Paper:
VAIN: Attentional Multi-agent Predictive Modeling
Multi-agent predictive modeling is an essential step for understanding physical, social and team-play systems. Recently, Interaction Networks (INs) were proposed for the task of modeling multi-agent physical systems. One of the drawbacks of INs is scaling with the number of interactions in the system (typically quadratic or higher order in the number of agents). In this paper we introduce VAIN, a novel attentional architecture for multi-agent predictive modeling that scales linearly with the number of agents. We show that VAIN is effective for multiagent predictive modeling. Our method is evaluated on tasks from challenging multi-agent prediction domains: chess and soccer, and outperforms competing multi-agent approaches.

Review:
This paper extends interaction networks (INs) with an attentional mechanism so that it scales linearly (as opposed to quadratically in vanilla INs) with the number of agents in a multi-agent predictive modeling setting: the embedding network is evaluated once per agent rather than once for every interaction. This allows to model higher-order interactions between agents in a computationally efficient way. The method is evaluated on two new non-physical tasks of predicting chess piece selection and soccer player movements.
The paper proposes a simple and elegant attentional extension of Interaction Networks, and convincingly shows the benefit of the approach with two interesting experiments. The idea is not groundbreaking but seems sufficiently novel, especially in light of its effectiveness. The paper is clear and well written. I appreciate that the authors provide an intuitive yet precise explanation (in words) of their mechanism instead of resorting to unnecessarily complicated notation and formulas.
Some confusion comes from the discussions about single-hop and multi-hop, terms that should probably be defined somewhere. On line 105, the authors write: "The architecture can be described as a single-hop CommNet with attention. Although CommNets typically use more hops for learning communications, more than one hop did not help on our predictive modeling tasks", but on lines 136 and 262 it says that VAIN uses multiple hops.
The experiments are well thought-out and interesting. I'm only missing some more insights or visualizations on what kind of interactions the attention mechanism learns to focus on or ignore, as the attention mechanism is the main contribution of the paper.
Further, I wonder if a disadvantage of the proposed attention mechanism (with the fixed-length softmax layer depending on the number of agents) does not take away one of the benefits of vanilla INs, namely that it is straightforward to dynamically add or remove agents during inference. If so, perhaps this can be mentioned.
Some minor remarks and typo's:
- typo in sentence on line 103-104: two times "be"
- equation (3) should be C = (P_i, F_i), or the preceding sentence should be changed
- line 138: sentence should start with "*While* the original formulation ..."
- line 284: generally *fares* poorly.
Overall, I believe this work would be a valuable contribution to NIPS.