We introduce a theoretical and algorithmic framework for multi-way graph partitioning that relies on a multiplicative cut-based objective. We refer to this objective as the Product Cut. We provide a detailed investigation of the mathematical properties of this objective and an effective algorithm for its optimization. The proposed model has strong mathematical underpinnings, and the corresponding algorithm achieves state-of-the-art performance on benchmark data sets.

Many tasks in AI require the collaboration of multiple agents. Typically, the communication protocol between agents is manually specified and not altered during training. In this paper we explore a simple neural model, called CommNet, that uses continuous communication for fully cooperative tasks. The model consists of multiple agents and the communication between them is learned alongside their policy. We apply this model to a diverse set of tasks, demonstrating the ability of the agents to learn to communicate amongst themselves, yielding improved performance over non-communicative agents and baselines. In some cases, it is possible to interpret the language devised by the agents, revealing simple but effective strategies for solving the task at hand.