  Team formation is ubiquitous in many sectors: education, labor markets,
sports, etc. A team's success depends on its members' latent types, which are
not directly observable but can be (partially) inferred from past performances.
From the viewpoint of a principal trying to select teams, this leads to a
natural exploration-exploitation trade-off: retain successful teams that are
discovered early, or reassign agents to learn more about their types? We study
a natural model for online team formation, where a principal repeatedly
partitions a group of agents into teams. Agents have binary latent types, each
team comprises two members, and a team's performance is a symmetric function of
its members' types. Over multiple rounds, the principal selects matchings over
agents and incurs regret equal to the deficit in the number of successful teams
versus the optimal matching for the given function. Our work provides a
complete characterization of the regret landscape for all symmetric functions
of two binary inputs. In particular, we develop team-selection policies that,
despite being agnostic of model parameters, achieve optimal or near-optimal
regret against an adaptive adversary.
