# Multi-task learning via robust regularized clustering with non-convex group penalties

arXiv: https://arxiv.org/abs/2404.03250 · HTML: https://mlsanity.com/paper/2404.03250/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 9 of its 43 references that are in the map.
- First posted on arXiv 4 Apr 2024.

## Builds on (most cited first, 9 of 9)

- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Global Convergence of ADMM in Nonconvex Nonsmooth Optimization](https://mlsanity.com/paper/1511.06324/) (2015)
- [Network Lasso: Clustering and Optimization in Large Graphs](https://mlsanity.com/paper/1507.00280/) (2015)
- [Subgradient methods for sharp weakly convex functions](https://mlsanity.com/paper/1803.02461/) (2018)
- [Localized Lasso for High-Dimensional Regression](https://mlsanity.com/paper/1603.06743/) (2016)
- [Efficient and Scalable Multi-task Regression on Massive Number of Tasks](https://mlsanity.com/paper/1811.05695/) (2018)
- [Sparse and Robust Linear Regression: An Optimization Algorithm and Its Statistical Properties](https://mlsanity.com/paper/1505.05257/) (2015)
- [Multi-Task Learning Regression via Convex Clustering](https://mlsanity.com/paper/2304.13342/) (2023)
- [Converting ADMM to a Proximal Gradient for Efficient Sparse Estimation](https://mlsanity.com/paper/2104.10911/) (2021)

## Abstract (arXiv)

Multi-task learning (MTL) aims to improve estimation and prediction performance by sharing common information among related tasks. One natural assumption in MTL is that tasks are classified into clusters based on their characteristics. However, existing MTL methods based on this assumption often ignore outlier tasks that have large task-specific components or no relation to other tasks. To address this issue, we propose a novel MTL method called Multi-Task Learning via Robust Regularized Clustering (MTLRRC). MTLRRC incorporates robust regularization terms inspired by robust convex clustering, which is further extended to handle non-convex and group-sparse penalties. The extension allows MTLRRC to simultaneously perform robust task clustering and outlier task detection. The connection between the extended robust clustering and the multivariate M-estimator is also established. This provides an interpretation of the robustness of MTLRRC against outlier tasks. An efficient algorithm based on a modified alternating direction method of multipliers is developed for the estimation of the parameters. The effectiveness of MTLRRC is demonstrated through simulation studies and application to real data.