# Cross-Learning from Scarce Data via Multi-Task Constrained Optimization

arXiv: https://arxiv.org/abs/2511.13680 · HTML: https://mlsanity.com/paper/2511.13680/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 19 of its 39 references that are in the map.
- First posted on arXiv 17 Nov 2025.

## Builds on (most cited first, 19 of 19)

- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Deep Hashing Network for Unsupervised Domain Adaptation](https://mlsanity.com/paper/1706.07522/) (2017)
- [A Survey on Multi-Task Learning](https://mlsanity.com/paper/1707.08114/) (2017)
- [Cross-stitch Networks for Multi-task Learning](https://mlsanity.com/paper/1604.03539/) (2016)
- [Which Tasks Should Be Learned Together in Multi-task Learning?](https://mlsanity.com/paper/1905.07553/) (2019)
- [The Benefit of Multitask Representation Learning](https://mlsanity.com/paper/1505.06279/) (2015)
- [Anomaly Detection in Video via Self-Supervised and Multi-Task Learning](https://mlsanity.com/paper/2011.07491/) (2020)
- [MultiNet: Real-time Joint Semantic Reasoning for Autonomous Driving](https://mlsanity.com/paper/1612.07695/) (2016)
- [Deep Multi-task Representation Learning: A Tensor Factorisation Approach](https://mlsanity.com/paper/1605.06391/) (2016)
- [Probably Approximately Correct Constrained Learning](https://mlsanity.com/paper/2006.05487/) (2020)
- [Constrained Learning with Non-Convex Losses](https://mlsanity.com/paper/2103.05134/) (2021)
- [Task Adaptive Parameter Sharing for Multi-Task Learning](https://mlsanity.com/paper/2203.16708/) (2022)
- [How Fine-Tuning Allows for Effective Meta-Learning](https://mlsanity.com/paper/2105.02221/) (2021)
- [A Brief Review of Deep Multi-task Learning and Auxiliary Task Learning](https://mlsanity.com/paper/2007.01126/) (2020)
- [The empirical duality gap of constrained statistical learning](https://mlsanity.com/paper/2002.05183/) (2020)
- [Multi-task Reinforcement Learning in Reproducing Kernel Hilbert Spaces via Cross-learning](https://mlsanity.com/paper/2008.11895/) (2020)
- [Multi-task Supervised Learning via Cross-learning](https://mlsanity.com/paper/2010.12993/) (2020)
- [Multi-task Bias-Variance Trade-off Through Functional Constraints](https://mlsanity.com/paper/2210.15573/) (2022)

## Abstract (arXiv)

A learning task, understood as the problem of fitting a parametric model from supervised data, fundamentally requires the dataset to be large enough to be representative of the underlying distribution of the source. When data is limited, the learned models fail generalize to cases not seen during training. This paper introduces a multi-task cross-learning framework to overcome data scarcity by jointly estimating deterministic parameters across multiple, related tasks. We formulate this joint estimation as a constrained optimization problem, where the constraints dictate the resulting similarity between the parameters of the different models, allowing the estimated parameters to differ across tasks while still combining information from multiple data sources. This framework enables knowledge transfer from tasks with abundant data to those with scarce data, leading to more accurate and reliable parameter estimates, providing a solution for scenarios where parameter inference from limited data is critical. We provide theoretical guarantees in a controlled framework with Gaussian data, and show the efficiency of our cross-learning method in applications with real data including image classification and propagation of infectious diseases.