SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives

Aaron Defazio (1) , Francis Bach (2, 3) , Simon Lacoste-Julien (2)

1 NICTA - National ICT Australia [Sydney]
2 SIERRA - Statistical Machine Learning and Parsimony
3 LIENS - Laboratoire d'informatique de l'école normale supérieure

In this work we introduce a new optimisation method called SAGA in the spirit of SAG, SDCA, MISO and SVRG, a set of recently proposed incremental gradient algorithms with fast linear convergence rates. SAGA improves on the theory behind SAG and SVRG, with better theoretical convergence rates, and has support for composite objectives where a proximal operator is used on the regulariser. Unlike SDCA, SAGA supports non-strongly convex problems directly, and is adaptive to any inherent strong convexity of the problem. We give experimental results showing the effectiveness of our method.

Domaines: Apprentissage [cs.LG]; Optimisation et contrôle [math.OC]

Aaron Defazio, Francis Bach, Simon Lacoste-Julien. SAGA: A Fast Incremental Gradient Method With Support for Non-Strongly Convex Composite Objectives. 2014. ⟨hal-01016843v1⟩