Generalization of Hamiltonian algorithms

2024/05/23 by Andreas Maurer, Maurer, Andreas · 1 citation
Mathematics · Computer Science · #Advanced Optimization Algorithms Research #Matrix Theory and Algorithms #Numerical methods for differential equations

paper · pdf · doi:10.48550/arxiv.2405.14469

Abstract

The paper proves generalization results for a class of stochastic learning algorithms. The method applies whenever the algorithm generates an absolutely continuous distribution relative to some a-priori measure and the Radon Nikodym derivative has subgaussian concentration. Applications are bounds for the Gibbs algorithm and randomizations of stable deterministic algorithms as well as PAC-Bayesian bounds with data-dependent priors.

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• Generalization of Gibbs and Langevin Monte Carlo Algorithms in the Interpolation Regime

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