# On regret bounds for continual single-index learning

arXiv: https://arxiv.org/abs/2102.12961 · HTML: https://mlsanity.com/paper/2102.12961/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 6 of its 24 references that are in the map.
- First posted on arXiv 25 Feb 2021.

## Builds on (most cited first, 6 of 6)

- [Variational Continual Learning](https://mlsanity.com/paper/1710.10628/) (2017)
- [A PAC-Bayesian bound for Lifelong Learning](https://mlsanity.com/paper/1311.2838/) (2013)
- [Regret Bounds for Lifelong Learning](https://mlsanity.com/paper/1610.08628/) (2016)
- [A Generalization Bound for Online Variational Inference](https://mlsanity.com/paper/1904.03920/) (2019)
- [Incremental Learning-to-Learn with Statistical Guarantees](https://mlsanity.com/paper/1803.08089/) (2018)
- [Multi-task and Lifelong Learning of Kernels](https://mlsanity.com/paper/1602.06531/) (2016)

## Abstract (arXiv)

In this paper, we generalize the problem of single-index model to the context of continual learning in which a learner is challenged with a sequence of tasks one by one and the dataset of each task is revealed in an online fashion. We propose a randomized strategy that is able to learn a common single-index (meta-parameter) for all tasks and a specific link function for each task. The common single-index allows to transfer the information gained from the previous tasks to a new one. We provide a rigorous theoretical analysis of our proposed strategy by proving some regret bounds under different assumption on the loss function.