potentially biased perturbations, then produce asymptotic bounds using the ratio between the variance of the noise and the accuracy of the current point. Finally, we apply this acceleration technique to stochastic algorithms such as SGD, SAGA, SVRG and Katyusha in different settings, and show significant performance gains
Acceleration Methods
This monograph covers some recent advances in a range of acceleration
techniques frequently used in convex optimization. We first use quadratic
optimization problems to introduce two key families of methods, namely momentum
and nested optimization schemes. They coincide in the quadratic case to form
the Chebyshev method. We discuss momentum methods in detail, starting with the
seminal work of Nesterov and structure convergence proofs using a few master
templates, such as that for optimized gradient methods, which provide the key
benefit of showing how momentum methods optimize convergence guarantees. We
further cover proximal acceleration, at the heart of the Catalyst and
Accelerated Hybrid Proximal Extragradient frameworks, using similar algorithmic
patterns. Common acceleration techniques rely directly on the knowledge of some
of the regularity parameters in the problem at hand. We conclude by discussing
restart schemes, a set of simple techniques for reaching nearly optimal
convergence rates while adapting to unobserved regularity parameters.Comment: Published in Foundation and Trends in Optimization (see
https://www.nowpublishers.com/article/Details/OPT-036