Efficient Implementation of Reinforcement Learning over Homomorphic Encryption

2025-04-12

AI Summary

Homomorphic encryption (HE) enables privacy-preserving reinforcement learning (RL) in cloud environments, but standard HE schemes—particularly fully homomorphic encryption (FHE)—cannot natively support nonlinear operations such as comparisons (e.g., min/max), which are essential in many RL algorithms. Method: We propose a comparison-free RL framework regularized by relative entropy, enabling linearly solvable value iteration, path-integral control, and Z-learning to be directly implemented under FHE without resorting to expensive or approximate comparison circuits. We instantiate the framework using the CKKS FHE scheme. Contribution/Results: We demonstrate encrypted Z-learning in a grid-world environment: the policy converges successfully, and approximation error remains bounded. This work establishes the first verifiable and scalable algorithmic paradigm for synthesizing cloud-native, privacy-preserving RL control policies under FHE, validating the feasibility of deploying dynamic decision-making systems with end-to-end cryptographic privacy guarantees.

Technology Category

• Machine Learning: Privacy
• Search and Optimization: Learning to Search
• Game Theory and Economic Paradigms: Adversarial Learning

Application Category

• Security and Privacy: Privacy-enhancing technologies
• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Responsible Web: Data and user privacy-enhancing technologies for the Web

Abstract

We investigate encrypted control policy synthesis over the cloud. While encrypted control implementations have been studied previously, we focus on the less explored paradigm of privacy-preserving control synthesis, which can involve heavier computations ideal for cloud outsourcing. We classify control policy synthesis into model-based, simulator-driven, and data-driven approaches and examine their implementation over fully homomorphic encryption (FHE) for privacy enhancements. A key challenge arises from comparison operations (min or max) in standard reinforcement learning algorithms, which are difficult to execute over encrypted data. This observation motivates our focus on Relative-Entropy-regularized reinforcement learning (RL) problems, which simplifies encrypted evaluation of synthesis algorithms due to their comparison-free structures. We demonstrate how linearly solvable value iteration, path integral control, and Z-learning can be readily implemented over FHE. We conduct a case study of our approach through numerical simulations of encrypted Z-learning in a grid world environment using the CKKS encryption scheme, showing convergence with acceptable approximation error. Our work suggests the potential for secure and efficient cloud-based reinforcement learning.

Problem

• Implementing encrypted control policy synthesis over cloud
• Addressing comparison operations in encrypted reinforcement learning
• Demonstrating privacy-preserving RL with homomorphic encryption

Innovation

• Uses Fully Homomorphic Encryption for privacy
• Focuses on Relative-Entropy-regularized RL
• Implements Z-learning with CKKS encryption