Construction of non-convex polynomial loss functions for training a binary classifier with quantum annealing
This addresses the challenge of efficiently using quantum annealing for machine learning, though it appears incremental as it adapts existing loss function concepts to quantum constraints.
The researchers tackled the problem of training binary classifiers with quantum annealing by constructing non-convex polynomial loss functions that map efficiently to quantum hardware, showing these functions are robust to label noise and outperform convex methods.
Quantum annealing is a heuristic quantum algorithm which exploits quantum resources to minimize an objective function embedded as the energy levels of a programmable physical system. To take advantage of a potential quantum advantage, one needs to be able to map the problem of interest to the native hardware with reasonably low overhead. Because experimental considerations constrain our objective function to take the form of a low degree PUBO (polynomial unconstrained binary optimization), we employ non-convex loss functions which are polynomial functions of the margin. We show that these loss functions are robust to label noise and provide a clear advantage over convex methods. These loss functions may also be useful for classical approaches as they compile to regularized risk expressions which can be evaluated in constant time with respect to the number of training examples.