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# Stochastic Composite Least-Squares Regression with Convergence Rate $O(1/n)$

*Proceedings of the 2017 Conference on Learning Theory*, PMLR 65:831-875, 2017.

#### Abstract

We consider the minimization of composite objective functions composed of the expectation of quadratic functions and an arbitrary convex function. We study the stochastic dual averaging algorithm with a constant step-size, showing that it leads to a convergence rate of O(1/n) without strong convexity assumptions. This thus extends earlier results on least-squares regression with the Euclidean geometry to (a) all convex regularizers and constraints, and (b) all geometries represented by a Bregman divergence. This is achieved by a new proof technique that relates stochastic and deterministic recursions