Collaborative Learning of Stochastic Bandits over a Social Network
This addresses the challenge of efficient decision-making in networked multi-agent systems, offering a novel approach to reduce regret, though it is incremental in extending bandit theory to social networks.
The paper tackles the problem of collaborative online learning among agents in a social network playing stochastic multi-armed bandits, finding that naive extensions of single-agent policies lead to high regret, while a network-aware algorithm based on dominating sets improves overall regret, with analytical and numerical results showing significant gains.
We consider a collaborative online learning paradigm, wherein a group of agents connected through a social network are engaged in playing a stochastic multi-armed bandit game. Each time an agent takes an action, the corresponding reward is instantaneously observed by the agent, as well as its neighbours in the social network. We perform a regret analysis of various policies in this collaborative learning setting. A key finding of this paper is that natural extensions of widely-studied single agent learning policies to the network setting need not perform well in terms of regret. In particular, we identify a class of non-altruistic and individually consistent policies, and argue by deriving regret lower bounds that they are liable to suffer a large regret in the networked setting. We also show that the learning performance can be substantially improved if the agents exploit the structure of the network, and develop a simple learning algorithm based on dominating sets of the network. Specifically, we first consider a star network, which is a common motif in hierarchical social networks, and show analytically that the hub agent can be used as an information sink to expedite learning and improve the overall regret. We also derive networkwide regret bounds for the algorithm applied to general networks. We conduct numerical experiments on a variety of networks to corroborate our analytical results.