  Multi-task learning (MTL) is a learning paradigm that enables the
simultaneous training of multiple communicating algorithms. Although MTL has
been successfully applied to ether regression or classification tasks alone,
incorporating mixed types of tasks into a unified MTL framework remains
challenging, primarily due to variations in the magnitudes of losses associated
with different tasks. This challenge, particularly evident in MTL applications
with joint feature selection, often results in biased selections. To overcome
this obstacle, we propose a provable loss weighting scheme that analytically
determines the optimal weights for balancing regression and classification
tasks. This scheme significantly mitigates the otherwise biased feature
selection. Building upon this scheme, we introduce MTLComb, an MTL algorithm
and software package encompassing optimization procedures, training protocols,
and hyperparameter estimation procedures. MTLComb is designed for learning
shared predictors among tasks of mixed types. To showcase the efficacy of
MTLComb, we conduct tests on both simulated data and biomedical studies
pertaining to sepsis and schizophrenia.
