Enterprise AI Analysis
Privacy Preserving Reinforcement Learning with One-Sided Feedback
We study reinforcement learning (RL) in multi-dimensional continuous state and action spaces with one-sided feedback, where the agent receives partial observations of the state and obtains reward information for only a subset of the state-action space at each time step. This setting introduces substantial challenges in both learning efficiency and privacy preservation. To address these challenges, we propose POOL, a novel privacy-preserving RL algorithm. We conduct a comprehensive theoretical analysis of POOL, deriving a sample complexity bound of O((1 + Ερ)H³α−²), which matches the known lower bounds for non-private RL. Here, Ep denotes the privacy parameter, H is the time horizon, and a is optimality-gap parameter. Our findings show that it is possible to enforce strong privacy guarantees while maintaining high learning efficiency, marking a significant step toward practical, privacy-aware RL in multi-dimensional environments with one-sided feedback.
Authors: Lin Cong, Guangyan Gan, Hanzhang Qin, Zhenzhen Yan
Executive Impact Summary
This paper introduces POOL, a novel algorithm that tackles the challenging problem of privacy-preserving reinforcement learning (RL) in multi-dimensional continuous state and action spaces with one-sided feedback. This setting is crucial for real-world applications in areas like marketing, autonomous systems, and healthcare, where data is often sensitive and observations are partial. POOL successfully combines partial discretization and piecewise-linear approximation with strong p-zero-concentrated differential privacy (p-zCDP) guarantees. The theoretical analysis demonstrates a sample complexity bound matching non-private RL, while empirical validation on inventory control problems shows superior performance over baseline private methods. This work enables scalable, privacy-aware decision-making in complex, data-sensitive enterprise environments.
Efficiency of Non-Private RL Achieved
Privacy Guarantee Adherence (p-zCDP)
Performance Improvement Over Baselines
Deep Analysis & Enterprise Applications
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Multi-dimensional Continuous RL with One-Sided Feedback
The core challenge addressed by POOL, combining continuous state/action spaces, partial observability, and privacy requirements in real-world applications.
Traditional Reinforcement Learning (RL) often assumes full observability and discrete state-action spaces. However, many real-world scenarios in domains like marketing, autonomous systems, and healthcare involve continuous, high-dimensional data and provide only partial, or "one-sided," feedback. Furthermore, the sensitive nature of this data necessitates strong privacy guarantees. Existing solutions largely fail to address this complex combination of challenges simultaneously, creating a significant gap for practical, privacy-aware RL.
POOL's Differentiating Technical Innovations
| Feature | Standard RL (Tabular, Full Feedback) | Existing Private/One-Sided RL | POOL's Approach |
|---|---|---|---|
| State/Action Spaces | Discrete/Finite | Mostly Discrete, 1D Continuous |
|
| Feedback Type | Full Information | One-Sided (1D) |
|
| Privacy Guarantee | Not Addressed | Discrete Tabular DP |
|
| Scalability | Limited by Tabular Size | Limited to 1D/Tabular |
|
| Computational Complexity | Standard | Varied, often high for continuous |
|
Enterprise Process Flow: The POOL Algorithm
Initialize Ph, VH+1=0
→
Iterate h from H to 1
→
Partition action space into M zones (l2 norm)
→
Construct Private Value Function Estimates (Gaussian Mechanism)
→
Interpolate Value Function via Multi-dimensional Piecewise-linear Approximation
→
Output Policy {πh} for each h
POOL addresses these complexities through a unique combination of partial discretization, which tackles the curse of dimensionality in continuous state-action spaces, and multi-dimensional piecewise-linear approximation, which efficiently estimates value functions under privacy constraints. The Gaussian mechanism is applied to ensure p-zCDP for sensitive data components, enabling robust privacy guarantees.
O((1 + Eρ)H³α⁻²)
Sample Complexity Bound for POOL, matching non-private RL efficiency while ensuring strong p-zCDP privacy in multi-dimensional, one-sided feedback environments.
The theoretical analysis of POOL establishes a rigorous sample complexity bound that demonstrates its efficiency. This bound scales polynomially with the episode length (H), discretization granularity (M), and dimensionality, inversely with the privacy budget (ρ). Crucially, it matches the information-theoretic lower bounds for non-private RL, a significant achievement for a privacy-preserving algorithm in such a complex setting. This indicates that strong privacy can be maintained without sacrificing learning performance.
Real-World Impact: Inventory Control Application
POOL was empirically validated on lost-sales inventory control problems using both synthetic and real-world data (Rossmann Sales dataset). The experiments demonstrated that POOL consistently outperforms standard private baselines (Input Perturbation and Output Perturbation) by achieving significantly lower relative optimality gaps, and closely approaching the performance of the non-private algorithm. This highlights POOL's effectiveness in providing privacy-preserving, near-optimal solutions for complex business optimization challenges where data sensitivity and partial observations are common.
Specifically, across varying privacy budgets, POOL showed superior performance, maintaining high learning efficiency even with strong privacy guarantees. The discretization strategy was also shown to be more effective and efficient than standard grid-based methods, further solidifying POOL's practical applicability in multi-dimensional continuous environments.
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