## 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) łog (T) / Δ) regret in this setting, where K is the number of arms and Δis the arm gap. For m łl K, this improves over the single-agent baseline regret of O(Kłog(T)/Δ). 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(( dmal (i) + K/n) łog(T)/Δ) on any connected and undirected graph, where dmal(i) is the number of i's neighbors who are malicious. Thus, we generalize existing regret bounds beyond the complete graph (where dmal(i) = m), and show the effect of malicious agents is entirely local (in the sense that only the dmal (i) malicious agents directly connected to i affect its long-term regret).

Original language | English (US) |
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Article number | 53 |

Journal | Proceedings of the ACM on Measurement and Analysis of Computing Systems |

Volume | 6 |

Issue number | 3 |

DOIs | |

State | Published - Dec 8 2022 |

## Keywords

- malicious agents
- multi-armed bandits

## ASJC Scopus subject areas

- Computer Science (miscellaneous)
- Safety, Risk, Reliability and Quality
- Hardware and Architecture
- Computer Networks and Communications