Non-parametric method improves learning in uncertain decision problems
Non-Parametric Optimization for Scalable Learning in Stochastic Decision Problems
Machine Learning
Summary
Making good decisions when things are uncertain can be very tricky, especially when the problem changes over time. The authors developed a new mathematical approach that doesn’t rely on fixed assumptions about the problem’s shape. They built a learning algorithm that stays effective even as conditions shift and the problem size grows. Experiments showed their method works better and scales well compared to other popular approaches.
What this means in practice
- •For machine learning engineers: Improve adaptation and scalability of learning models under changing data distributions using a scalable algorithm insensitive to model parameter dimension.
- •For control system developers: Enhance adaptive control systems that require decisions under uncertainty by applying scalable stochastic optimization with non-parametric optimality conditions.
Authors
Mohsen Amidzadeh, Lauri Viitasaari, Mario Di Francesco
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.