# Nonparametric Online Learning Using Lipschitz Regularized Deep Neural Networks

## TL;DR

This paper investigates the use of Lipschitz regularized deep neural networks for online learning, demonstrating their ability to adapt and converge to optimal predictions in non-i.i.d. stationary and ergodic environments.

## Contribution

It provides the first theoretical analysis of Lipschitz regularized deep neural networks in online learning, establishing their generalization and convergence guarantees.

## Key findings

- Proves generalization abilities of Lipschitz regularized DNNs in online settings.
- Shows convergence to the optimal prediction strategy under stationary ergodic processes.
- Extends understanding of DNN performance beyond offline, i.i.d. assumptions.

## Abstract

Deep neural networks are considered to be state of the art models in many offline machine learning tasks. However, their performance and generalization abilities in online learning tasks are much less understood. Therefore, we focus on online learning and tackle the challenging problem where the underlying process is stationary and ergodic and thus removing the i.i.d. assumption and allowing observations to depend on each other arbitrarily. We prove the generalization abilities of Lipschitz regularized deep neural networks and show that by using those networks, a convergence to the best possible prediction strategy is guaranteed.