Finite-Time Frequentist Regret Bounds of Multi-Agent Thompson Sampling on Sparse Hypergraphs
This work addresses a theoretical gap in multi-agent bandit algorithms for researchers in reinforcement learning and decision-making, though it is incremental as it builds on prior Bayesian regret results.
The paper tackles the problem of deriving a frequentist regret bound for multi-agent Thompson sampling in sparse hypergraph bandit settings, proposing an ε-exploring variant (ε-MATS) that achieves a sublinear regret bound shown to be optimal up to constant and logarithmic terms for sparse hypergraphs.
We study the multi-agent multi-armed bandit (MAMAB) problem, where $m$ agents are factored into $ρ$ overlapping groups. Each group represents a hyperedge, forming a hypergraph over the agents. At each round of interaction, the learner pulls a joint arm (composed of individual arms for each agent) and receives a reward according to the hypergraph structure. Specifically, we assume there is a local reward for each hyperedge, and the reward of the joint arm is the sum of these local rewards. Previous work introduced the multi-agent Thompson sampling (MATS) algorithm \citep{verstraeten2020multiagent} and derived a Bayesian regret bound. However, it remains an open problem how to derive a frequentist regret bound for Thompson sampling in this multi-agent setting. To address these issues, we propose an efficient variant of MATS, the $ε$-exploring Multi-Agent Thompson Sampling ($ε$-MATS) algorithm, which performs MATS exploration with probability $ε$ while adopts a greedy policy otherwise. We prove that $ε$-MATS achieves a worst-case frequentist regret bound that is sublinear in both the time horizon and the local arm size. We also derive a lower bound for this setting, which implies our frequentist regret upper bound is optimal up to constant and logarithm terms, when the hypergraph is sufficiently sparse. Thorough experiments on standard MAMAB problems demonstrate the superior performance and the improved computational efficiency of $ε$-MATS compared with existing algorithms in the same setting.