A Dynamic Observation Strategy for Multi-agent Multi-armed Bandit Problem
This addresses optimization in networked multi-agent systems with observation constraints, representing an incremental improvement over existing bandit methods.
The paper tackles the multi-agent multi-armed bandit problem by introducing a dynamic observation strategy with linear costs, where agents observe neighbors in a network to maximize rewards, and proves that total cumulative regret is logarithmically bounded, verified through numerical simulations.
We define and analyze a multi-agent multi-armed bandit problem in which decision-making agents can observe the choices and rewards of their neighbors under a linear observation cost. Neighbors are defined by a network graph that encodes the inherent observation constraints of the system. We define a cost associated with observations such that at every instance an agent makes an observation it receives a constant observation regret. We design a sampling algorithm and an observation protocol for each agent to maximize its own expected cumulative reward through minimizing expected cumulative sampling regret and expected cumulative observation regret. For our proposed protocol, we prove that total cumulative regret is logarithmically bounded. We verify the accuracy of analytical bounds using numerical simulations.