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- W2808079723 abstract "We study the stochastic batched convex optimization problem, in which we use many emph{parallel} observations to optimize a convex function given limited rounds of interaction. In each of (M) rounds, an algorithm may query for information at n points, and after issuing all (n) queries, it receives unbiased noisy function and/or (sub)gradient evaluations at the (n) points. After (M) such rounds, the algorithm must output an estimator. We provide lower and upper bounds on the performance of such batched convex optimization algorithms in zeroth and first-order settings for the collections of Lipschitz convex and smooth strongly convex functions. The rates we provide exhibit two interesting phenomena: (1) in terms of the batch size (n), the rate of convergence of batched algorithms (nearly) achieves the conventional fully sequential rate once (M = O(d log log n)), where d is the dimension of the domain, while (2) the rate may exponentially degrade as the dimension d increases, in distinction from fully sequential settings." @default.
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- W2808079723 date "2018-07-05" @default.
- W2808079723 modified "2023-09-26" @default.
- W2808079723 title "Minimax Bounds on Stochastic Batched Convex Optimization" @default.
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