Tree-structured Parzen estimator (TPE) is a versatile hyperparameter optimization (HPO) method supported by popular HPO tools. Since these HPO tools have been developed in line with the trend of deep learning (DL), the problem setups often used in the DL domain have been discussed for TPE such as multi-objective optimization and multi-fidelity optimization. However, the practical applications of HPO are not limited to DL, and black-box combinatorial optimization is actively utilized in some domains, e.g., chemistry and biology. As combinatorial optimization has been an untouched, yet very important, topic in TPE, we propose an efficient combinatorial optimization algorithm for TPE. In this paper, we first generalize the categorical kernel with the numerical kernel in TPE, enabling us to introduce a distance structure to the categorical kernel. Then we discuss modifications for the newly developed kernel to handle a large combinatorial search space. These modifications reduce the time complexity of the kernel calculation with respect to the size of a combinatorial search space. In the experiments using synthetic problems, we verified that our proposed method identifies better solutions with fewer evaluations than the original TPE. Our algorithm is available in Optuna, an open-source framework for HPO.
We introduce Auto-Surprise, an Automated Recommender System library. Auto-Surprise is an extension of the Surprise recommender system library and eases the algorithm selection and configuration process. Compared to out-of-the-box Surprise library, Auto-Surprise performs better when evaluated with MovieLens, Book Crossing and Jester Datasets. It may also result in the selection of an algorithm with significantly lower runtime. Compared to Surprise's grid search, Auto-Surprise performs equally well or slightly better in terms of RMSE, and is notably faster in finding the optimum hyperparameters.
Thinking Out of the Box: Hybrid SAT Solving by Unconstrained Continuous Optimization
Department of Computer Science, Rice University（计算机科学系，里士大学）；Department of Applied Mathematics and Statistics, Colorado School of Mines（应用数学与统计系，科罗拉多矿业学院）；Department of Mathematics, University of California, Los Angeles（数学系，加州大学洛杉矶分校）
IBM Research（IBM研究）；Argonne National Laboratory（阿贡国家实验室）；University of Illinois at Chicago（伊利诺伊大学芝加哥分校）
We consider the problem of black-box function optimization over the boolean hypercube. Despite the vast literature on black-box function optimization over continuous domains, not much attention has been paid to learning models for optimization over combinatorial domains until recently. However, the computational complexity of the recently devised algorithms are prohibitive even for moderate numbers of variables; drawing one sample using the existing algorithms is more expensive than a function evaluation for many black-box functions of interest. To address this problem, we propose a computatio…
When a black-box optimization objective can only be evaluated with costly or noisy measurements, most standard optimization algorithms are unsuited to find the optimal solution. Specialized algorithms that deal with exactly this situation make use of surrogate models. These models are usually continuous and smooth, which is beneficial for continuous optimization problems, but not necessarily for combinatorial problems. However, by choosing the basis functions of the surrogate model in a certain way, we show that it can be guaranteed that the optimal solution of the surrogate model is integer. …
We consider the problem of optimizing combinatorial spaces (e.g., sequences, trees, and graphs) using expensive black-box function evaluations. For example, optimizing molecules for drug design using physical lab experiments. Bayesian optimization (BO) is an efficient framework for solving such problems by intelligently selecting the inputs with high utility guided by a learned surrogate model. A recent BO approach for combinatorial spaces is through a reduction to BO over continuous spaces by learning a latent representation of structures using deep generative models (DGMs). The selected inpu…
Seoul National University（首尔国立大学）；Neural Processing Research Center（神经处理研究中心）
Solving for adversarial examples with projected gradient descent has been demonstrated to be highly effective in fooling the neural network based classifiers. However, in the black-box setting, the attacker is limited only to the query access to the network and solving for a successful adversarial example becomes much more difficult. To this end, recent methods aim at estimating the true gradient signal based on the input queries but at the cost of excessive queries. We propose an efficient discrete surrogate to the optimization problem which does not require estimating the gradient and conseq…
The University of Sydney（悉尼大学）；College of Control Science and Engineering, China University of Petroleum (East China)（中国石油大学（华东）控制科学与工程学院）；Shanghai Jiao Tong University（上海交通大学）；JD Explore Academy（京东探索研究院）
School of EECS, Washington State University（华盛顿州立大学电气工程与计算机科学学院）
Bayesian optimization (BO) is an efficient framework for solving black-box optimization problems with expensive function evaluations. This paper addresses the BO problem setting for combinatorial spaces (e.g., sequences and graphs) that occurs naturally in science and engineering applications. A prototypical example is molecular optimization guided by expensive experiments. The key challenge is to balance the complexity of statistical models and tractability of search to select combinatorial structures for evaluation. In this paper, we propose an efficient approach referred as Mercer Features …
Bayesian optimization is a popular method for solving the problem of global optimization of an expensive-to-evaluate black-box function. It relies on a probabilistic surrogate model of the objective function, upon which an acquisition function is built to determine where next to evaluate the objective function. In general, Bayesian optimization with Gaussian process regression operates on a continuous space. When input variables are categorical or discrete, an extra care is needed. A common approach is to use one-hot encoded or Boolean representation for categorical variables which might yield…
Massachusetts Institute of Technology（麻省理工学院）；The University of Arizona（亚利桑那大学）
The optimization of expensive-to-evaluate black-box functions over combinatorial structures is an ubiquitous task in machine learning, engineering and the natural sciences. The combinatorial explosion of the search space and costly evaluations pose challenges for current techniques in discrete optimization and machine learning, and critically require new algorithmic ideas. This article proposes, to the best of our knowledge, the first algorithm to overcome these challenges, based on an adaptive, scalable model that identifies useful combinatorial structure even when data is scarce. Our acquisi…
