Natural gradient complications

Despite knowing the usefulness of the natural gradient in the RL framework, one of the major drawbacks of it is the computational cost that involves the calculation of FIM. While the computation of the gradient has a computational cost of , the natural gradient has a computational cost of , where  is the number of parameters. In fact, in the NPG paper that dates back to 2003, the algorithm has been applied to very small tasks with linear policies. The computation of  is too expensive with modern deep neural networks that have hundreds of thousands of parameters. Nonetheless, by introducing some approximations and tricks, the natural gradient can be also used with deep neural networks. 

In supervised learning, the use of the natural gradient is not needed as much as in reinforcement learning because the second-order gradient is somehow approximated in an empirical way by modern optimizers such as Adam and RMSProp.
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