Policy Optimization Algorithms in a Unified Framework

2025-04-04

AI Summary

Policy optimization algorithms suffer from poor interpretability and error-prone implementation due to the complexity of Markov decision process (MDP) modeling and inconsistent use of discounted versus average-reward settings. Method: This paper introduces a unified analytical framework that, for the first time, systematically integrates generalized ergodicity theory with perturbation analysis to characterize the steady-state behavior of diverse policy optimization algorithms under both discounted and average-reward criteria. Contribution/Results: The framework clarifies fundamental algorithmic principles, identifies and corrects common implementation pitfalls, and significantly enhances interpretability and robustness. Empirical validation on MDP modeling and linear quadratic regulator (LQR) benchmarks confirms the framework’s ability to capture algorithmic consistency. Quantitative analysis further demonstrates that minor adjustments to key design parameters exert decisive influence on convergence properties and performance.

Technology Category

• Reasoning under Uncertainty: Stochastic Optimization
• Search and Optimization: Learning to Search
• Intelligent Robots: Learning & Optimization for ROB

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• Economics, Online Markets and Human Computation: Incentives in network design for Web infrastructures and ecosystems

Abstract

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.

Problem

• Clarify policy optimization algorithms' complex calculations and setups
• Unify framework using ergodicity theory and perturbation analysis
• Reduce misuse and improve accessibility of optimization algorithms

Innovation

• Unified framework using generalized ergodicity theory
• Perturbation analysis for policy optimization principles
• Case study on Linear Quadratic Regulator problems