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The Brain & Neural Networks

Black-box Optimization by Annealing Machines

Shu Tanaka, Masashi Yamashita, Yuya Seki

Published Dec 5, 2022• 2 citations
Publisher

Abstract

最適化計算の新技術としてアニーリングマシンが注目を集めている．本解説では，アニーリングマシンやブラックボックス最適化の一般論について見てから，アニーリングマシンを用いたブラックボックス最適化の解法ならびに適用事例について紹介する．

DOI
10.3902/jnns.29.164

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最適化計算の新技術としてアニーリングマシンが注目を集めている．本解説では，アニーリングマシンやブラックボックス最適化の一般論について見てから，アニーリングマシンを用いたブラックボックス最適化の解法ならびに適用事例について紹介する．
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Black-box optimization (BBO) is used in materials design, drug discovery, and hyperparameter tuning in machine learning. The world is experiencing several of these problems. In this review, a factorization machine with quantum annealing or with quadratic-optimization annealing (FMQA) algorithm to realize fast computations of BBO using Ising machines (IMs) is discussed. The FMQA algorithm uses a factorization machine (FM) as a surrogate model for BBO. The FM model can be directly transformed into a quadratic unconstrained binary optimization model that can be solved using IMs. This makes it possible to optimize the acquisition function in BBO, which is a difficult task using conventional methods without IMs. Consequently, it has the advantage of handling large BBO problems. To be able to perform BBO with the FMQA algorithm immediately, we introduce the FMQA algorithm along with Python packages to run it. In addition, we review examples of applications of the FMQA algorithm in various fields, including physics, chemistry, materials science, and social sciences. These successful examples include binary and integer optimization problems, as well as more general optimization problems involving graphs, networks, and strings, using a binary variational autoencoder. We believe that BBO using the FMQA algorithm will become a key technology in IMs, including quantum annealers.
Black-box optimization has potential in numerous applications such as hyperparameter optimization in machine learning and optimization in design of experiments. Ising machines are useful for binary optimization problems because variables can be represented by a single binary variable of Ising machines. However, conventional approaches using an Ising machine cannot handle black-box optimization problems with non-binary values. To overcome this limitation, we propose an approach for integer-variable black-box optimization problems by using Ising/annealing machines and factorization machines in cooperation with three different integer-encoding methods. The performance of our approach is numerically evaluated with different encoding methods using a simple problem of calculating the energy of the hydrogen molecule in the most stable state. The proposed approach can calculate the energy using any of the integer-encoding methods. However, one-hot encoding is useful for problems with a small size.
本稿では，近年国内外で活発に研究開発されているイジングマシンについて述べる．イジングマシンとは，イジング問題と呼ばれる組合せ最適化問題に特化した専用計算機である．世界初の商用量子コンピュータである量子アニーラがイジングマシンの一種であり，それをGoogleとNASAが創設した量子人工知能研究所が購入したことをきっかけに，イジングマシンが注目を集めるようになった．現在では，超伝導や光といった特殊なハードウェアだけでなく，従来の半導体デジタル計算機を利用して実用性を高めたものも多く，ドメイン指向コンピューティングの新たな潮流となっている．後者は主にアルゴリズムに特徴があり，中には量子計算にインスパイアされて発見されたものもある．そもそも量子アニーラに端を発した研究という経緯もあり，メディアはこれらを「疑似量子コンピュータ」と呼ぶことがある．イジングマシンと似たものとして，ホップフィールドニューラルネットワークをご存じの読者は多いだろう．実際，ホップフィールドニューラルネットワークの派生物であるボルツマンマシンなどは，現在のイジングマシンとの関係が深い．そこで，本稿の前半では，特殊ハードウェアから疑似量子コンピュータまで，現在開発中の多種多様なイジングマシンをホップフィールドニューラルネットワークやその派生物との類似に触れながら紹介する．後半は，筆者が提案し，現在も研究開発中である疑似量子コンピュータ，シミュレーテッド分岐マシンについて解説する．
A black-box optimization algorithm such as Bayesian optimization finds the extremum of an unknown function by alternating the 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 Ising machines to overcome the difficulty in the continuous black-box optimization. As an Ising machine specializes in optimization of binary problems, a continuous vector has to be encoded to binary, and the solution by Ising machines 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 the acquisition function based on the nonnegative-weighted linear regression model, which is solved by Ising machines, and (3) a penalization scheme to ensure that the solution can be translated back. It is shown with benchmark tests that its performance using the D-Wave Advantage quantum annealer and simulated annealing is competitive with a state-of-the-art method based on the Gaussian process in high-dimensional problems. Our method may open up the possibility of Ising machines and other QUBO solvers, including a quantum approximate optimization algorithm using gated-quantum computers, and may expand its range of application to continuous-valued problems.