  Task allocation can enable effective coordination of multi-robot teams to
accomplish tasks that are intractable for individual robots. However, existing
approaches to task allocation often assume that task requirements or reward
functions are known and explicitly specified by the user. In this work, we
consider the challenge of forming effective coalitions for a given
heterogeneous multi-robot team when task reward functions are unknown. To this
end, we first formulate a new class of problems, dubbed COncurrent Constrained
Online optimization of Allocation (COCOA). The COCOA problem requires online
optimization of coalitions such that the unknown rewards of all the tasks are
simultaneously maximized using a given multi-robot team with constrained
resources. To address the COCOA problem, we introduce an online optimization
algorithm, named Concurrent Multi-Task Adaptive Bandits (CMTAB), that leverages
and builds upon continuum-armed bandit algorithms. Experiments involving
detailed numerical simulations and a simulated emergency response task reveal
that CMTAB can effectively trade-off exploration and exploitation to
simultaneously and efficiently optimize the unknown task rewards while
respecting the team's resource constraints.
