# Continuous black-box optimization with quantum annealing and random subspace coding

arXiv: https://arxiv.org/abs/2104.14778 · HTML: https://mlsanity.com/paper/2104.14778/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 1 of its 35 references that are in the map.
- First posted on arXiv 30 Apr 2021.

## Builds on (most cited first, 1 of 1)

- [High Dimensional Bayesian Optimisation and Bandits via Additive Models](https://mlsanity.com/paper/1503.01673/) (2015)

## Built on by (most cited first, 2 of 2)

- [Application of QUBO solver using black-box optimization to structural design for resonance avoidance](https://mlsanity.com/paper/2204.04906/) (2022)
- [Quantum-Enhanced Selection Operators for Evolutionary Algorithms](https://mlsanity.com/paper/2206.10743/) (2022)

## Abstract (arXiv)

A black-box optimization algorithm such as Bayesian optimization finds extremum of an unknown function by alternating inference of the underlying function and optimization of an acquisition function. In a high-dimensional space, such algorithms perform poorly due to the difficulty of acquisition function optimization. Herein, we apply quantum annealing (QA) to overcome the difficulty in the continuous black-box optimization. As QA specializes in optimization of binary problems, a continuous vector has to be encoded to binary, and the solution of QA has to be translated back. Our method has the following three parts: 1) Random subspace coding based on axis-parallel hyperrectangles from continuous vector to binary vector. 2) A quadratic unconstrained binary optimization (QUBO) defined by acquisition function based on nonnegative-weighted linear regression model which is solved by QA. 3) A penalization scheme to ensure that the QA solution can be translated back. It is shown in benchmark tests that its performance using D-Wave Advantagerm TM quantum annealer is competitive with a state-of-the-art method based on the Gaussian process in high-dimensional problems. Our method may open up a new possibility of quantum annealing and other QUBO solvers including quantum approximate optimization algorithm (QAOA) using a gated-quantum computers, and expand its range of application to continuous-valued problems.