Training a Large Scale Classifier with the Quantum Adiabatic Algorithm

TL;DR

This paper explores training large-scale classifiers using quantum adiabatic algorithms, proposing an iterative optimization method that outperforms traditional boosting techniques and demonstrates potential quantum advantages through simulations.

Contribution

It introduces a scalable, iterative quantum-inspired training method for classifiers that surpasses AdaBoost and incorporates L0 regularization for improved performance.

Findings

Iterative approach effectively handles large classifier dictionaries.

Quantum adiabatic algorithm shows promise in efficiently solving training problems.

Proposed method outperforms standard boosting in numerical studies.

Abstract

In a previous publication we proposed discrete global optimization as a method to train a strong binary classifier constructed as a thresholded sum over weak classifiers. Our motivation was to cast the training of a classifier into a format amenable to solution by the quantum adiabatic algorithm. Applying adiabatic quantum computing (AQC) promises to yield solutions that are superior to those which can be achieved with classical heuristic solvers. Interestingly we found that by using heuristic solvers to obtain approximate solutions we could already gain an advantage over the standard method AdaBoost. In this communication we generalize the baseline method to large scale classifier training. By large scale we mean that either the cardinality of the dictionary of candidate weak classifiers or the number of weak learners used in the strong classifier exceed the number of variables that can be handled effectively in a single global optimization. For such situations we propose an iterative and piecewise approach in which a subset of weak classifiers is selected in each iteration via global optimization. The strong classifier is then constructed by concatenating the subsets of weak classifiers. We show in numerical studies that the generalized method again successfully competes with AdaBoost. We also provide theoretical arguments as to why the proposed optimization method, which does not only minimize the empirical loss but also adds L0-norm regularization, is superior to versions of boosting that only minimize the empirical loss. By conducting a Quantum Monte Carlo simulation we gather evidence that the quantum adiabatic algorithm is able to handle a generic training problem efficiently.