The third method that we'll compare uses a different approach to address SGD stability. In the paper by Yuhuai Wu and others called Scalable Trust-Region Method for Deep Reinforcement Learning Using Kronecker-Factored Approximation published in 2017 (arXiv:1708.05144), the authors combined the second-order optimization methods and trust region approach.

The idea of the second-order methods is to improve the traditional SGD by taking the second-order derivatives of the optimized function (in other words, its curvature) to improve the convergence of the optimization process. To make things more complicated, working with the second derivatives usually requires you to build and invert a Hessian matrix, which can be prohibitively large, so the practical methods typically approximate it in some way. This area is currently very active in research, as developing robust, scalable optimization methods is very important for the whole machine learning domain.

One of the...