Robust Multi-Agent Bandits Over Undirected Graphs

• URL: http://arxiv.org/abs/2203.00076v1
• Date: Mon, 28 Feb 2022 20:21:55 GMT
• Title: Robust Multi-Agent Bandits Over Undirected Graphs
• Authors: Daniel Vial, Sanjay Shakkottai, R. Srikant
• Abstract summary: We consider a multi-agent multi-armed bandit setting in which honest agents collaborate over a network to minimize regret. We show the situation is murkier beyond the case of a complete graph. We propose a new algorithm for which the $i$-th agent has regret $O( d_textmal(i) + K/n) log(T)/Delta)$ on any connected and undirected graph.
• Score: 26.26185074977412
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: We consider a multi-agent multi-armed bandit setting in which $n$ honest agents collaborate over a network to minimize regret but $m$ malicious agents can disrupt learning arbitrarily. Assuming the network is the complete graph, existing algorithms incur $O( (m + K/n) \log (T) / \Delta )$ regret in this setting, where $K$ is the number of arms and $\Delta$ is the arm gap. For $m \ll K$, this improves over the single-agent baseline regret of $O(K\log(T)/\Delta)$. In this work, we show the situation is murkier beyond the case of a complete graph. In particular, we prove that if the state-of-the-art algorithm is used on the undirected line graph, honest agents can suffer (nearly) linear regret until time is doubly exponential in $K$ and $n$. In light of this negative result, we propose a new algorithm for which the $i$-th agent has regret $O( ( d_{\text{mal}}(i) + K/n) \log(T)/\Delta)$ on any connected and undirected graph, where $d_{\text{mal}}(i)$ is the number of $i$'s neighbors who are malicious. Thus, we generalize existing regret bounds beyond the complete graph (where $d_{\text{mal}}(i) = m$), and show the effect of malicious agents is entirely local (in the sense that only the $d_{\text{mal}}(i)$ malicious agents directly connected to $i$ affect its long-term regret).

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