多任务约束优化提升小样本下的模型参数估计精度

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 \emph{cross-learning} framework to overcome data scarcity by jointly estimating \emph{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.