# Local Rademacher Complexity-based Learning Guarantees for Multi-Task Learning

arXiv: https://arxiv.org/abs/1602.05916 · HTML: https://mlsanity.com/paper/1602.05916/

## Key facts

- Cited by 16 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 18 Feb 2016.

## Built on by (most cited first, 16 of 16)

- [Theoretical Insights into Overparameterized Models in Multi-Task and Replay-Based Continual Learning](https://mlsanity.com/paper/2408.16939/) (2024)
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- [From Low Intrinsic Dimensionality to Non-Vacuous Generalization Bounds in Deep Multi-Task Learning](https://mlsanity.com/paper/2501.19067/) (2025)
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- [A Unified Analysis of Multi-task Functional Linear Regression Models with Manifold Constraint and Composite Quadratic Penalty](https://mlsanity.com/paper/2211.04874/) (2022)
- [Operator-Based Generalization Bound for Deep Learning: Insights on Multi-Task Learning](https://mlsanity.com/paper/2512.19184/) (2025)
- [On the Koopman-Based Generalization Bounds for Multi-Task Deep Learning](https://mlsanity.com/paper/2512.19199/) (2025)
- [Operator-Theoretic Generalization Bounds for Multitask Deep Learning](https://mlsanity.com/paper/2608.15982/) (2026)
- [Mixture of Online and Offline Experts for Non-stationary Time Series](https://mlsanity.com/paper/2202.05996/) (2022)
- [A Statistical Analysis of Deep Federated Learning for Intrinsically Low-dimensional Data](https://mlsanity.com/paper/2410.20659/) (2024)
- [Sharper Risk Bound for Multi-Task Learning with Multi-Graph Dependent Data](https://mlsanity.com/paper/2502.18167/) (2025)
- [Federated Learning with Unlabeled Clients: Personalization Can Happen in Low Dimensions](https://mlsanity.com/paper/2505.15579/) (2025)

## Abstract (arXiv)

We show a Talagrand-type concentration inequality for Multi-Task Learning (MTL), using which we establish sharp excess risk bounds for MTL in terms of distribution- and data-dependent versions of the Local Rademacher Complexity (LRC). We also give a new bound on the LRC for norm regularized as well as strongly convex hypothesis classes, which applies not only to MTL but also to the standard i.i.d. setting. Combining both results, one can now easily derive fast-rate bounds on the excess risk for many prominent MTL methods, including---as we demonstrate---Schatten-norm, group-norm, and graph-regularized MTL. The derived bounds reflect a relationship akeen to a conservation law of asymptotic convergence rates. This very relationship allows for trading off slower rates w.r.t. the number of tasks for faster rates with respect to the number of available samples per task, when compared to the rates obtained via a traditional, global Rademacher analysis.