QuantumBoost: A lazy, yet fast, quantum algorithm for learning with weak hypotheses
Amira Abbas, Yanlin Chen, Tuyen Nguyen, Ronald de Wolf
TL;DR
QuantumBoost introduces a quantum-accelerated boosting framework that leverages approximate Bregman projections onto high-density measures and a lazy projection strategy to achieve superior runtimes. The algorithm attains empirical error $\epsilon$ with cost $\tilde{O}\left(\frac{W}{\sqrt{\epsilon}\gamma^{4}}\right)$ and ensures generalization guarantees with a modest training set size, matching AdaBoost in $\gamma$-scaling while improving the $1/\epsilon$ dependence to $\tilde{O}(1/\sqrt{\epsilon})$. The key contributions are the quantum speeding of Bregman projections, the implicit representation of weight updates, and the novel use of lazy projections in boosting, supported by a rigorous regret and error analysis. This work advances the theoretical understanding of quantum-accelerated learning and provides a framework with potential practical impact for speeding up boosting on large-scale datasets under realistic quantum access constraints.
Abstract
The technique of combining multiple votes to enhance the quality of a decision is the core of boosting algorithms in machine learning. In particular, boosting provably increases decision quality by combining multiple weak learners-hypotheses that are only slightly better than random guessing-into a single strong learner that classifies data well. There exist various versions of boosting algorithms, which we improve upon through the introduction of QuantumBoost. Inspired by classical work by Barak, Hardt and Kale, our QuantumBoost algorithm achieves the best known runtime over other boosting methods through two innovations. First, it uses a quantum algorithm to compute approximate Bregman projections faster. Second, it combines this with a lazy projection strategy, a technique from convex optimization where projections are performed infrequently rather than every iteration. To our knowledge, QuantumBoost is the first algorithm, classical or quantum, to successfully adopt a lazy projection strategy in the context of boosting.