A Lower Bound for the Optimization of Finite Sums

2 Oct 2014Alekh AgarwalLeon Bottou

This paper presents a lower bound for optimizing a finite sum of $n$ functions, where each function is $L$-smooth and the sum is $\mu$-strongly convex. We show that no algorithm can reach an error $\epsilon$ in minimizing all functions from this class in fewer than $\Omega(n + \sqrt{n(\kappa-1)}\log(1/\epsilon))$ iterations, where $\kappa=L/\mu$ is a surrogate condition number... (read more)

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