We propose an efficient transfer Bayesian optimization method, which finds the maximum of an expensive-to-evaluate black-box function by using data on related optimization tasks. Our method uses auxiliary information that represents the task characteristics to effectively transfer knowledge for estimating a distribution over target functions. In particular, we use a Gaussian process, in which the mean and covariance functions are modeled with neural networks that simultaneously take both the auxiliary information and feature vectors as input. With a neural network mean function, we can estimate the target function even without evaluations. By using the neural network covariance function, we can extract nonlinear correlation among feature vectors that are shared across related tasks. Our Gaussian process-based formulation not only enables an analytic calculation of the posterior distribution but also swiftly adapts the target function to observations. Our method is also advantageous because the computational costs scale linearly with the number of source tasks. Through experiments using a synthetic dataset and datasets for finding the optimal pedestrian traffic regulations and optimal machine learning algorithms, we demonstrate that our method identifies the optimal points with fewer target function evaluations than existing methods.
We consider black box optimization of an unknown function in the nonparametric Gaussian process setting when the noise in the observed function values can be heavy tailed. This is in contrast to existing literature that typically assumes sub-Gaussian noise distributions for queries. Under the assumption that the unknown function belongs to the Reproducing Kernel Hilbert Space (RKHS) induced by a kernel, we first show that an adaptation of the well-known GP-UCB algorithm with reward truncation enjoys sublinear $\tilde{O}(T^{\frac{2 + \alpha}{2(1+\alpha)}})$ regret even with only the $(1+\alpha)$-th moments, $\alpha \in (0,1]$, of the reward distribution being bounded ($\tilde{O}$ hides logarithmic factors). However, for the common squared exponential (SE) and Mat\'{e}rn kernels, this is seen to be significantly larger than a fundamental $\Omega(T^{\frac{1}{1+\alpha}})$ lower bound on regret. We resolve this gap by developing novel Bayesian optimization algorithms, based on kernel approximation techniques, with regret bounds matching the lower bound in order for the SE kernel. We numerically benchmark the algorithms on environments based on both synthetic models and real-world data sets.
Kernel-based nonparametric models have become very attractive for model-based control approaches for nonlinear systems. However, the selection of the kernel and its hyperparameters strongly influences the quality of the learned model. Classically, these hyperparameters are optimized to minimize the prediction error of the model but this process totally neglects its later usage in the control loop. In this work, we present a framework to optimize the kernel and hyperparameters of a kernel-based model directly with respect to the closed-loop performance of the model. Our framework uses Bayesian optimization to iteratively refine the kernel-based model using the observed performance on the actual system until a desired performance is achieved. We demonstrate the proposed approach in a simulation and on a 3-DoF robotic arm.
Adversarial example generation becomes a viable method for evaluating the robustness of a machine learning model. In this paper, we consider hard-label black-box attacks (a.k.a. decision-based attacks), which is a challenging setting that generates adversarial examples based on only a series of black-box hard-label queries. This type of attacks can be used to attack discrete and complex models, such as Gradient Boosting Decision Tree (GBDT) and detection-based defense models. Existing decision-based attacks based on iterative local updates often get stuck in a local minimum and fail to generate the optimal adversarial example with the smallest distortion. To remedy this issue, we propose an efficient meta algorithm called BOSH-attack, which tremendously improves existing algorithms through Bayesian Optimization (BO) and Successive Halving (SH). In particular, instead of traversing a single solution path when searching an adversarial example, we maintain a pool of solution paths to explore important regions. We show empirically that the proposed algorithm converges to a better solution than existing approaches, while the query count is smaller than applying multiple random initializations by a factor of 10.
Finite-horizon sequential experimental design (SED) arises naturally in many contexts, including hyperparameter tuning in machine learning among more traditional settings. Computing the optimal policy for such problems requires solving Bellman equations, which are generally intractable. Most existing work resorts to severely myopic approximations by limiting the decision horizon to only a single time-step, which can underweight exploration in favor of exploitation. We present BINOCULARS: Batch-Informed NOnmyopic Choices, Using Long-horizons for Adaptive, Rapid SED, a general framework for deriving efficient, nonmyopic approximations to the optimal experimental policy. Our key idea is simple and surprisingly effective: we first compute a one-step optimal batch of experiments, then select a single point from this batch to evaluate. We realize BINOCULARS for Bayesian optimization and Bayesian quadrature -- two notable SED problems with radically different objectives -- and demonstrate that BINOCULARS significantly outperforms myopic alternatives in real-world scenarios.
