Robust Classification with Adiabatic Quantum Optimization

TL;DR

This paper introduces a novel non-convex loss function, q-loss, designed for robust binary classification that is compatible with adiabatic quantum optimization hardware, demonstrating improved robustness against label noise.

Contribution

The paper presents a new hardware-compatible non-convex loss function, q-loss, for robust classification, validated with classical heuristics as a stand-in for quantum hardware.

Findings

q-loss improves robustness against label noise

Testing shows lower test error with q-loss on various datasets

Non-convexity of q-loss enhances robustness

Abstract

We propose a non-convex training objective for robust binary classification of data sets in which label noise is present. The design is guided by the intention of solving the resulting problem by adiabatic quantum optimization. Two requirements are imposed by the engineering constraints of existing quantum hardware: training problems are formulated as quadratic unconstrained binary optimization; and model parameters are represented as binary expansions of low bit-depth. In the present work we validate this approach by using a heuristic classical solver as a stand-in for quantum hardware. Testing on several popular data sets and comparing with a number of existing losses we find substantial advantages in robustness as measured by test error under increasing label noise. Robustness is enabled by the non-convexity of our hardware-compatible loss function, which we name q-loss.