Paper:
Learning Others' Intentional Models in Multi-Agent Settings Using Interactive POMDPs
Interactive partially observable Markov decision processes (I-POMDPs) provide a principled framework for planning and acting in a partially observable, stochastic and multi-agent environment. It extends POMDPs to multi-agent settings by including models of other agents in the state space and forming a hierarchical belief structure. In order to predict other agents' actions using I-POMDPs, we propose an approach that effectively uses Bayesian inference and sequential Monte Carlo sampling to learn others' intentional models which ascribe to them beliefs, preferences and rationality in action selection. Empirical results show that our algorithm accurately learns models of the other agent and has superior performance than methods that use subintentional models. Our approach serves as a generalized Bayesian learning algorithm that learns other agents' beliefs, strategy levels, and transition, observation and reward functions. It also effectively mitigates the belief space complexity due to the nested belief hierarchy.

Review:
The paper describes a sampling method for learning agent behaviors in interactive POMDPs (I-POMDPs). In general, I-POMDPs are a multi-agent POMDP model which, in addition to a belief about the environment state, the belief space includes nested recursive beliefs about the other agents' models. I-POMDP solutions, including the one proposed in the paper, largely approximate using a finite depth with either intentional models of others (e.g., their nested beliefs, state transitions, optimality criterion, etc.) or subintentional models of others (e.g., essentially "summaries of behavior" such as fictitious play). The proposed approach uses samples of the other agent at a particular depth to compute its values and policy. Related work on an interactive particle filter assumed the full frame was known (b, S, A, Omega, T, R, OC). The main unique characteristic of the proposed approach is to relax this assumption: only S, A, Omega are known, with beliefs, T, O, and R learned from n samples. The algorithm essentially proceeds by sampling from these distributions instead to generate beliefs and thus compute value and policy. Experiments were conducted on the multi-agent tiger and UAV domains, comparing a fictitious play I-POMDP baseline versus 0-, 1-, 2-, 3-level intentional I-POMDPs. In summary, results show that the intentional outperforms the baseline.  The paper does a great job of explaining the I-POMDP and the issues surrounding the nested modeling of other agents' models. While the algorithm suffers from the necessary notational overhead, each step is well explained in the surrounding companion paragraphs. As there are no theoretical results, experiments attempt to serve as marginally convincing evidence that the approach works.  Here are some comments and questions:  1. The experiments require up to 1000 or 2000 samples to obtain solid performance to accurately model T, O, R, etc. These problems are quite small, with simple transition and observation functions to learn. Given this fact, and the long run times for basic 2-level nesting, what is the main motivation for the usefulness of this approach? Why not use a subintentional model for any larger I-POMDPs? The number of samples in this approach will need to grow rapidly to astronomical sizes, with likely large computation times. Perhaps a stronger motivation to contrast this with the much less sample-dependent---but knowingly lower performant---subintentional models.  2. Experiments show interesting behavior regarding the performance, number of samples, and even KL-divergence between learned model parameters and ground truth. However, in application, how do we know how many samples are sufficient to accurately model the problem? Are there any techniques for determining a stopping point, especially in larger I-POMDPs when there are many more samples?  Overall, the idea clearly is how one would solve the problem of not having T, O, and R for other agents a priori: Monte Carlo sample. The paper partially delivers on the promise of such a scalable algorithm, for which simple subintentional models like fictitious play already serve this role well. That said, the idea is good and broadly moving in this model-based direction is well-motivated.  Some minor comments: - Line 208: "...with an subintentional..." -> "...with a subintentional...". - Line 219: "Then we fixe the..." -> "Then we fixed the..." - There are a lot of figures, many of which could be saved for the supplement in favor of some theoretical result, perhaps regarding number of samples (as above), error bound, etc. - References have a few typographic errors. "POMDP" needs to be capitalized, "Markov", "Bayesian", etc.