Creating efficient deep neural networks involves repetitive manual optimization of the topology and the hyperparameters. This human intervention significantly inhibits the process. Recent publications propose various Neural Architecture Search (NAS) algorithms that automate this work. We have applied a customized NAS algorithm with network morphism and Bayesian optimization to the problem of cryptocurrency predictions, where it achieved results on par with our best manually designed models. This is consistent with the findings of other teams, while several known experiments suggest that given enough computing power, NAS algorithms can surpass state-of-the-art neural network models designed by humans. In this paper, we propose a blockchain network protocol that incentivises independent computing nodes to run NAS algorithms and compete in finding better neural network models for a particular task. If implemented, such network can be an autonomous and self-improving source of machine learning models, significantly boosting and democratizing the access to AI capabilities for many industries.
Financial markets are complex environments that produce enormous amounts of noisy and non-stationary data. One fundamental problem is online portfolio selection, the goal of which is to exploit this data to sequentially select portfolios of assets to achieve positive investment outcomes while managing risks. Various algorithms have been proposed for solving this problem in fields such as finance, statistics and machine learning, among others. Most of the methods have parameters that are estimated from backtests for good performance. Since these algorithms operate on non-stationary data that reflects the complexity of financial markets, we posit that adaptively tuning these parameters in an intelligent manner is a remedy for dealing with this complexity. In this paper, we model the mapping between the parameter space and the space of performance metrics using a Gaussian process prior. We then propose an oracle based on adaptive Bayesian optimization for automatically and adaptively configuring online portfolio selection methods. We test the efficacy of our solution on algorithms operating on equity and index data from various markets.
Parallel surrogate optimization algorithms have proven to be efficient methods for solving expensive noisy optimization problems. In this work we develop a new parallel surrogate optimization algorithm (ProSRS), using a novel tree-based "zoom strategy" to improve the efficiency of the algorithm. We prove that if ProSRS is run for sufficiently long, with probability converging to one there will be at least one point among all the evaluations that will be arbitrarily close to the global minimum. We compare our algorithm to several state-of-the-art Bayesian optimization algorithms on a suite of standard benchmark functions and two real machine learning hyperparameter-tuning problems. We find that our algorithm not only achieves significantly faster optimization convergence, but is also 1-4 orders of magnitude cheaper in computational cost.
Rationale and objectives: Several studies have evaluated the usefulness of deep learning for lung segmentation using chest x-ray (CXR) images with small- or medium-sized abnormal findings. Here, we built a database including both CXR images with severe abnormalities and experts' lung segmentation results, and aimed to evaluate our network's efficacy in lung segmentation from these images. Materials and Methods: For lung segmentation, CXR images from the Japanese Society of Radiological Technology (JSRT, N = 247) and Montgomery databases (N = 138), were included, and 65 additional images depicting severe abnormalities from a public database were evaluated and annotated by a radiologist, thereby adding lung segmentation results to these images. Baseline U-net was used to segment the lungs in images from the three databases. Subsequently, the U-net network architecture was automatically optimized for lung segmentation from CXR images using Bayesian optimization. Dice similarity coefficient (DSC) was calculated to confirm segmentation. Results: Our results demonstrated that using baseline U-net yielded poorer lung segmentation results in our database than those in the JSRT and Montgomery databases, implying that robust segmentation of lungs may be difficult because of severe abnormalities. The DSC values with baseline U-net for the JSRT, Montgomery and our databases were 0.979, 0.941, and 0.889, respectively, and with optimized U-net, 0.976, 0.973, and 0.932, respectively. Conclusion: For robust lung segmentation, the U-net architecture was optimized via Bayesian optimization, and our results demonstrate that the optimized U-net was more robust than baseline U-net in lung segmentation from CXR images with large-sized abnormalities.
