This thesis aims at constructing, calibrating and studying multi-task estimators, in a frequentist non-parametric and non-asymptotic framework. We consider here kernel ridge regression and extend the existing multi-task regression methods in this setting. The main question is the calibration of a matricial regularization parameter, which encodes the similarity between the tasks. We propose a method to calibrate this parameter, based on the estimation of the covariance matrix of the noise between tasks. We then show optimality guarantees for the estimator thus obtained, via an oracle inequality. We also check its behaviour on simulated examples. We carefully bound the risks of both multi-task and single-task oracle estimators in some specific settings. This allows us to discern several interesting situations, whether the multi-task oracle outperforms the single-task one or not. This ensure the oracle inequality enforces the multi-task oracle to have a lower risk than the single-task one in the studied settings. Finally, we check the behaviour of the oracles on simulated examples.
