# Policy Optimization Algorithms in a Unified Framework

arXiv: https://arxiv.org/abs/2504.03328 · HTML: https://mlsanity.com/paper/2504.03328/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 11 of its 29 references that are in the map.
- First posted on arXiv 4 Apr 2025.

## Builds on (most cited first, 11 of 11)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [Proximal Policy Optimization Algorithms](https://mlsanity.com/paper/1707.06347/) (2017)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Soft Actor-Critic: Off-Policy Maximum Entropy Deep Reinforcement Learning with a Stochastic Actor](https://mlsanity.com/paper/1801.01290/) (2018)
- [Trust Region Policy Optimization](https://mlsanity.com/paper/1502.05477/) (2015)
- [Dota 2 with Large Scale Deep Reinforcement Learning](https://mlsanity.com/paper/1912.06680/) (2019)
- [Learning robust perceptive locomotion for quadrupedal robots in the wild](https://mlsanity.com/paper/2201.08117/) (2022)
- [A Theory of Regularized Markov Decision Processes](https://mlsanity.com/paper/1901.11275/) (2019)
- [On the Global Convergence Rates of Softmax Policy Gradient Methods](https://mlsanity.com/paper/2005.06392/) (2020)
- [How to Train Your Robot with Deep Reinforcement Learning; Lessons We've Learned](https://mlsanity.com/paper/2102.02915/) (2021)
- [Is the Policy Gradient a Gradient?](https://mlsanity.com/paper/1906.07073/) (2019)

## Abstract (arXiv)

Policy optimization algorithms are crucial in many fields but challenging to grasp and implement, often due to complex calculations related to Markov decision processes and varying use of discount and average reward setups. This paper presents a unified framework that applies generalized ergodicity theory and perturbation analysis to clarify and enhance the application of these algorithms. Generalized ergodicity theory sheds light on the steady-state behavior of stochastic processes, aiding understanding of both discounted and average rewards. Perturbation analysis provides in-depth insights into the fundamental principles of policy optimization algorithms. We use this framework to identify common implementation errors and demonstrate the correct approaches. Through a case study on Linear Quadratic Regulator problems, we illustrate how slight variations in algorithm design affect implementation outcomes. We aim to make policy optimization algorithms more accessible and reduce their misuse in practice.