Paper:
Multi-agent systems exhibit complex behaviors that emanate from the interactions of multiple agents in a shared environment. In this work, we are interested in controlling one agent in a multi-agent system and successfully learn to interact with the other agents that have fixed policies. Modeling the behavior of other agents (opponents) is essential in understanding the interactions of the agents in the system. By taking advantage of recent advances in unsupervised learning, we propose modeling opponents using variational autoencoders. Additionally, many existing methods in the literature assume that the opponent models have access to opponent's observations and actions during both training and execution. To eliminate this assumption, we propose a modification that attempts to identify the underlying opponent model, using only local information of our agent, such as its observations, actions, and rewards. The experiments indicate that our opponent modeling methods achieve equal or greater episodic returns in reinforcement learning tasks against another modeling method.

Review:
The authors propose a variational autoencoding (VAE) framework for agent/opponent modeling in multi-agent games. Interestingly, as the authors show, it looks like it is possible to compute accurate embeddings of the opponent policies without having access to opponent observations and actions. The paper is well written, the methods are simple yet still interesting/informative, but there are a few questions that I find necessary to be addressed.
Methods:
1. I find the idea of learning to infer embeddings of the opponent policies from the agent's own local observations quite interesting. Intuitively, it makes sense -- since the opponent's policy effectively specifies the dynamics of the environment (from the agent's perspective), opponent's behavior must be reflected in the agent's observations. Comparing figures 1 and 2, the proposed encoder architecture also uses information about the reward (and episode termination). How critical is this information for opponent identification? Would it work without r_{t-1} and d_{t-1}?
 
2. Sec. 4.2: "We assume a number of K provided episode trajectories for each pretrained opponent" -- how exactly are these trajectories obtained? Similarly, how exactly are the opponents pretrained? (Self-play, hardcoded, or something else?)
3. As the authors mention, the triplet loss that discriminates between the opponents loosens the lower bound. Since the regularized objective is still a lower bound, I wonder if the triplet loss can be re-interpreted/expresses as a specific prior on the opponent model?
Experiments:
1. Sec. 5.1: to understand the effect of opponent modeling, it would be nice to see how baselines perform in this setup against a randomly picked opponent (otherwise, the curve in Fig. 3-c is not informative). I suggest the following baselines: tit-for-tat (hardcoded), a couple of classical learning algorithms for iterated games (e.g., policy hill-climbing, WoLF), an agent that learns using policy gradients but without opponent embeddings. Without any baselines, Sec. 5.1 seems like a sanity check which just shows that the implementation works unless I am missing something.
2. Sec. 5.3: (1) Why is mutual information between the approximate posterior q and the prior p makes sense as the policy embedding quality metric here? (2) Could you intuitively (or formally) justify the fact that the triplet loss degrades MI metric? Right now, this is stated as a fact but not justified. (3) It looks like Grover et al. (2018a) used deterministic trajectory encoders; how exactly is MI measured in that case?
3. If I understand correctly from Fig. 4, SMA2C (which uses local information) underperforms as compared to the methods that use opponent trajectories in 6/8 cases. To me, this somewhat confirms the point opposite to what the authors claim -- local observations, while containing some information about the opponent, are still inferior. Also, having baselines that do not use opponent embeddings on the charts of Fig.4 would help understand the contribution of opponent modeling.
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I acknowledge reading the author's response, which addressed some of my questions/concerns to some extent. However, I believe that while estimating accurate embeddings of the opponent behavior from the agent's observations only is interesting, the approach has limitations, and I feel those are not studied in-depth enough (e.g., as a reader, I would like to understand if and when I should use the proposed approach and expect it to work). My assessment of the paper stays the same.