Homomorphic Advantage Operator: Stabilizing Reinforcement Learning Under Fully Homomorphic Encryption Constraints

Problem

The application of Fully Homomorphic Encryption (FHE) in reinforcement learning (RL) necessitates polynomial approximations due to the non-linear operations involved. This requirement can lead to divergence from the Bellman drift, which is critical for maintaining the stability and convergence of RL algorithms. The authors address this gap by proposing a novel approach that stabilizes RL under FHE constraints. The work is presented as a preprint and has not undergone peer review.

Method

The core technical contribution is the Homomorphic Advantage Operator (HAO), which adapts a zero-mean centering projection from advantage-based value estimation to temporal-difference (TD) targets. This method preserves per-state action rankings and operates without introducing additional non-linear multiplicative depth, thus avoiding the need for ciphertext bootstrapping. The evaluation methodology consists of a three-tier experimental framework that includes:

• A Tabular Markov Decision Process (MDP) to assess basic RL performance.
• An encrypted CartPole environment utilizing CKKS cryptographic operations to evaluate performance under FHE constraints.
• A 20-node logistics routing benchmark featuring dense continuous features to test scalability and robustness in more complex scenarios.

Results

The results demonstrate significant improvements in stability and performance:

• HAO agents achieved 0% boundary breaches across all random seeds, compared to 3 out of 5 seeds for regularization alone and 83.8% of episodes for the unstabilized baseline.
• In tabular domains, the optimal policy accuracy improved by 18.0 percentage points, indicating a substantial enhancement in learning effectiveness under FHE constraints.

Limitations

The authors do not report any limitations in their work. However, the lack of peer review may imply that further validation and scrutiny are necessary to confirm the robustness of the proposed method.

Why it matters

The implications of this work are significant for the integration of privacy-preserving techniques in RL applications. By stabilizing RL under FHE constraints, the HAO framework opens avenues for secure and efficient learning in sensitive environments, such as healthcare and finance, where data privacy is paramount. This advancement could lead to broader adoption of RL in real-world applications that require stringent security measures.