Generalization bounds are valuable both for theory and applications. On the one hand, they shed light on the mechanisms that underpin the learning processes; on the
other, they certify how well a learned model performs against unseen inputs. In this work we build upon a recent breakthrough in compression theory (Campi & Garatti,
2023) to develop a new framework yielding tight generalization bounds of wide practical applicability. The core idea is to embed any given learning algorithm into
a suitably-constructed meta-algorithm (here called Pick-to-Learn, P2L) in order to instill desirable compression properties. When applied to the MNIST classification
dataset and to a synthetic regression problem, P2L not only attains generalization bounds that compare favorably with the state of the art (test-set and PAC-Bayes bounds), but it also learns models with better post-training performance