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Register a new userEfficient Nonmyopic Bayesian Optimization via One-Shot Multi-Step Trees
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Added by
Shali Jiang
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Bayesian optimization is a sequential decision making framework for optimizing expensive-to-evaluate black-box functions. Computing a full lookahead policy amounts to solving a highly intractable stochastic dynamic program. Myopic approaches, such as expected improvement, are often adopted in practice, but they ignore the long-term impact of the immediate decision. Existing nonmyopic approaches are mostly heuristic and/or computationally expensive. In this paper, we provide the first efficient implementation of general multi-step lookahead Bayesian optimization, formulated as a sequence of nested optimization problems within a multi-step scenario tree. Instead of solving these problems in a nested way, we equivalently optimize all decision variables in the full tree jointly, in a ``one-shot fashion. Combining this with an efficient method for implementing multi-step Gaussian process ``fantasization, we demonstrate that multi-step expected improvement is computationally tractable and exhibits performance superior to existing methods on a wide range of benchmarks.
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This paper concerns the problem of 1-bit compressed sensing, where the goal is to estimate a sparse signal from a few of its binary measurements. We study a non-convex sparsity-constrained program and present a novel and concise analysis that moves away from the widely used notion of Gaussian width. We show that with high probability a simple algorithm is guaranteed to produce an accurate approximation to the normalized signal of interest under the $ell_2$-metric. On top of that, we establish an ensemble of new results that address norm estimation, support recovery, and model misspecification. On the computational side, it is shown that the non-convex program can be solved via one-step hard thresholding which is dramatically efficient in terms of time complexity and memory footprint. On the statistical side, it is shown that our estimator enjoys a near-optimal error rate under standard conditions. The theoretical results are substantiated by numerical experiments.
Decision-based attacks (DBA), wherein attackers perturb inputs to spoof learning algorithms by observing solely the output labels, are a type of severe adversarial attacks against Deep Neural Networks (DNNs) requiring minimal knowledge of attackers. State-of-the-art DBA attacks relying on zeroth-order gradient estimation require an excessive number of queries. Recently, Bayesian optimization (BO) has shown promising in reducing the number of queries in score-based attacks (SBA), in which attackers need to observe real-valued probability scores as outputs. However, extending BO to the setting of DBA is nontrivial because in DBA only output labels instead of real-valued scores, as needed by BO, are available to attackers. In this paper, we close this gap by proposing an efficient DBA attack, namely BO-DBA. Different from existing approaches, BO-DBA generates adversarial examples by searching so-called emph{directions of perturbations}. It then formulates the problem as a BO problem that minimizes the real-valued distortion of perturbations. With the optimized perturbation generation process, BO-DBA converges much faster than the state-of-the-art DBA techniques. Experimental results on pre-trained ImageNet classifiers show that BO-DBA converges within 200 queries while the state-of-the-art DBA techniques need over 15,000 queries to achieve the same level of perturbation distortion. BO-DBA also shows similar attack success rates even as compared to BO-based SBA attacks but with less distortion.
The alternating direction method of multipliers (ADMM) is a popular approach for solving optimization problems that are potentially non-smooth and with hard constraints. It has been applied to various computer graphics applications, including physical simulation, geometry processing, and image processing. However, ADMM can take a long time to converge to a solution of high accuracy. Moreover, many computer graphics tasks involve non-convex optimization, and there is often no convergence guarantee for ADMM on such problems since it was originally designed for convex optimization. In this paper, we propose a method to speed up ADMM using Anderson acceleration, an established technique for accelerating fixed-point iterations. We show that in the general case, ADMM is a fixed-point iteration of the second primal variable and the dual variable, and Anderson acceleration can be directly applied. Additionally, when the problem has a separable target function and satisfies certain conditions, ADMM becomes a fixed-point iteration of only one variable, which further reduces the computational overhead of Anderson acceleration. Moreover, we analyze a particular non-convex problem structure that is common in computer graphics, and prove the convergence of ADMM on such problems under mild assumptions. We apply our acceleration technique on a variety of optimization problems in computer graphics, with notable improvement on their convergence speed.
Hyperparameter optimization (HPO) is a central pillar in the automation of machine learning solutions and is mainly performed via Bayesian optimization, where a parametric surrogate is learned to approximate the black box response function (e.g. validation error). Unfortunately, evaluating the response function is computationally intensive. As a remedy, earlier work emphasizes the need for transfer learning surrogates which learn to optimize hyperparameters for an algorithm from other tasks. In contrast to previous work, we propose to rethink HPO as a few-shot learning problem in which we train a shared deep surrogate model to quickly adapt (with few response evaluations) to the response function of a new task. We propose the use of a deep kernel network for a Gaussian process surrogate that is meta-learned in an end-to-end fashion in order to jointly approximate the response functions of a collection of training data sets. As a result, the novel few-shot optimization of our deep kernel surrogate leads to new state-of-the-art results at HPO compared to several recent methods on diverse metadata sets.
In few-shot domain adaptation (FDA), classifiers for the target domain are trained with accessible labeled data in the source domain (SD) and few labeled data in the target domain (TD). However, data usually contain private information in the current era, e.g., data distributed on personal phones. Thus, the private information will be leaked if we directly access data in SD to train a target-domain classifier (required by FDA methods). In this paper, to thoroughly prevent the privacy leakage in SD, we consider a very challenging problem setting, where the classifier for the TD has to be trained using few labeled target data and a well-trained SD classifier, named few-shot hypothesis adaptation (FHA). In FHA, we cannot access data in SD, as a result, the private information in SD will be protected well. To this end, we propose a target orientated hypothesis adaptation network (TOHAN) to solve the FHA problem, where we generate highly-compatible unlabeled data (i.e., an intermediate domain) to help train a target-domain classifier. TOHAN maintains two deep networks simultaneously, where one focuses on learning an intermediate domain and the other takes care of the intermediate-to-target distributional adaptation and the target-risk minimization. Experimental results show that TOHAN outperforms competitive baselines significantly.
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