The formulation of history-dependent material laws has been a significant challenge in solid mechanics for over a century. Recently, data-driven techniques have generated accurate and reliable surrogates for elasto-plastic constitutive laws. However, most of these methods are deeply rooted in the big data domain, \cite{Flaschel2022}, and would fail when only a few physically obtained data points are available. To combat this, we propose a plasticity formulation with model-data-driven yield functions that is designed to work in the small data regime \cite{Fuhg2023}. A phenomenological yield model is locally improved by a data-driven correction term obtained from a machine learning (ML) metamodel. The training procedure relies on small datasets of the true location of the initial yield surface in the stress space. This allows seamless merging of conventional material models with their data-driven counterparts enabling the derivation of hybrid models that significantly improve the accuracy and robustness of traditional approaches, as well as the applicability of modern ML techniques. The proposed working principle is demonstrated with different ML approaches, i.e. Support Vector Regression (SVR), Gaussian Process Regression (GPR), and Neural Networks (NN), thus proving its versatility. In order to guarantee the convexity of model-data yield functions, convex extensions of the adopted ML techniques are introduced. The proposed approach is tested based on knowledge of a few synthetic data points on the true yield locus, obtained from standard uniaxial/biaxial tests, in limited number. The presented case study allows to reproduce a highly anisotropic yield response with tension/compression asymmetries.