Alternating Diffusion for Proximal Sampling with Zeroth Order Queries
arXiv:2603.19633v1 Announce Type: new Abstract: This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and backward iterations of the heat flow. The backward step was originally implemented by rejection sampling, whereas we directly simulate the dynamics. Unlike diffusion-based sampling methods that estimate scores via learned models or by invoking auxiliary samplers, our method treats the intermediate particle distribution as a Gaussian mixture, thereby yielding a Monte Carlo score estimator from directly samplable distributions. Theoretically, when the score estimation error is sufficiently controlled, our method inherits the exponential convergence of proximal sampling under isoperimetric conditions on the target distribution. In practice, the algorithm avoids rejection sampling, permits flexible step sizes
arXiv:2603.19633v1 Announce Type: new Abstract: This work introduces a new approximate proximal sampler that operates solely with zeroth-order information of the potential function. Prior theoretical analyses have revealed that proximal sampling corresponds to alternating forward and backward iterations of the heat flow. The backward step was originally implemented by rejection sampling, whereas we directly simulate the dynamics. Unlike diffusion-based sampling methods that estimate scores via learned models or by invoking auxiliary samplers, our method treats the intermediate particle distribution as a Gaussian mixture, thereby yielding a Monte Carlo score estimator from directly samplable distributions. Theoretically, when the score estimation error is sufficiently controlled, our method inherits the exponential convergence of proximal sampling under isoperimetric conditions on the target distribution. In practice, the algorithm avoids rejection sampling, permits flexible step sizes, and runs with a deterministic runtime budget. Numerical experiments demonstrate that our approach converges rapidly to the target distribution, driven by interactions among multiple particles and by exploiting parallel computation.
Executive Summary
This article introduces Alternating Diffusion for Proximal Sampling with Zeroth-Order Queries, a novel approximate proximal sampler that relies solely on zeroth-order information of the potential function. Building upon the theoretical foundation of proximal sampling as alternating forward and backward iterations of the heat flow, the authors propose a direct simulation of the backward step, avoiding rejection sampling and enabling flexible step sizes and deterministic runtime budgets. Numerical experiments demonstrate the algorithm's rapid convergence to the target distribution, driven by particle interactions and parallel computation. The methodology has the potential to improve the efficiency of proximal sampling in various applications.
Key Points
- ▸ Alternating Diffusion proposes a novel proximal sampler based on zeroth-order information of the potential function.
- ▸ The algorithm avoids rejection sampling and enables flexible step sizes and deterministic runtime budgets.
- ▸ Numerical experiments demonstrate rapid convergence to the target distribution driven by particle interactions and parallel computation.
Merits
Strength in Theoretical Foundation
The article builds upon the established theoretical foundation of proximal sampling, providing a solid basis for the proposed methodology.
Flexibility and Determinism
The algorithm's ability to avoid rejection sampling and enable flexible step sizes and deterministic runtime budgets enhances its practicality and reliability.
Efficiency and Convergence
Numerical experiments demonstrate the algorithm's rapid convergence to the target distribution, driven by particle interactions and parallel computation, which is a significant improvement over existing methods.
Demerits
Assumption of Isoperimetric Conditions
The algorithm's theoretical convergence relies on the assumption of isoperimetric conditions on the target distribution, which may not always hold in practice.
Limited Interpretability
The algorithm's reliance on zeroth-order information of the potential function may limit its interpretability and ability to provide insights into the underlying dynamics.
Expert Commentary
The article presents a novel and innovative approach to proximal sampling, leveraging the concept of Alternating Diffusion to improve the efficiency and reliability of the algorithm. While the theoretical foundation is solid, the assumption of isoperimetric conditions on the target distribution may limit the algorithm's applicability in practice. Nevertheless, the article's findings on the importance of particle interactions and parallel computation in proximal sampling are timely and relevant, and the proposed algorithm has the potential to make a significant impact in various fields. Further research is needed to fully explore the algorithm's capabilities and limitations.
Recommendations
- ✓ Future research should investigate the extension of the proposed algorithm to more complex distributions and scenarios, including those with non-isoperimetric conditions.
- ✓ The algorithm's performance in real-world applications should be thoroughly evaluated to assess its practicality and reliability.
Sources
Original: arXiv - cs.LG
