Tighter Generalisation Bounds via Interpolation
This work addresses the need for more accurate generalization bounds in machine learning, offering incremental improvements over existing methods.
The paper tackles the problem of deriving tighter generalization bounds in statistical learning by introducing a recipe for new PAC-Bayes bounds based on (f, Γ)-divergence and interpolating between multiple probability divergences, resulting in improved theoretical guarantees and practical performance.
This paper contains a recipe for deriving new PAC-Bayes generalisation bounds based on the $(f, Γ)$-divergence, and, in addition, presents PAC-Bayes generalisation bounds where we interpolate between a series of probability divergences (including but not limited to KL, Wasserstein, and total variation), making the best out of many worlds depending on the posterior distributions properties. We explore the tightness of these bounds and connect them to earlier results from statistical learning, which are specific cases. We also instantiate our bounds as training objectives, yielding non-trivial guarantees and practical performances.