Metastatic melanoma remains a life-threatening disease because most tumors develop resistance to targeted kinase inhibitors thereby regaining tumorigenic capacity. We show the 2nd generation hexavalent TRAIL receptor-targeted agonist IZI1551 to induce pronounced apoptotic cell death in mutBRAF melanoma cells. Aiming to identify molecular changes that may confer IZI1551 resistance we combined Dynamic Bayesian Network modelling with a sophisticated regularization strategy resulting in sparse and context-sensitive networks and show the performance of this strategy in the detection of cell line-specific deregulations of a signalling network. Comparing IZI1551-sensitive to IZI1551-resistant melanoma cells the model accurately and correctly predicted activation of NF$\kappa$B in concert with upregulation of the anti-apoptotic protein XIAP as the key mediator of IZI1551 resistance. Thus, the incorporation of multiple regularization functions in logical network optimization may provide a promising avenue to assess the effects of drug combinations and to identify responders to selected combination therapies.