In many business settings, task-specific labeled data are scarce or costly to obtain, which limits supervised learning on a specific task. To address this challenge, we study sample sharing in the case of ridge regression: leveraging an auxiliary data set while explicitly protecting against negative transfer. We introduce a principled, data-driven rule that decides how many samples from an auxiliary dataset to add to the target training set. The rule is based on an estimate of the transfer gain i.e. the marginal reduction in the predictive error. Building on this estimator, we derive finite-sample guaranties: under standard conditions, the procedure borrows when it improves parameter estimation and abstains otherwise. In the Gaussian feature setting, we analyze which data set properties ensure that borrowing samples reduces the predictive error. We validate the approach in synthetic and real datasets, observing consistent gains over strong baselines and single-task training while avoiding negative transfer.

This paper presents a novel approach to task grouping in Multitask Learning (MTL), advancing beyond existing methods by addressing key theoretical and practical limitations. Unlike prior studies, our approach offers a more theoretically grounded method that does not rely on restrictive assumptions for constructing transfer gains. We also propose a flexible mathematical programming formulation which can accommodate a wide spectrum of resource constraints, thus enhancing its versatility. Experimental results across diverse domains, including computer vision datasets, combinatorial optimization benchmarks and time series tasks, demonstrate the superiority of our method over extensive baselines, validating its effectiveness and general applicability in MTL.

With the development of new sensors and monitoring devices, more sources of data become available to be used as inputs for machine learning models. These can on the one hand help to improve the accuracy of a model. On the other hand however, combining these new inputs with historical data remains a challenge that has not yet been studied in enough detail. In this work, we propose a transfer-learning algorithm that combines the new and the historical data, that is especially beneficial when the new data is scarce. We focus the approach on the linear regression case, which allows us to conduct a rigorous theoretical study on the benefits of the approach. We show that our approach is robust against negative transfer-learning, and we confirm this result empirically with real and simulated data.