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.