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This research introduces D-IMPL, a novel algorithm that utilizes diffusion models to solve parameterized black-box optimization problems by learning efficient minimization policies. By amortizing computational costs during the inference stage, the method effectively handles non-convex objectives while maintaining strong theoretical sample complexity guarantees. This advancement highlights the expanding utility of generative AI beyond simple content creation into complex mathematical optimization tasks.
D-IMPL: A Diffusion-based Solver for Parameterized BBOs
arXiv:2609.22752v1 Announce Type: new Abstract: Diffusion models have demonstrated strong power in generative modeling tasks across multiple domains, exhibiting a remarkable capability of learning complex distributions from samples. In this paper, we leverage such capability to design an efficient universal diffusion-based solver for parameterized black-box optimizations (BBO), where the optimizer has only black-box access to queries of the objective function at the learning stage, yet is able to reduce the additional computational cost at the inference stage for each BBO instance while also capturing the potential multi-modal landscape of non-convex objectives. To cast our formulation as a compatible generative modeling task, we introduce the notion of minimization policy as a new solution concept, which defines a sampling distribution over the solutions that should concentrate around the minimizer set for each BBO instance. We then propose Diffusion-based Iterative Minimization Policy Learning (D-IMPL), a practical generative-model-based solver for solving parameterized BBOs that employs diffusion models to learn a minimization policy, whose density is proportional to the exponential of the negated objective values, thereby amortizing the computational costs across different BBO instances. Furthermore, we demonstrate the performance of our D-IMPL algorithm by establishing a sample complexity guarantee showing that a $\delta$-approximate minimization policy can be effectively learned within $O(\log(1/\delta))$ iterations, and by extensive empirical evaluations over a range of constrained and unconstrained BBO tasks.
Abstract:Diffusion models have demonstrated strong power in generative modeling tasks across multiple domains, exhibiting a remarkable capability of learning complex distributions from samples. In this paper, we leverage such capability to design an efficient universal diffusion-based solver for parameterized black-box optimizations (BBO), where the optimizer has only black-box access to queries of the objective function at the learning stage, yet is able to reduce the additional computational cost at the inference stage for each BBO instance while also capturing the potential multi-modal landscape of non-convex objectives. To cast our formulation as a compatible generative modeling task, we introduce the notion of minimization policy as a new solution concept, which defines a sampling distribution over the solutions that should concentrate around the minimizer set for each BBO instance. We then propose Diffusion-based Iterative Minimization Policy Learning (D-IMPL), a practical generative-model-based solver for solving parameterized BBOs that employs diffusion models to learn a minimization policy, whose density is proportional to the exponential of the negated objective values, thereby amortizing the computational costs across different BBO instances. Furthermore, we demonstrate the performance of our D-IMPL algorithm by establishing a sample complexity guarantee showing that a $\delta$-approximate minimization policy can be effectively learned within $O(\log(1/\delta))$ iterations, and by extensive empirical evaluations over a range of constrained and unconstrained BBO tasks.
Machine Learning (cs.LG); Optimization and Control (math.OC)
arXiv:2609.22752 [cs.LG]
(or arXiv:2609.22752v1 [cs.LG] for this version)
https://doi.org/10.48550/arXiv.2609.22752 Focus to learn more arXiv-issued DOI via DataCite (pending registration)
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