Competing Bandits in Non-Stationary Matching Markets

Understanding complex dynamics of two-sided online matching markets, where the demand-side agents compete to match with the supply-side (arms), has recently received substantial interest. To that end, in this paper, we introduce the framework of decentralized two-sided matching market under non stationary (dynamic) environments. We adhere to the serial dictatorship setting, where the demand-side agents have unknown and different preferences over the supply-side (arms), but the arms have fixed and known preference over the agents. We propose and analyze an asynchronous and decentralized learning algorithm, namely Non-Stationary Competing Bandits (NSCB), where the agents play (restrictive) successive elimination type learning algorithms to learn their preference over the arms. The complexity in understanding such a system stems from the fact that the competing bandits choose their actions in an asynchronous fashion, and the lower ranked agents only get to learn from a set of arms, not dominated by the higher ranked agents, which leads to forced exploration . With carefully defined complexity parameters, we characterize this forced exploration and obtain sub-linear (logarithmic) regret of NSCB. Furthermore, we validate our theoretical findings via experiments.