Online Coalitional Skill Formation

Efficiently allocating heterogeneous tasks to agents that arrive dynamically and have diverse skills is a central problem in multi-agent systems called online task allocation. In many cases, a single agent does not meet the skill levels required by a particular task, which incentivizes the agents to form coalitions for handling it. In this paper, we propose a new framework, termed as online coalitional skill formation (OCSF), for handling online task allocation via coalition formation, where tasks require different skills for being successfully fulfilled, and each agent has different levels at mastering each skill. The goal of the organizer is therefore to assign agents that arrive online to a coalition responsible for performing some task, so as to optimally approach the desired skill levels of all tasks. Focusing on the case in which the set of possible mastering levels for each skill is discrete, we suggest different assignment algorithms based on the knowledge the organizer has on the arriving agents. When agents arrive i.i.d. according to some unknown distribution, we propose a greedy and adaptive scheme that assigns an agent to a task, proving a tight bound on the system's performance. If the distribution is known, we devise a novel correlation to Constrained Markov Decision Processes whose goal is maximizing the rate at which agents are assigned to each task while respecting their requirements. We then construct a non-adaptive approach that terminates when all the tasks' requirements are met. Finally, if the distribution is unknown, we provide two algorithms that learn it online. We have fully implemented the algorithms, showing that in many cases a higher diversity in skills may yield poor assignments.