When performing imitation learning from expert demonstrations, distribution matching is a popular approach, in which one alternates between estimating distribution ratios and then using these ratios as rewards in a standard reinforcement learning (RL) algorithm. Traditionally, estimation of the distribution ratio requires on-policy data, which has caused previous work to either be exorbitantly datainefficient or alter the original objective in a manner that can drastically change its optimum. In this work, we show how the original distribution ratio estimation objective may be transformed in a principled manner to yield a completely off-policy objective. In addition to the data-efficiency that this provides, we are able to show that this objective also renders the use of a separate RL optimization unnecessary. Rather, an imitation policy may be learned directly from this objective without the use of explicit rewards. We call the resulting algorithm ValueDICE and evaluate it on a suite of popular imitation learning benchmarks, finding that it can achieve state-of-the-art sample efficiency and performance.
The primary contribution of this paper is a principled algorithm for off-policy imitation learning. Generative Adversarial Imitation Learning (GAIL), proposed by Ho and Ermon in 2016, is an on-policy imitation learning method that (provably) minimizes the divergence between a target state-action distribution and the policy state-action distribution. Followups to this work (Kostrikov et al., 2019) show that the same algorithm can be applied to an off-policy setting (replacing the on-policy samples with samples from the replay buffer) and the method still works, but is no longer theoretically justified. I believe using importance ratios would make this approach justified as well, but Kostrikov et al. found that using importance ratios actually degrades the performance of their method (due the difficulty associated with estimating importance ratios). This paper attempts to bridge this gap: a method that is theoretically justified, and still works. 
The paper takes most of its inspiration from the recently proposed DualDICE paper (Nachum et al, 2019), where the authors introduce a method for estimating discounted stationary distribution ratios (i.e. d^{\pi}/d^{D}, where \pi is some (known) policy, and D is a given dataset of experience (for example, a replay buffer)). The authors essentially apply the method proposed in DualDICE to estimate d^{\pi}/d^{exp} instead, where d^{exp} is a dataset of expert trajectories. While it would be possible to simply use this term as a reward and then run reinforcement learning, the authors note that the specific form of estimating d^{\pi}/d^{exp} allows them to instead directly a train a value function, which can then be used for updating a policy.
The authors also argue that their method reduces complexity since it does not require a separate RL optimization routine. However, I think having a separate RL optimization routine has its own advantages - it is relatively easy to implement GAIL on top of any existing RL algorithm, which makes it easy to take advantage of recent advances in RL. For the method proposed in this paper, it would not be straightforward to do so. 
The authors also note that they need a number of practical modifications to their original ValueDICE objective in order to make things work (Section 5: Some practical considerations). Notably, the the original ValueDICE objective only needs access to expert samples and the initial state distribution, and does not need access to the the replay buffer samples (apart from the initial state ones). This would likely not work well in practice - similar to how behavior cloning often does worse than GAIL when learning from a small number of expert examples. In order to combat this, the authors incorporate replay buffer regularization 
The authors provide experiments on  a simple synthetic "ring MDP", and on four continuous control tasks from OpenAI gym - HalfCheetah, Hopper, Ant and Walker2d. When compared to prior approaches (i.e. Kostrikov et al 2019) in the low-data regime (where behavior cloning fails), the proposed method does significantly better on one task (Ant), slightly worse on one task (walker), and about the same on two tasks (Hopper and HalfCheetah). I do notice the proposed method as being somewhat unstable though - the reward appears to be going down after reaching the max on two of the tasks - HalfCheetah and Ant. Overall, I don't thing experiments are thorough enough to demonstrate that the method is empirically better than competing approaches, but I believe that is not the main point of the paper. 
Overall, my recommendation is a weak accept. It is interesting that the authors were able to get a principled method for off-policy imitation learning working (large following from prior work in Nachum et al 2019), but I don't think the method currently offers any significant practical advantages over competing methods.