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A Lower Bound for the Optimization of Finite Sums
[article]
2015
arXiv
pre-print
This paper presents a lower bound for optimizing a finite sum of n functions, where each function is L-smooth and the sum is μ-strongly convex. We show that no algorithm can reach an error ϵ in minimizing all functions from this class in fewer than Ω(n + √(n(κ-1))(1/ϵ)) iterations, where κ=L/μ is a surrogate condition number. We then compare this lower bound to upper bounds for recently developed methods specializing to this setting. When the functions involved in this sum are not arbitrary,
arXiv:1410.0723v4
fatcat:352cw5wfknc53asldkjztrw6za