Non-Parametric Optimization for Scalable Learning in Stochastic Decision Problems

Mohsen Amidzadeh; Lauri Viitasaari; Mario Di Francesco

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arXiv · 2610.23204

Non-Parametric Optimization for Scalable Learning in Stochastic Decision Problems

Mohsen Amidzadeh·Lauri Viitasaari·Mario Di Francesco

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Abstract

Stochastic optimization (SO) plays a central role in decision-making under uncertainty. Among SO problems, time-varying stochastic optimization (TV-SO) is particularly important due to its applications in adaptive control and machine learning. Non-parametric approaches have been proposed for time-varying deterministic optimization; however, they have not been developed for their stochastic counterparts. This work addresses that gap by developing a stochastic variational framework based on Malliavin calculus. This framework yields non-parametric optimality conditions for SO problems with stochastic decisions and supports the design of a scalable deep-learning algorithm that is insensitive to the parameterization dimension. This algorithm, called the Stochastic Path Follower (SPF), is applied to two important problems under distribution drift, namely least-squares recovery and logistic regression. Experimental results show that the proposed approach outperforms state-of-the-art learning-based and gradient-based methods in both performance and scalability.

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BibTeX RIS

Mohsen Amidzadeh, Lauri Viitasaari, Mario Di Francesco. 2026-10-16. Non-Parametric Optimization for Scalable Learning in Stochastic Decision Problems. https://arxiv.org/abs/2610.23204

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