Collaborative Multi-agent Stochastic Linear Bandits
- URL: http://arxiv.org/abs/2205.06331v1
- Date: Thu, 12 May 2022 19:46:35 GMT
- Title: Collaborative Multi-agent Stochastic Linear Bandits
- Authors: Ahmadreza Moradipari, Mohammad Ghavamzadeh, and Mahnoosh Alizadeh
- Abstract summary: We study a collaborative multi-agent linear bandit setting, where $N$ agents that form a network communicate locally to minimize their overall regret.
All the agents observe the corresponding rewards of the played actions and use an accelerated consensus procedure to compute an estimate of the average of the rewards obtained by all the agents.
- Score: 28.268809091816287
- License: http://creativecommons.org/licenses/by/4.0/
- Abstract: We study a collaborative multi-agent stochastic linear bandit setting, where
$N$ agents that form a network communicate locally to minimize their overall
regret. In this setting, each agent has its own linear bandit problem (its own
reward parameter) and the goal is to select the best global action w.r.t. the
average of their reward parameters. At each round, each agent proposes an
action, and one action is randomly selected and played as the network action.
All the agents observe the corresponding rewards of the played actions and use
an accelerated consensus procedure to compute an estimate of the average of the
rewards obtained by all the agents. We propose a distributed upper confidence
bound (UCB) algorithm and prove a high probability bound on its $T$-round
regret in which we include a linear growth of regret associated with each
communication round. Our regret bound is of order
$\mathcal{O}\Big(\sqrt{\frac{T}{N \log(1/|\lambda_2|)}}\cdot (\log T)^2\Big)$,
where $\lambda_2$ is the second largest (in absolute value) eigenvalue of the
communication matrix.
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