We study the fair division problem consisting in allocating one item per agent so as to avoid (or minimize) envy, in a setting where only agents connected in a given social network may experience envy. In a variant of the problem, agents themselves can be located on the network by the central authority. These problems turn out to be difficult even on very simple graph structures, but we identify several tractable cases. We further provide practical algorithms and experimental insights.

One of the difficulties to adapt MDPs for the control of cooperative multi-agent systems, is the complexity issued from Decentralized MDPs. Moreover, existing approaches can not be used for real applications because they do not take into account complex constraints about the execution. In this paper, we present a class of DEC-MDPs, OC-DEC-MDP, that can handle temporal and precedence constraints. This model allows several autonomous agents to cooperate so as to complete a set of tasks without communication. In order to allow the agents to coordinate, we introduce an opportunity cost. Each agent builds its own local MDP independently of the other agents but, it takes into account the lost in value provoked, by its local decision, on the other agents. Existing approaches solving DEC-MDP are NEXP complete or exponential, while our OC-DEC-MDP can be solved by a polynomial algorithm with good approximation.

International audienceThis paper addresses the interest of using Punctual versus Continuous coordination for mobile multi-robot systems where robots use auction sales to allocate tasks between them and to compute their policies in a distributed way. In Continuous coordination, one task at a time is assigned and performed per robot. In Punctual coordination, all the tasks are distributed in Rendezvous phases during the mission execution. However , tasks allocation problem grows exponentially with the number of tasks. The proposed approach consists in two aspects: (1) a control architecture based on topo-logical representation of the environment which reduces the planning complexity and (2) a protocol based on Sequential Simultaneous Auctions (SSA) to coordinate Robots' policies. The policies are individually computed using Markov Decision Processes oriented by several goal-task positions to reach. Experimental results on both real robots and simulation describe an evaluation of the proposed robot architecture coupled wih the SSA protocol. The efficiency of missions' execution is empirically evaluated regarding continuous planning

Abstract. Hidden-Mode Markov Decision Processes (HM-MDPs) were proposed to represent sequential decision-making problems in non-stationary environments that evolve according to a Markov chain. We introduce in this paper Hidden-Semi-Markov-Mode Markov Decision Processes (HS3MDPs), a generalization of HM-MDPs to the more realistic case of non-stationary environments evolving according to a semi-Markov chain. Like HM-MDPs, HS3MDPs form a subclass of Partially Observable Markov Decision Processes. Therefore, large instances of HS3MDPs (and HM-MDPs) can be solved using an online algorithm, the Partially Observable Monte Carlo Planning (POMCP) algorithm, based on Monte Carlo Tree Search exploiting particle filters for belief state approximation. We propose a first adaptation of POMCP to solve HS3MDPs more efficiently by exploiting their structure. Our empirical results show that the first adapted POMCP reaches higher cumulative rewards than the original algorithm. However, in larger instances, POMCP may run out of particles. To solve this issue, we propose a second adaptation of POMCP, replacing particle filters by exact representations of beliefs. Our empirical results indicate that this new version reaches high cumulative rewards faster than the former adapted POMCP and still remains efficient even for large problems.