Decentralized Multi-Agent Linear Bandits with Safety Constraints

We study decentralized stochastic linear bandits, where a network of N agents acts cooperatively to efficiently solve bandit-optimization problem over d-dimensional space. For this problem, we propose DLUCB: fully algorithm that minimizes the cumulative regret entire network. At each round agent chooses its actions following an upper confidence bound (UCB) strategy and share information with their immediate neighbors through carefully designed consensus procedure repeats cycles. Our analysis adjusts duration these communication cycles ensuring near-optimal performance O(d \log{NT}\sqrt{NT}) at rate O(dN^2) per round. The structure affects via small additive term – coined delay depends on spectral gap underlying graph. Notably, our results apply arbitrary topologies without requirement for dedicated acting as server. In consideration situations high cost, RC-DLUCB: modification DLUCB rare among agents. new trades off significantly reduced total cost O(d^3N^5/2) all T rounds. Finally, show ideas extend naturally emerging, albeit more challenging, setting safe bandits. recently studied bandits unknown safety constraints, first algorithm. contributes towards applying bandit techniques in safety-critical distributed systems repeatedly deal environments. present numerical simulations various corroborate theoretical findings.