Group Learning and Opinion Diffusion in a Broadcast Network

We analyze the following group learning problem in the context of opinion diffusion: Consider a network with $M$ users, each facing $N$ options. In a discrete time setting, at each time step, each user chooses $K$ out of the $N$ options, and receive randomly generated rewards, whose statistics depend on the options chosen as well as the user itself, and are unknown to the users. Each user aims to maximize their expected total rewards over a certain time horizon through an online learning process, i.e., a sequence of exploration (sampling the return of each option) and exploitation (selecting empirically good options) steps. Within this context we consider two group learning scenarios, (1) users with uniform preferences and (2) users with diverse preferences, and examine how a user should construct its learning process to best extract information from other's decisions and experiences so as to maximize its own reward. Performance is measured in {\em weak regret}, the difference between the user's total reward and the reward from a user-specific best single-action policy (i.e., always selecting the set of options generating the highest mean rewards for this user). Within each scenario we also consider two cases: (i) when users exchange full information, meaning they share the actual rewards they obtained from their choices, and (ii) when users exchange limited information, e.g., only their choices but not rewards obtained from these choices.