统一框架揭示策略优化算法本质，减少实现错误。
Policy Optimization Algorithms in a Unified Framework
- 基于广义遍历性与扰动分析构建统一理论框架。
- 发现并修正常见实现错误，提升算法可靠性。
- 适合强化学习研究者与工程实践者参考。
策略优化算法在多个领域至关重要，但因其涉及马尔可夫决策过程的复杂计算以及折扣回报与平均回报设定的差异，难以理解和实现。本文提出一个统一框架，结合广义遍历性理论与扰动分析，阐明并增强这些算法的应用。广义遍历性理论揭示了随机过程的稳态行为，有助于理解折扣与平均回报机制。扰动分析深入揭示了策略优化算法的基本原理。我们利用该框架识别常见实现错误，并展示正确方法。通过线性二次调节器（Linear Quadratic Regulator）问题的案例研究，说明算法设计微小差异对实现结果的影响。旨在使策略优化算法更易理解，减少实际应用中的误用。
原文摘要 · Abstract (English)
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.
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