Paper:
A Bayesian Approach to Generative Adversarial Imitation Learning
Generative adversarial training for imitation learning has shown promising results on high-dimensional and continuous control tasks. This paradigm is based on reducing the imitation learning problem to the density matching problem, where the agent iteratively refines the policy to match the empirical state-action visitation frequency of the expert demonstration. Although this approach can robustly learn to imitate even with scarce demonstration, one must still address the inherent challenge that collecting trajectory samples in each iteration is a costly operation. To address this issue, we first propose a Bayesian formulation of generative adversarial imitation learning (GAIL), where the imitation policy and the cost function are represented as stochastic neural networks. Then, we show that we can significantly enhance the sample efficiency of GAIL leveraging the predictive density of the cost, on an extensive set of imitation learning tasks with high-dimensional states and actions.

Review:
SUMMARY The paper proposes an improvement to the Generative Adversarial Imitation Learning (GAIL) approach. In GAIL, a discriminator (critic) function is updated to provide feedback on how close the distribution induced by the policy is to the expert distribution. The generator (policy) is then updated to make these distributions more similar. These updates happen interatively. The paper proposes to make this procedure more robust by defining a *distribution* over discriminator parameters, from which multiple samples are drawn. The generator then tries to improve wrt all of these samples, rather than a point estimate.   TECHNICAL QUALITY The paper uses mostly experiments (rather than, say, theoretical proofs) to support the claimed contributions. The new method is compared to two relevant baselines - published GAIL and a 'tuned GAIL' that uses the proposed innovations except the use of multiple posterior samples. Experiments are over five different common benchmarks for imitation and reinforcement learning, using as much as possible standardised settings from earlier papers. It is not clear how many trials were performed for each setting - and thus how reliable the averages are. It seems single trials were used in each environment. (but at least the findings were relatively consistent over the five tasks).   The development of the method seems mostly correct, I found the following (relatively minor) issues:   - paper states ML is a surrogate objective for a bayesian approach. It could be regarded as surrogate objective for a MAP estimate, but in a full Bayesian approach p(\phi|...) or p(\theta|...) aren't objectives, but the sought quantity (i.e., one doesn't maximise the posterior). - The main reason for the efficiency of BGAIL seems to be that using multiple samples of the posterior over discriminators (cost functions) seems more robust than using a point estimate. It would be interesting to describe this point in more detail: why is using a point estimate so brittle? Is there an experiment that could be done to get more insight in this point? - The paper implies (23) as another estimate for the quantity in (17), but in fact it is a different objective altogether (I.e. doesn't share LHS with (17)). That could be clearer.  - It seems that BGAIL would be more costly computationally because of the SVGD procedure. (as a tradeoff for a higher sample efficiency). Could you quantify the difference in computation time? - It wasn't clear to me what the +- indicates in table 1. Standard deviation over independent trials (how many)? Or st. dev within a trial? Or standard error, or multiple deviations, etc. Interpreting them as, say, 95 % confidence interval, most differences do not seem statistically significant between tuned GAIL and BGAIL in table 1 (but besides this asymptotic performance, learning seems to be a lot quicker for BGAIL) in the shown run. That makes it hard to judge the impact on asymptotic performance.   RELEVANCE, SIGNIFICANCE, NOVELTY The imitation learning problem is a relevant problem to the machine learning community, as a problem in itself and as a promising way to initialise reinforcement learning policies. The approach seems to be more sample efficient then tuned GAIL (the most competitive baseline) - although the effect depends a lot on the environment, with relatively modest improvements on some of the environments. Asymptotic performance is roughly the same. I would thus judge the work as somewhat significant. (I think the impact could increase if a bit more focused was put on the problem with brittleness and how that is solved by the BGAIL approach). The approach is somewhat novel, although it is still quite similar to the conventional GAIL approach. The derivation it self is interesting, although in some part it isn't clear whether a full Bayesian approach or using MAP estimates / posterior means are meant.   CLARITY The writing is mostly clear and well-structured. At times, there are small grammar issues (e.g. a missing article in "related to variational approach").  At two points, I felt the clarity of the text could be improved: -In 2.1 RL machinery is introduced - maybe it would be better to explain this step: we want to learn a cost function such that the gibbs policy follows the expert distribution as well as possible. For that, we need, Q, V, etc Derivation around the introduction of the 'discrimination events' is a bit meandering. - The discussion in paragraph 3.1 feels a bit convoluted with the introduction of the variables o_A, o_E, values 0_A, 1_E etcetera. It seems that this could perhaps be expressed more concisely using the output of the discriminator (and the true label) as functions, rather than introducing new random variables.    Further, it seems the algorithm is described in sufficient detail to be re-implemented. The experiments are missing some detail to be reproduced or interpreted (e.g. how can the +- in table 1 be interpreted, how many independent training runs were performed for each method). Without knowing the number of independent training runs, it is hard to judge the confidence in obtaining the same result in a reproduction study.   MINOR COMMENTS - Line 127: In general, we can't obtain MLE from posterior - The notation with C as wildcard for {A or E} is a bit confusing. It makes it seems like C is a variable and A and E are values.  - Line 162: "Imitation learning requires experience samples"-> not always, for example in the case of behaviour cloning where the learned policy is never run - There are many types of RBF kernel, please specify which one you used. (line 218)  I have read the rebuttal, and appreciate the extra results as well as the clarification regarding the experimental procedure and the number of policy runs performed with different random seeds. I have updated my score accordingly.