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

arXiv: https://arxiv.org/abs/2503.02961 · HTML: https://mlsanity.com/paper/2503.02961/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in RL for energy, networks and operations, one of 15 directions in Deep reinforcement learning methods.
- Builds on 17 of its 38 references that are in the map.
- First posted on arXiv 4 Mar 2025.

## Placed in

- Deep reinforcement learning methods / [RL for energy, networks and operations](https://mlsanity.com/deeprl/rl-for-energy-networks-and-operations/)

## Builds on (most cited first, 17 of 17)

- [Domain Generalization: A Survey](https://mlsanity.com/paper/2103.02503/) (2021)
- [Deep k-Nearest Neighbors: Towards Confident, Interpretable and Robust Deep Learning](https://mlsanity.com/paper/1803.04765/) (2018)
- [Towards a Theoretical Framework of Out-of-Distribution Generalization](https://mlsanity.com/paper/2106.04496/) (2021)
- [A Survey on Interpretable Reinforcement Learning](https://mlsanity.com/paper/2112.13112/) (2021)
- [Generalization Bounds: Perspectives from Information Theory and PAC-Bayes](https://mlsanity.com/paper/2309.04381/) (2023)
- [Optimizing Neural Networks via Koopman Operator Theory](https://mlsanity.com/paper/2006.02361/) (2020)
- [Koopman Q-learning: Offline Reinforcement Learning via Symmetries of Dynamics](https://mlsanity.com/paper/2111.01365/) (2021)
- [Information Flow in Deep Neural Networks](https://mlsanity.com/paper/2202.06749/) (2022)
- [PyDMD: A Python package for robust dynamic mode decomposition](https://mlsanity.com/paper/2402.07463/) (2024)
- [Domain Generalization in Machine Learning Models for Wireless Communications: Concepts, State-of-the-Art, and Open Issues](https://mlsanity.com/paper/2303.08106/) (2023)
- [Koopman-Assisted Reinforcement Learning](https://mlsanity.com/paper/2403.02290/) (2024)
- [Information-Theoretic Generalization Bounds for Deep Neural Networks](https://mlsanity.com/paper/2404.03176/) (2024)
- [An Information-Theoretic Approach to Generalization Theory](https://mlsanity.com/paper/2408.13275/) (2024)
- [PAC-Bayes Bounds for Bandit Problems: A Survey and Experimental Comparison](https://mlsanity.com/paper/2211.16110/) (2022)
- [The Method of Gaps: Exact Expressions for the Generalization Error of Supervised Learning Algorithms](https://mlsanity.com/paper/2411.12030/) (2024)
- [Self-Organizing mmWave MIMO Cell-Free Networks With Hybrid Beamforming: A Hierarchical DRL-Based Design](https://mlsanity.com/paper/2103.11823/) (2021)
- [Meta Reinforcement Learning for Resource Allocation in Aerial Active-RIS-assisted Networks with Rate-Splitting Multiple Access](https://mlsanity.com/paper/2403.08648/) (2024)

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

- [Generalization Analysis and Method for Domain Generalization for a Family of Recurrent Neural Networks](https://mlsanity.com/paper/2601.08122/) (2026)

## Abstract (arXiv)

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_∞ 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.