Paper:
In this paper, we propose the StochAstic Recursive grAdient Policy Optimization (SARAPO) algorithm which is a novel variance reduction method on Trust Region Policy Optimization (TRPO). The algorithm incorporates the StochAstic Recursive grAdient algoritHm(SARAH) into the TRPO framework. Compared with the existing Stochastic Variance Reduced Policy Optimization (SVRPO), our algorithm is more stable in the variance. Furthermore, by theoretical analysis the ordinary differential equation and the stochastic differential equation (ODE/SDE) of SARAH, we analyze its convergence property and stability. Our experiments demonstrate its performance on a variety of benchmark tasks. We show that our algorithm gets better improvement in each iteration and matches or even outperforms SVRPO and TRPO.
In this paper, we focus on studying variance reduction method on TRPO. We discussed an alternative variance reduction method called SARAH, recently proposed by (Nguyen et al., 2017) whose convergence rate matches that of SVRG in the convex case and has the inner-loop convergence property that SVRG does not possess. We propose a new algorithm named SARAPO which hybrids the SARAH method with TRPO and analyze the dynamics of SVRG/SARAH on natural gradient updates via its approximating ordinary and stochastic differential equation (ODE/SDE).
In experiments, we test the performance and sample efficiency of SARAPO, SVRPO, and TRPO. To allow larger steps in SVRPO/SARAPO, we remove the KL constraint in the line search of TRPO. We verify that variance reduction enables a larger leap towards the optima and find that SARAPO outperforms TRPO and matches the performance of SVRPO in most of the tasks.
The rest of this paper is organized as the following: we introduce some background, propose and analyze our algorithm in Section 2. In Section 3, we theoretically analyze our proposed SARAPO algorithm from a dynamical system viewpoint. We present the numerical results of experiments in Section 4 and conclude our paper in Section 5.

Review:
This paper investigates how the SARAH stochastic recursive gradient algorithm can be applied to Trust Region Policy Optimization. The authors analyze the SARAH algorithm using its approximating ordinary and stochastic differential equations. The empirical performance of SARAPO is then compared with SVRPO and TRPO on several benchmark problems.
Although the idea of applying SARAH to reduce the variance of gradient estimates in policy gradient algorithms is interesting and potentially quite significant (variance of gradient estimates is a major problem in policy gradient algorithms), I recommend rejecting this paper at the present time due to issues with clarity and quality, particularly of the experiments.
Not enough of the possible values for experimental settings were tested to say anything conclusive about the performance of the algorithms being compared. For the values that were tested, no measures of the variability of performance or statistical significance of the results were given. This is important because the performance of the algorithms is similar on many of the environments, and it is important to know if the improved performance of SARAPO observed on some of the environments is statistically significant or simply due to the small sample size.
The paper also needs improvements in clarity. Grammatical errors and sentence fragments make it challenging to understand at times. Section 2.3 seemed very brief, and did not include enough discussion of design decisions made in the algorithm. For example, the authors say ``"the Fisher Information Matrix can be approximated by Hessian matrix of the KL divergence when the current distribution exactly matches that of the base distribution" but then suggest using the Hessian of the KL of the old parameters and the new parameters which are not the same. What are the consequences of this approximation? Are there alternative approaches?
The analysis in section 3 is interesting, but the technique has been applied to SGD before and the results only seem to confirm findings from the original SARAH paper.
To improve the paper, I would suggest moving section 3 to an appendix and using the extra space to further explain details and conduct additional simpler experiments. Additional experiments on simpler environments and policy gradient algorithms (REINFORCE, REINFORCE with baseline) would allow the authors to try more possible values for experimental settings and do enough runs to obtain more conclusive results about performance. Then the authors can present their results applying SARAH to TRPO with some measure of statistical significance.