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• W3173959178 abstract "We consider a standard distributed optimisation setting where $N$ machines, each holding a $d$-dimensional function $f_i$, aim to jointly minimise the sum of the functions $sum_{i = 1}^N f_i (x)$. This problem arises naturally in large-scale distributed optimisation, where a standard solution is to apply variants of (stochastic) gradient descent. We focus on the communication complexity of this problem: our main result provides the first fully unconditional bounds on total number of bits which need to be sent and received by the $N$ machines to solve this problem under point-to-point communication, within a given error-tolerance. Specifically, we show that $Omega( Nd log d / Nvarepsilon)$ total bits need to be communicated between the machines to find an additive $epsilon$-approximation to the minimum of $sum_{i = 1}^N f_i (x)$. The result holds for both deterministic and randomised algorithms, and, importantly, requires no assumptions on the algorithm structure. The lower bound is tight under certain restrictions on parameter values, and is matched within constant factors for quadratic objectives by a new variant of quantised gradient descent, which we describe and analyse. Our results bring over tools from communication complexity to distributed optimisation, which has potential for further applications." @default.
• W3173959178 created "2021-07-05" @default.
• W3173959178 creator A5083822059 @default.
• W3173959178 creator A5085809864 @default.
• W3173959178 date "2020-10-16" @default.
• W3173959178 modified "2023-09-27" @default.
• W3173959178 title "Towards Tight Communication Lower Bounds for Distributed Optimisation" @default.
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• W3173959178 hasPublicationYear "2020" @default.
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