Koopman-Based Generalization of Deep Reinforcement Learning With Application to Wireless Communications

2025-03-04

AI Summary

Deep reinforcement learning (DRL) suffers from poor generalization and limited interpretability in wireless communications. Method: This paper pioneers the integration of Koopman operator theory into DRL generalization analysis, establishing an interpretable representation grounded in dynamical systems modeling; it further proposes a quantification framework for generalization error that jointly incorporates spectral features and the $H_infty$ norm, yielding the first strictly computable upper bound on DRL generalization error. Results: Evaluated in an unmanned aerial vehicle (UAV)-assisted millimeter-wave communication scenario, the framework enables rigorous cross-channel generalization comparison between SAC and PPO policies under unseen channel conditions, accurately predicting policy stability and performance degradation. This work introduces a novel theoretical tool and a verifiable evaluation paradigm for DRL generalization in wireless networks.

Technology Category

• Machine Learning: Online Learning & Bandits
• Search and Optimization: Learning to Search
• Reasoning under Uncertainty: Stochastic Optimization

Application Category

• Systems and Infrastructure for Web, Mobile and WoT: Applied ML and AI for Web-based mobile applications
• Responsible Web: Machine-in-the-loop, human agency and autonomy
• Graph Algorithms and Modeling for the Web: Graph neural networks and deep learning approaches for Web-related graphs

Abstract

Deep Reinforcement Learning (DRL) is a key machine learning technology driving progress across various scientific and engineering fields, including wireless communication. However, its limited interpretability and generalizability remain major challenges. In supervised learning, generalizability is commonly evaluated through the generalization error using information-theoretic methods. In DRL, the training data is sequential and not independent and identically distributed (i.i.d.), rendering traditional information-theoretic methods unsuitable for generalizability analysis. To address this challenge, this paper proposes a novel analytical method for evaluating the generalizability of DRL. Specifically, we first model the evolution of states and actions in trained DRL algorithms as unknown discrete, stochastic, and nonlinear dynamical functions. Then, we employ a data-driven identification method, the Koopman operator, to approximate these functions, and propose two interpretable representations. Based on these interpretable representations, we develop a rigorous mathematical approach to evaluate the generalizability of DRL algorithms. This approach is formulated using the spectral feature analysis of the Koopman operator, leveraging the H_infty norm. Finally, we apply this generalization analysis to compare the soft actor-critic method, widely recognized as a robust DRL approach, against the proximal policy optimization algorithm for an unmanned aerial vehicle-assisted mmWave wireless communication scenario.

Problem

• Evaluate generalizability of Deep Reinforcement Learning (DRL) algorithms.
• Use Koopman operator for interpretable DRL state-action evolution modeling.
• Apply generalization analysis to compare DRL methods in wireless communication.

Innovation

• Uses Koopman operator for DRL generalizability analysis
• Develops interpretable representations for DRL algorithms
• Applies spectral feature analysis with H_infty norm