A Markovian Model for Learning-to-Optimize

TL;DR

This paper introduces a probabilistic Markovian model for stochastic optimization algorithms, providing theoretical bounds on their convergence and empirical validation through five experiments.

Contribution

It develops a general probabilistic framework for analyzing stochastic algorithms, enabling learning and performance guarantees beyond traditional methods.

Findings

PAC-Bayesian bounds for convergence rates

Model applicable to various stochastic algorithms

Experimental validation of theoretical claims

Abstract

We present a probabilistic model for stochastic iterative algorithms with the use case of optimization algorithms in mind. Based on this model, we present PAC-Bayesian generalization bounds for functions that are defined on the trajectory of the learned algorithm, for example, the expected (non-asymptotic) convergence rate and the expected time to reach the stopping criterion. Thus, not only does this model allow for learning stochastic algorithms based on their empirical performance, it also yields results about their actual convergence rate and their actual convergence time. We stress that, since the model is valid in a more general setting than learning-to-optimize, it is of interest for other fields of application, too. Finally, we conduct five practically relevant experiments, showing the validity of our claims.