From Black Box to Bijection: Interpreting Machine Learning to Build a Zeta Map Algorithm
Department of Mathematics, Temple University, Philadelphia, PA 19122, U.S.A.（特拉华大学数学系）；Department of Mathematics, University of Connecticut, Storrs, CT 06269, U.S.A.（康涅狄格大学数学系）；Korea Institute for Advanced Study, Seoul 02455, Republic of Korea（韩国高级研究院）
Russian Quantum Center（俄罗斯量子中心）；University of Oxford（牛津大学）
Quantum hardware and quantum-inspired algorithms are becoming increasingly popular for combinatorial optimization. However, these algorithms may require careful hyperparameter tuning for each problem instance. We use a reinforcement learning agent in conjunction with a quantum-inspired algorithm to solve the Ising energy minimization problem, which is equivalent to the Maximum Cut problem. The agent controls the algorithm by tuning one of its parameters with the goal of improving recently seen solutions. We propose a new Rescaled Ranked Reward (R3) method that enables stable single-player vers…
University of California, Davis（加州大学戴维斯分校）；IBM Research（IBM研究院）；JD AI Research（京东AI研究院）
We study the problem of attacking a machine learning model in the hard-label black-box setting, where no model information is revealed except that the attacker can make queries to probe the corresponding hard-label decisions. This is a very challenging problem since the direct extension of state-of-the-art white-box attacks (e.g., CW or PGD) to the hard-label black-box setting will require minimizing a non-continuous step function, which is combinatorial and cannot be solved by a gradient-based optimizer. The only current approach is based on random walk on the boundary, which requires lots of…
Solving combinatorial optimization (CO) on graphs is among the fundamental tasks for upper-stream applications in data mining, machine learning and operations research. Despite the inherent NP-hard challenge for CO, heuristics, branch-and-bound, learning-based solvers are developed to tackle CO problems as accurately as possible given limited time budgets. However, a practical metric for the sensitivity of CO solvers remains largely unexplored. Existing theoretical metrics require the optimal solution which is infeasible, and the gradient-based adversarial attack metric from deep learning is n…
We consider the problem of optimizing expensive black-box functions over high-dimensional combinatorial spaces which arises in many science, engineering, and ML applications. We use Bayesian Optimization (BO) and propose a novel surrogate modeling approach for efficiently handling a large number of binary and categorical parameters. The key idea is to select a number of discrete structures from the input space (the dictionary) and use them to define an ordinal embedding for high-dimensional combinatorial structures. This allows us to use existing Gaussian process models for continuous spaces. …
We demonstrate that model-based derivative free optimisation algorithms can generate adversarial targeted misclassification of deep networks using fewer network queries than non-model-based methods. Specifically, we consider the black-box setting, and show that the number of networks queries is less impacted by making the task more challenging either through reducing the allowed $\ell^{\infty}$ perturbation energy or training the network with defences against adversarial misclassification. We illustrate this by contrasting the BOBYQA algorithm with the state-of-the-art model-free adversarial t…
Combinatorial Bandit Bayesian Optimization for Tensor Outputs
Department of Industrial Engineering, Tsinghua University, Beijing 100084, China（清华大学工业工程系）；College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China（南京航空航天大学经济管理学院）
Quadratic unconstrained binary optimization (QUBO) solvers can be applied to design an optimal structure to avoid resonance. QUBO algorithms that work on a classical or quantum device have succeeded in some industrial applications. However, their applications are still limited due to the difficulty of transforming from the original optimization problem to QUBO. Recently, black-box optimization (BBO) methods have been proposed to tackle this issue using a machine learning technique and a Bayesian treatment for combinatorial optimization. We employed the BBO methods to design a printed circuit b…
Adversarial machine learning is an emerging area showing the vulnerability of deep learning models. Exploring attack methods to challenge state of the art artificial intelligence (A.I.) models is an area of critical concern. The reliability and robustness of such A.I. models are one of the major concerns with an increasing number of effective adversarial attack methods. Classification tasks are a major vulnerable area for adversarial attacks. The majority of attack strategies are developed for colored or gray-scaled images. Consequently, adversarial attacks on binary image recognition systems …
Predicting structured outputs can be computationally onerous due to the combinatorially large output spaces. In this paper, we focus on reducing the prediction time of a trained black-box structured classifier without losing accuracy. To do so, we train a speedup classifier that learns to mimic a black-box classifier under the learning-to-search approach. As the structured classifier predicts more examples, the speedup classifier will operate as a learned heuristic to guide search to favorable regions of the output space. We present a mistake bound for the speedup classifier and identify infer…
In the machine learning algorithms, the choice of the hyperparameter is often an art more than a science, requiring labor-intensive search with expert experience. Therefore, automation on hyperparameter optimization to exclude human intervention is a great appeal, especially for the black-box functions. Recently, there have been increasing demands of solving such concealed tasks for better generalization, though the task-dependent issue is not easy to solve. The Black-Box Optimization challenge (NeurIPS 2020) required competitors to build a robust black-box optimizer across different domains o…
In this article we give several new results on the complexity of algorithms that learn Boolean functions from quantum queries and quantum examples. Hunziker et al. conjectured that for any class C of Boolean functions, the number of quantum black-box queries which are required to exactly identify an unknown function from C is $O(\frac{\log |C|}{\sqrt{{\hatγ}^{C}}})$, where $\hatγ^{C}$ is a combinatorial parameter of the class C. We essentially resolve this conjecture in the affirmative by giving a quantum algorithm that, for any class C, identifies any unknown function from C using $O(\frac{\l…
