Better Bounds for the Distributed Experts Problem

• URL: http://arxiv.org/abs/2603.09168v1
• Date: Tue, 10 Mar 2026 04:17:34 GMT
• Title: Better Bounds for the Distributed Experts Problem
• Abstract summary: We study the distributed experts problem, where $n$ experts are distributed across $s$ servers for $T$ timesteps.<n>We give a protocol that achieves regret roughly $Rgtrsimfrac1sqrtTcdottextpolylog(nsT)$, using $mathcalOleft(fracnR2+fracsR2right)cdotmax(s1-2/p,1)cdottextpolylog(nsT)$
• Score: 69.88181841362488
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: In this paper, we study the distributed experts problem, where $n$ experts are distributed across $s$ servers for $T$ timesteps. The loss of each expert at each time $t$ is the $\ell_p$ norm of the vector that consists of the losses of the expert at each of the $s$ servers at time $t$. The goal is to minimize the regret $R$, i.e., the loss of the distributed protocol compared to the loss of the best expert, amortized over the all $T$ times, while using the minimum amount of communication. We give a protocol that achieves regret roughly $R\gtrsim\frac{1}{\sqrt{T}\cdot\text{poly}\log(nsT)}$, using $\mathcal{O}\left(\frac{n}{R^2}+\frac{s}{R^2}\right)\cdot\max(s^{1-2/p},1)\cdot\text{poly}\log(nsT)$ bits of communication, which improves on previous work.

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