arXiv:2601.22932v2 Announce Type: replace Abstract: We study a sampling problem whose target distribution is $\pi \propto \exp(-f-r)$ where the data fidelity term $f$ is Lipschitz smooth while the regularizer term $r=r_1-r_2$ is a non-smooth difference-of-convex (DC) function, i.e., $r_1,r_2$ are convex. By leveraging the DC structure of $r$, we can smooth out $r$ by applying Moreau envelopes to $r_1$ and $r_2$ separately. In line with DC programming, we then redistribute the concave part of the regularizer to the data fidelity and study its corresponding proximal Langevin algorithm (termed DC
This research addresses a fundamental challenge in complex optimization for AI and machine learning, an area of continuous and rapid advancement. The focus on Langevin algorithms and non-smooth convex optimization reflects the current drive for more efficient and robust sampling in high-dimensional spaces.
Improved sampling algorithms can lead to more efficient training of complex AI models, especially in areas like Bayesian inference and generative models, enhancing their capabilities and reducing computational costs.
This research introduces a novel approach using Difference-of-Convex Langevin Algorithm (DC-LA) to handle non-smooth regularizers, potentially making previously intractable optimization problems solvable or more efficient.
- · AI/ML researchers
- · Developers of generative AI models
- · Sectors using complex Bayesian inference
More robust and efficient AI models are developed for various applications.
Reduced computational overhead for certain classes of AI problems, potentially accelerating research and deployment in areas like drug discovery or materials science.
The broader accessibility of complex AI techniques due to lower computational barriers could foster new applications and innovation across industries.
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Read at arXiv cs.LG