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.

翻译：任务分配能够有效协调多机器人团队完成单个机器人难以应对的任务。然而，现有任务分配方法通常假设任务需求或奖励函数是已知的，并由用户明确指定。本研究针对异构多机器人团队在任务奖励函数未知的情况下形成有效联盟的挑战展开探索。为此，我们首先提出一类新问题——"并发约束在线优化分配"（COCOA）。COCOA问题要求利用资源受限的多机器人团队，通过在线优化联盟使得所有任务的未知奖励同时最大化。针对COCOA问题，我们提出一种名为"并发多任务自适应赌博机"（CMTAB）的在线优化算法，该算法基于并扩展了连续臂赌博机算法。通过详细数值模拟与模拟应急响应任务的实验表明，CMTAB能够在遵守团队资源约束的前提下，有效权衡探索与利用，同时高效优化未知任务奖励。