Relying on reduced models is nowadays a standard cunning to tackle the computational complexity of multi-contact locomotion. To be really effective, reduced models must respect some feasibility constraints in regards to the full model. However, such kind of constraints are either partially considered or just neglected inside the existing reduced problem formulation. This work presents a systematic approach to incorporate feasibility constraints inside trajectory optimization problems. In particular, we show how to learn the kinematic feasibility of the centre of mass to be achievable by the whole-body model. We validate the proposed method in the context of multi-contact locomotion: we perform two stairs climbing experiments on two humanoid robots, namely the HRP-2 robot and the new TALOS platform.