Parallel Best Arm Identification in Heterogeneous Environments

In this paper, we study the tradeoffs between the time and the number of communication rounds of the best arm identification problem in the heterogeneous collaborative learning model, where multiple agents interact with possibly different environments and they want to learn in parallel an objective function in the aggregated environment. By proving almost tight upper and lower bounds, we show that collaborative learning in the heterogeneous setting is inherently more difficult than that in the homogeneous setting in terms of the time-round tradeoff.