Prospective Learning: Learning for a Dynamic Future

TL;DR

This paper introduces Prospective Learning, a new theoretical framework and algorithm for machine learning in dynamic environments where data distributions and goals change over time, demonstrating improved performance over traditional methods.

Contribution

It develops the Prospective ERM algorithm that incorporates time into learning, with theoretical guarantees and empirical validation on synthetic and real datasets.

Findings

Prospective ERM converges to the Bayes risk under certain conditions.

Standard ERM fails in dynamic distribution scenarios.

Empirical results on MNIST and CIFAR-10 show improved adaptability.

Abstract

In real-world applications, the distribution of the data, and our goals, evolve over time. The prevailing theoretical framework for studying machine learning, namely probably approximately correct (PAC) learning, largely ignores time. As a consequence, existing strategies to address the dynamic nature of data and goals exhibit poor real-world performance. This paper develops a theoretical framework called "Prospective Learning" that is tailored for situations when the optimal hypothesis changes over time. In PAC learning, empirical risk minimization (ERM) is known to be consistent. We develop a learner called Prospective ERM, which returns a sequence of predictors that make predictions on future data. We prove that the risk of prospective ERM converges to the Bayes risk under certain assumptions on the stochastic process generating the data. Prospective ERM, roughly speaking, incorporates time as an input in addition to the data. We show that standard ERM as done in PAC learning, without incorporating time, can result in failure to learn when distributions are dynamic. Numerical experiments illustrate that prospective ERM can learn synthetic and visual recognition problems constructed from MNIST and CIFAR-10. Code at https://github.com/neurodata/prolearn.