Pay to Learn, Share to Earn: Incentivized Federated Multi-Player Bandits

Federated multi-player multi-armed bandit problems model collaborative sequential decision-making where multiple players interact with a common bandit environment and share information through a central server to accelerate learning. Existing federated bandit frameworks typically assume that all players willingly share their local observations with the server. However, this assumption is often unrealistic in practical settings where players are self-interested and may not participate in collaboration without explicit incentives. To address this challenge, we propose an incentive-aware federated bandit framework in which players receive rewards for sharing information with the server and incur costs when buying information from the server. We develop a UCB-based algorithm, termed Buying-UCB, that balances individual exploration and collaborative learning by incorporating both sharing incentives and information acquisition costs into the learning process. We theoretically analyze the proposed algorithm and derive upper bounds on the group regret and buying cost. Our analysis further characterizes the trade-off between fully collaborative federated learning and completely independent learning. Extensive numerical experiments validate the theoretical findings and demonstrate the effectiveness of the proposed framework under different collaboration and pricing regimes.