Collective Multi-Objective Planning

Multi-Objective Multi-Agent Planning addresses the problem of resolving conflicts between individual agent interests and the group interests. In this paper, we address this problem using a Vector-Valued Decentralized Markov Decision Process (2V-DEC-MDP). The formal framework of a Vector-Valued MDP considered uses the value function which returns a vector representing the individual and the group interests. Indeed, local decisions of each agent are guided by the local reward of the agent, the opportunity gain to the group and the opportunity cost of its nuisance. An optimal policy in such contextes is not clear but in this approach we develop a regret-based technique to find a good tradeoff between the group and induvidual interests. To do that, the approach we present uses Egalitarian Social Welfare orderings that allow an agent to consider during its local optimization the satisfaction of all criteria and reducing their differences. The obtained result is an equilibrium of individual and group satisfactions where the local policies can lead to more global satisfying behaviors in some settings. This result is illustrated in an example and compared to alternate local policies.