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- W4313484015 abstract "We introduce a new tool for stochastic convex optimization (SCO): a Reweighted Stochastic Query (ReSQue) estimator for the gradient of a function convolved with a (Gaussian) probability density. Combining ReSQue with recent advances in ball oracle acceleration [CJJJLST20, ACJJS21], we develop algorithms achieving state-of-the-art complexities for SCO in parallel and private settings. For a SCO objective constrained to the unit ball in $mathbb{R}^d$, we obtain the following results (up to polylogarithmic factors). We give a parallel algorithm obtaining optimization error $epsilon_{text{opt}}$ with $d^{1/3}epsilon_{text{opt}}^{-2/3}$ gradient oracle query depth and $d^{1/3}epsilon_{text{opt}}^{-2/3} + epsilon_{text{opt}}^{-2}$ gradient queries in total, assuming access to a bounded-variance stochastic gradient estimator. For $epsilon_{text{opt}} in [d^{-1}, d^{-1/4}]$, our algorithm matches the state-of-the-art oracle depth of [BJLLS19] while maintaining the optimal total work of stochastic gradient descent. We give an $(epsilon_{text{dp}}, delta)$-differentially private algorithm which, given $n$ samples of Lipschitz loss functions, obtains near-optimal optimization error and makes $min(n, n^2epsilon_{text{dp}}^2 d^{-1}) + min(n^{4/3}epsilon_{text{dp}}^{1/3}, (nd)^{2/3}epsilon_{text{dp}}^{-1})$ queries to the gradients of these functions. In the regime $d le n epsilon_{text{dp}}^{2}$, where privacy comes at no cost in terms of the optimal loss up to constants, our algorithm uses $n + (nd)^{2/3}epsilon_{text{dp}}^{-1}$ queries and improves recent advancements of [KLL21, AFKT21]. In the moderately low-dimensional setting $d le sqrt n epsilon_{text{dp}}^{3/2}$, our query complexity is near-linear." @default.
- W4313484015 created "2023-01-06" @default.
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- W4313484015 date "2023-01-01" @default.
- W4313484015 modified "2023-09-30" @default.
- W4313484015 title "ReSQueing Parallel and Private Stochastic Convex Optimization" @default.
- W4313484015 doi "https://doi.org/10.48550/arxiv.2301.00457" @default.
- W4313484015 hasPublicationYear "2023" @default.
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