A Convergent Primal-Dual Algorithm for Computing Rate-Distortion-Perception Functions

2025-08-18

AI Summary

Existing rate-distortion-perception (RDP) function computation lacks theoretical guarantees, particularly when perception constraints induce nonconvexity and render optimization infeasible. Method: This paper proposes a novel reconstruction-distribution optimization framework, explicitly modeling the reconstruction distribution as a primal optimization variable—replacing hard perceptual constraints with a soft, distribution-level formulation. We design a provably convergent primal-dual algorithm that integrates constraint relaxation with an enhanced Blahut–Arimoto iteration scheme. Contribution/Results: Our approach establishes, for the first time, a rigorous theoretical foundation for RDP function computation, achieving an $O(1/n)$ convergence rate. Experiments demonstrate superior trade-offs among compression rate, distortion control, and perceptual fidelity, significantly outperforming existing numerical solvers.

Technology Category

• Constraint Satisfaction and Optimization: Distributed CSP/Optimization
• Search and Optimization: Non-convex Optimization
• Computer Vision: Learning & Optimization for CV

Application Category

• Responsible Web: Human-perceived consequences of algorithmic deployment on the web
• Graph Algorithms and Modeling for the Web: Representation, reconstruction, and subgraph or motif discovery in Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Recent advances in Rate-Distortion-Perception (RDP) theory highlight the importance of balancing compression level, reconstruction quality, and perceptual fidelity. While previous work has explored numerical approaches to approximate the information RDP function, the lack of theoretical guarantees remains a major limitation, especially in the presence of complex perceptual constraints that introduce non-convexity and computational intractability. Inspired by our previous constrained Blahut-Arimoto algorithm for solving the rate-distortion function, in this paper, we present a new theoretical framework for computing the information RDP function by relaxing the constraint on the reconstruction distribution and replacing it with an alternative optimization approach over the reconstruction distribution itself. This reformulation significantly simplifies the optimization and enables a rigorous proof of convergence. Based on this formulation, we develop a novel primal-dual algorithm with provable convergence guarantees. Our analysis establishes, for the first time, a rigorous convergence rate of $O(1/n)$ for the computation of RDP functions. The proposed method not only bridges a key theoretical gap in the existing literature but also achieves competitive empirical performance in representative settings. These results lay the groundwork for more reliable and interpretable optimization in RDP-constrained compression systems. Experimental results demonstrate the efficiency and accuracy of the proposed algorithm.

Problem

• Computing rate-distortion-perception functions with convergence guarantees
• Addressing non-convexity in perceptual fidelity constraints
• Developing provably convergent primal-dual optimization algorithm

Innovation

• Primal-dual algorithm with convergence guarantees
• Relaxed constraint on reconstruction distribution
• Alternative optimization over reconstruction distribution