Distributed Non-Stochastic Experts

We consider the online distributed non-stochastic experts problem, where the distributed system consists of one \emph{coordinator} node that is connected to $k$ \emph{sites}, and the sites are required to communicate with each other via the coordinator. At each time-step $t$, one of the $k$ site nodes has to pick an expert from the set $\{1, \ldots, n\}$, and the same site receives information about payoffs of all experts for that round. The goal of the distributed system is to minimize regret at time horizon $T$, while simultaneously keeping communication to a minimum. The two extreme solutions to this problem are:

(i) \emph{Full communication}: This essentially simulates the non-distributed setting to obtain the optimal $O(\sqrt{\log(n)T})$ regret bound at the cost of $T$ communication.

(ii) \emph{No communication}: Each site runs an independent copy -- the regret is $O(\sqrt{\log(n)kT})$ and the communication is $0$. This paper shows the difficulty of simultaneously achieving regret asymptotically better than $\sqrt{kT}$ and communication better than $T$. We give a novel algorithm that for an oblivious adversary achieves a non-trivial trade-off: regret $O(\sqrt{k^{5(1 + \epsilon)/6}T})$ and communication $O(T/k^{\epsilon})$, for any value of $\epsilon \in (0, 1/5)$.

We also consider a variant of the model, where the coordinator picks the expert. In this model, we show that the \emph{label-efficient} forecaster of Cesa-Bianchi et al. (2005) already gives us strategy that is near optimal in regret vs communication trade-off.

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Publisher  Neural Information Processing Systems Foundation


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