Reward-based region optimal quality guarantees

Distributed constraint optimization (DCOP) is a promising approach to coordination, scheduling and task allocation in multi-agent networks. DCOP is NP-hard [6], so an important line of work focuses on developing fast incomplete solution algorithms that can provide guarantees on the quality of their local optimal solutions. Region optimality [11] is a promising approach along this line: it provides quality guarantees for region optimal solutions, namely solutions that are optimal in a specific region of the DCOP. Region optimality generalises kand t-optimality [7, 4] by allowing to explore the space of criteria that define regions to look for solutions with better quality guarantees. Unfortunately, previous work in region-optimal quality guarantees fail to exploit any a-priori knowledge of the reward structure of the problem. This paper addresses this shortcoming by defining reward-dependent region optimal quality guarantees that exploit two different levels of knowledge about rewards, namely: (i) a ratio between the least minimum reward to the maximum reward among relations; and (ii) the minimum and maximum rewards per relation.