Paper:
Policy Gradient With Value Function Approximation For Collective Multiagent Planning
Decentralized (PO)MDPs provide an expressive framework for sequential decision making in a multiagent system. Given their computational complexity, recent research has focused on tractable yet practical subclasses of Dec-POMDPs. We address such a subclass called CDec-POMDP where the collective behavior of a population of agents affects the joint-reward and environment dynamics. Our main contribution is an actor-critic (AC) reinforcement learning method for optimizing CDec-POMDP policies. Vanilla AC has slow convergence for larger problems. To address this, we show how a particular decomposition of the approximate action-value function over agents leads to effective updates, and also derive a new way to train the critic based on local reward signals. Comparisons on a synthetic benchmark and a real world taxi fleet optimization problem show that our new AC approach provides better quality solutions than previous best approaches.

Review:
The paper presents a policy gradient algorithm for a multiagent cooperative problem, modeled in a formalism (CDEC-POMDP) whose dynamics, like congestion games, depend on groups of agents rather than individuals.
This paper follows the theme of several similar advances in theis field of complex multiagent planning, using factored models to propose practical/tractable approximations. The novelty here is the use of parameterized policies and training algorithms inspired by reinforcement learning (policy gradients). The work is well-motivated, relevant, and particularly well-presented. The theoretical results are new and important. The experiments (on a large taxi domain) are convincing. Overall, the paper advances the state-of-the-art.
I have several questions:
Q1. What is meant by a "DBN" (... dynamic Bayesian network?) and how does one sample from it? Why is this model shown without even a high-level description? How is it relevant to the rest of the paper?
Q2. What is the architecture of the neural net? What is the representation of the input to the network? How large is it (number of parameters, number of layers, units per layer, non-linearities, etc.) Are there two entirely separate networks, one for the critic and one for the policy, or is it a multiheaded network? What optimizer is used, what learning rates, etc. Without these details, these results would not be reproducible.
Q3. What is the main motivation for using policy gradient? At first, I thought it would reduce memory as opposed to sample-based tabular value methods. But, it seems like the count tables may dominate the space complexity. Is that true? If not, it would be great to show the reduction in memory by using this method. If so, is the answer then that the benefit of parameterized policy + policy gradient is due to generalization across similar states?
Q4. The results show that the algorithm produces better results than the competitor, but it's possible that this setup is particularly more sensitive to parameter values. Even through the authors' claims through the paper, it is implied that the algorithm could be sensitive to the particular choices of training setup. Is the algorithm robust to slight perturbations in values?
Comments to improve the paper (does not affect decision):
C1. Give some background, even if just a few sentences, on the relationship between policy gradient and actor-critic. This seemed to be assumed, but some readers may not be familiar with this and may be confused without any introduction. (Same goes for DBN, or just drop the term if it's unnecessary.)
C2. Somewhere it should be stated that proofs are in the appendix.
C3. The min_w should not be in expression (11), sicne the authors just call it a 'loss function', but this is the entire optimization problem.
C4. The notation using a superscript xi to represent samples is non-standard and slightly awkward. This xi has no meaning as far as I can tell, so why not use something more familiar like \hat{R}, \hat{\mathbf{n}}, or \tilde{...}?