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• W2954258052 abstract "A landmark result of non-smooth convex optimization is that gradient descent is an optimal algorithm whenever the number of computed gradients is smaller than the dimension $d$. In this paper we study the extension of this result to the parallel optimization setting. Namely we consider optimization algorithms interacting with a highly parallel gradient oracle, that is one that can answer $mathrm{poly}(d)$ gradient queries in parallel. We show that in this case gradient descent is optimal only up to $tilde{O}(sqrt{d})$ rounds of interactions with the oracle. The lower bound improves upon a decades old construction by Nemirovski which proves optimality only up to $d^{1/3}$ rounds (as recently observed by Balkanski and Singer), and the suboptimality of gradient descent after $sqrt{d}$ rounds was already observed by Duchi, Bartlett and Wainwright. In the latter regime we propose a new method with improved complexity, which we conjecture to be optimal. The analysis of this new method is based upon a generalized version of the recent results on optimal acceleration for highly smooth convex optimization." @default.
• W2954258052 created "2019-07-12" @default.
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• W2954258052 date "2019-06-25" @default.
• W2954258052 modified "2023-09-27" @default.
• W2954258052 title "Complexity of Highly Parallel Non-Smooth Convex Optimization" @default.
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