Paper:
Adaptive Skills Adaptive Partitions (ASAP)
We introduce the Adaptive Skills, Adaptive Partitions (ASAP) framework that (1) learns skills (i.e., temporally extended actions or options) as well as (2) where to apply them. We believe that both (1) and (2) are necessary for a truly general skill learning framework, which is a key building block needed to scale up to lifelong learning agents. The ASAP framework can also solve related new tasks simply by adapting where it applies its existing learned skills. We prove that ASAP converges to a local optimum under natural conditions. Finally, our experimental results, which include a RoboCup domain, demonstrate the ability of ASAP to learn where to reuse skills as well as solve multiple tasks with considerably less experience than solving each task from scratch.

Review:
This paper addresses the problem of learning temporally extended actions ("skills") as well as when to apply them in reinforcement learning. The main idea is to smoothly parameterize every component of the skill architecture (the state partition, the skill policies, and the assignment of partitions to skills) and to directly adapt those parameters using policy gradient. Experimental results show that the ASAP algorithm can effectively adapt its arbitrary initial skills to suit its environment.
***After Author Response***  I would only add that I hope the authors will take pains to clarify issues surrounding the number of partitions and policies if this paper is accepted. Several of the reviewers brought this up, and since the reviewers are at least somewhat representative of the paper's audience, it should be carefully addressed in the paper. I understand the authors to be saying that the algorithm is capable of making some partitions vanishingly small, and is capable of making some options vanishingly unlikely to be executed. In that sense, yes, ASAP can effectively learn how many partitions/policies are needed. However, I think the authors are being a little bit disingenuous about this point. For instance, ASAP can't create *more* partitions if they turn out to be necessary, which is I think what people mean when they say something like "how do you pick the correct number?". Also, even if ASAP might eventually find a structure that effectively uses only a few policies, on the way to get there (and actually even once it is there) it has to maintain and adapt the parameters for exponentially many policies. So that would suggest that it is not safe to just throw a whole bunch of partitions at it and let it sort it out. It seems that one does need to carefully consider how many partitions to start with -- not too few, not too many. So one of two things is happening. If, as I suspect, this is a genuine limitation of this approach, it's important that the authors straightforwardly and clearly acknowledge it as a limitation; the results are interesting anyway, and it points the way to remaining open questions. If basically all of the reviewers have misunderstood something and this is not a practical limitation, then there must be a clarity issue in the paper which must be addressed.  ---Technical Quality---  As far as I can tell the paper is technically sound. The derivations of the gradients are wholly contained within the supplemental material, and I did not pore over every detail, but they seemed correct and reasonable. The experiments are well-constructed and do effectively support the main claims.  I will say that the claim that ASAP re-uses skills seemed a bit weaker than the others. In "Three Rooms" the system apparently learned to apply the same skill in two different partitions, which is cool, but in the "Flipped Two Rooms" domain, the system apparently kept the hyperplane while re-learning the same two skills (just in the opposite regions), which is less cool. I think it's fair to say that the experiments demonstrate that skills *can* be re-used, but they also seem to show that this is highly dependent on the parameterization and search procedure. In other words, this framework permits skill re-use, but does nothing in particular to encourage/facilitate it.   ---Novelty---  The most similar work I am aware of is from Bacon and Precup (which the paper cites). They similarly parameterize the option policies, option termination conditions, and overall policy so all components can be adapted via policy gradient. This paper deals directly with continuous state spaces (defining state partitions using hyperplanes), which Bacon and Precup did not. This would not seem like sufficient novelty on its own, however the Bacon and Precup paper appeared in a workshop proceedings, not in an archival publication. Other than Bacon & Precup, as far as I am aware this approach of directly the entire skill architecture via PG is novel (and interesting).  ---Impact---  I believe this paper has the potential for substantial impact. Certainly the problems of learning and applying skills is an important one. This paper's approach of folding all of the relevant architectural decisions into one learning process is intriguing and shows demonstrated promise. This particular algorithm definitely has weaknesses; the exponental number of skill policies to learn is probably chief among them. However, the formulation of skill learning as purely a highly structured parameterization of the policy is a core idea that I can easily see being further explored in follow-up work. Furthermore, the experiments show some emergent desirable properties of this relatively straightforward approach (e.g. skill re-use, learning that fewer partitions are necessary) that immediately suggest follow-up research into how to more systematically encourage these behaviors.  ---Clarity---  I found the paper to be very well written. I thought the approach was well-motivated and clearly described, as were the presented results.  I felt that leaving the derivations for the supplementary appendix was sensible, since these are mostly algebra, and the derivation techniques applied are not really critical to the contribution. Even though some of the experimental results are left to the appendix, I felt that the authors did a good job of describing the results, and selected appropriate figures that could be left out without too much harm to the reader's flow. I will say that I personally don't like the format of making the supplementary materials simply a longer version of the paper. As a reader, it makes it harder to flip to the appendix to see what I want to see. Also, it is confusing that the supplementary version still refers to the supplementary materials!  A minor question: Why is Masson & Konidaris (2015) in Table 1? It is nowhere discussed in the paper, and, while I can see the relevance, it does not seem to be directly addressing the issue of skill learning in the same way as the others.  ---Summary of Revew---  This is a novel approach to skill learning that is intruiging in its directness and that shows significant promise. While there are some drawbacks to the specific algorithm presented here, the core idea is flexible and seems likely to inspire further investigation.