Learning-to-Optimize with PAC-Bayesian Guarantees: Theoretical Considerations and Practical Implementation

arXiv:2404.03290v1 Announce Type: new
Abstract: We use the PAC-Bayesian theory for the setting of learning-to-optimize. To the best of our knowledge, we present the first framework to learn optimization algorithms with provable generalization guarantees (PAC-Bayesian bounds) and explicit trade-off between convergence guarantees and convergence speed, which contrasts with the typical worst-case analysis. Our learned optimization algorithms provably outperform related ones derived from a (deterministic) worst-case analysis. The results rely on PAC-Bayesian bounds for general, possibly unbounded loss-functions based on exponential …

abstract algorithms arxiv bayesian best of case convergence cs.lg framework implementation knowledge learn math.oc optimization practical speed theory trade trade-off type