Distributed Multi-Agent Online Learning Based on Global Feedback

In this paper, we develop online learning algorithms that enable the agents to cooperatively learn how to maximize the overall reward in scenarios where only noisy global feedback is available without exchanging any information among themselves. We prove that our algorithms' learning regrets—the losses incurred by the algorithms due to uncertainty—are logarithmically increasing in time and thus the time average reward converges to the optimal average reward. Moreover, we also illustrate how the regret depends on the size of the action space, and we show that this relationship is influenced by the informativeness of the reward structure with regard to each agent's individual action. When the overall reward is fully informative, regret is shown to be linear in the total number of actions of all the agents. When the reward function is not informative, regret is linear in the number of joint actions. Our analytic and numerical results show that the proposed learning algorithms significantly outperform existing online learning solutions in terms of regret and learning speed. We illustrate how our theoretical framework can be used in practice by applying it to online Big Data mining using distributed classifiers.