Paper:
Safe Model-based Reinforcement Learning with Stability Guarantees
Reinforcement learning is a powerful paradigm for learning optimal policies from experimental data. However, to find optimal policies, most reinforcement learning algorithms explore all possible actions, which may be harmful for real-world systems. As a consequence, learning algorithms are rarely applied on safety-critical systems in the real world. In this paper, we present a learning algorithm that explicitly considers safety, defined in terms of stability guarantees. Specifically, we extend control-theoretic results on Lyapunov stability verification and show how to use statistical models of the dynamics to obtain high-performance control policies with provable stability certificates. Moreover, under additional regularity assumptions in terms of a Gaussian process prior, we prove that one can effectively and safely collect data in order to learn about the dynamics and thus both improve control performance and expand the safe region of the state space. In our experiments, we show how the resulting algorithm can safely optimize a neural network policy on a simulated inverted pendulum, without the pendulum ever falling down.

Review:
This paper addresses the problem of safe exploration for reinforcement learning. Safety is defined as the learner never entering a state where it can't return to a low cost part of the state space. The proposed method learns a Gaussian Process model of the system dynamics and uses Lyapunov functions to determine if a state-action pair is recoverable from. Theoretical results are given for safety and exploration quality under idealized conditions. A practical method is introduced and an experiment shows it explores much of the recoverable state-space without entering an unrecoverable state.
Overall, this paper addresses an important problem for real world RL problems. Being able to explore without risking entering a hazardous state would greatly enhance the applicability of RL. This problem is challenging and this work makes a nice step towards a solution. I have several comments for improvement but overall I think the work will have a good impact on the RL community and is a good fit for the NIPS conference.
One weakness of the paper is that empirical validation is confined to a single domain. It is nice to see the method works well on this domain but it would have been good to have tried it a more challenging domain. I suspect there are scalability issues and I think a clear discussion of what is preventing application to larger problems would benefit people wishing to build on this work. For example, the authors somewhat brush the issue of the curse of dimensionality under the rug by saying the policy can always be computed offline. But the runtime could be exponential in dimension and it would be preferable to just acknowledge the difficulty.
The authors should also give a clear definition of safety and the goal of the work early on in the text. The definition is somewhat buried in lines 91-92 and it wasn't until I looked for this definition that I found it. Emphasizing this would make the goal of the work much clearer.
Similarly, this paper could really benefit from paragraphs that clearly define notation. As is, it takes a lot of searching backwards in the text to make sense of theoretical results. New notation is often buried in paragraphs which makes it hard to access.
Updated post author feedback:
While I still think this is a good paper and recommend acceptance, after reflecting on the lack of clarity in the theoretical results, I've revised my recommendation to just accept. Theorem 4 seems of critical importance but its hard to see that the result maps to the description given after it. Clarifying the theoretical results would make this a much better paper than it already is.
Minor comments:
How is the full region of attraction computed in Figure 2A?
Line 89: What do you mean by state divergence?
Line 148: This section title could have a name that describes what the theoretical results will be, e.g., theoretical results on exploration and policy improvement
Line 308: Could footnote this statement.
Line 320: "as to" -> to
Theorem 4: How is n* used?