# Understanding the Effects of Second-Order Approximations in Natural Policy Gradient Reinforcement Learning

arXiv: https://arxiv.org/abs/2201.09104 · HTML: https://mlsanity.com/paper/2201.09104/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 12 of its 18 references that are in the map.
- First posted on arXiv 22 Jan 2022.

## Builds on (most cited first, 12 of 12)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [High-Dimensional Continuous Control Using Generalized Advantage Estimation](https://mlsanity.com/paper/1506.02438/) (2015)
- [Deep Reinforcement Learning at the Edge of the Statistical Precipice](https://mlsanity.com/paper/2108.13264/) (2021)
- [Optimizing Neural Networks with Kronecker-factored Approximate Curvature](https://mlsanity.com/paper/1503.05671/) (2015)
- [Monte Carlo Gradient Estimation in Machine Learning](https://mlsanity.com/paper/1906.10652/) (2019)
- [Implementation Matters in Deep Policy Gradients: A Case Study on PPO and TRPO](https://mlsanity.com/paper/2005.12729/) (2020)
- [Fast Approximate Natural Gradient Descent in a Kronecker-factored Eigenbasis](https://mlsanity.com/paper/1806.03884/) (2018)
- [Scalable trust-region method for deep reinforcement learning using Kronecker-factored approximation](https://mlsanity.com/paper/1708.05144/) (2017)
- [Q-Prop: Sample-Efficient Policy Gradient with An Off-Policy Critic](https://mlsanity.com/paper/1611.02247/) (2016)
- [TENGraD: Time-Efficient Natural Gradient Descent with Exact Fisher-Block Inversion](https://mlsanity.com/paper/2106.03947/) (2021)
- [Importance of using appropriate baselines for evaluation of data-efficiency in deep reinforcement learning for Atari](https://mlsanity.com/paper/2003.10181/) (2020)

## Built on by (most cited first, 1 of 1)

- [Simultaneous Training of First- and Second-Order Optimizers in Population-Based Reinforcement Learning](https://mlsanity.com/paper/2408.15421/) (2024)

## Abstract (arXiv)

Natural policy gradient methods are popular reinforcement learning methods that improve the stability of policy gradient methods by utilizing second-order approximations to precondition the gradient with the inverse of the Fisher-information matrix. However, to the best of the authors' knowledge, there has not been a study that has investigated the effects of different second-order approximations in a comprehensive and systematic manner. To address this, five different second-order approximations were studied and compared across multiple key metrics including performance, stability, sample efficiency, and computation time. Furthermore, hyperparameters which aren't typically acknowledged in the literature are studied including the effect of different batch sizes and optimizing the critic network with the natural gradient. Experimental results show that on average, improved second-order approximations achieve the best performance and that using properly tuned hyperparameters can lead to large improvements in performance and sample efficiency ranging up to +181%. We also make the code in this study available at https://github.com/gebob19/natural-policy-gradient-reinforcement-learning.