Flexible manufacturing processes demand robots to easily adapt to changes in the environment and interact with humans. In such dynamic scenarios, robotic tasks may be programmed through learning-from-demonstration approaches, where a nominal plan of the task is learned by the robot. However, the learned plan may need to be adapted in order to fulfill additional requirements or overcome unexpected environment changes. When the required adaptation occurs at the end-effector trajectory level, a human operator may want to intuitively show the robot the desired changes by physically interacting with it. In this scenario, the robot needs to understand the human intended changes from noisy haptic data, quickly adapt accordingly and execute the nominal task plan when no further adaptation is needed. This paper addresses the aforementioned challenges by leveraging LfD and Bayesian optimization to endow the robot with data-efficient adaptation capabilities. Our approach exploits the sensed interaction forces to guide the robot adaptation, and speeds up the optimization process by defining local search spaces extracted from the learned task model. We show how our framework quickly adapts the learned spatial-temporal patterns of the task, leading to deformed trajectory distributions that are consistent with the nominal plan and the changes introduced by the human.
Hyperparameter optimization and neural architecture search can become prohibitively expensive for regular black-box Bayesian optimization because the training and evaluation of a single model can easily take several hours. To overcome this, we introduce a comprehensive tool suite for effective multi-fidelity Bayesian optimization and the analysis of its runs. The suite, written in Python, provides a simple way to specify complex design spaces, a robust and efficient combination of Bayesian optimization and HyperBand, and a comprehensive analysis of the optimization process and its outcomes.
Bayesian Optimization (BO) is a common approach for hyperparameter optimization (HPO) in automated machine learning. Although it is well-accepted that HPO is crucial to obtain well-performing machine learning models, tuning BO's own hyperparameters is often neglected. In this paper, we empirically study the impact of optimizing BO's own hyperparameters and the transferability of the found settings using a wide range of benchmarks, including artificial functions, HPO and HPO combined with neural architecture search. In particular, we show (i) that tuning can improve the any-time performance of different BO approaches, that optimized BO settings also perform well (ii) on similar problems and (iii) partially even on problems from other problem families, and (iv) which BO hyperparameters are most important.
Variational quantum algorithms, a class of quantum heuristics, are promising candidates for the demonstration of useful quantum computation. Finding the best way to amplify the performance of these methods on hardware is an important task. Here, we evaluate the optimization of quantum heuristics with an existing class of techniques called `meta-learners'. We compare the performance of a meta-learner to Bayesian optimization, evolutionary strategies, L-BFGS-B and Nelder-Mead approaches, for two quantum heuristics (quantum alternating operator ansatz and variational quantum eigensolver), on three problems, in three simulation environments. We show that the meta-learner comes near to the global optima more frequently than all other optimizers we tested in a noisy parameter setting environment. We also find that the meta-learner is generally more resistant to noise, for example seeing a smaller reduction in performance in Noisy and Sampling environments and performs better on average by a `gain' metric than its closest comparable competitor L-BFGS-B. These results are an important indication that meta-learning and associated machine learning methods will be integral to the useful application of noisy near-term quantum computers.
In applications such as molecule design or drug discovery, it is desirable to have an algorithm which recommends new candidate molecules based on the results of past tests. These molecules first need to be synthesized and then tested for objective properties. We describe ChemBO, a Bayesian optimization framework for generating and optimizing organic molecules for desired molecular properties. While most existing data-driven methods for this problem do not account for sample efficiency or fail to enforce realistic constraints on synthesizability, our approach explores the synthesis graph in a sample-efficient way and produces synthesizable candidates. We implement ChemBO as a Gaussian process model and explore existing molecular kernels for it. Moreover, we propose a novel optimal-transport based distance and kernel that accounts for graphical information explicitly. In our experiments, we demonstrate the efficacy of the proposed approach on several molecular optimization problems.
This paper describes Plumbing for Optimization with Asynchronous Parallelism (POAP) and the Python Surrogate Optimization Toolbox (pySOT). POAP is an event-driven framework for building and combining asynchronous optimization strategies, designed for global optimization of expensive functions where concurrent function evaluations are useful. POAP consists of three components: a worker pool capable of function evaluations, strategies to propose evaluations or other actions, and a controller that mediates the interaction between the workers and strategies. pySOT is a collection of synchronous and asynchronous surrogate optimization strategies, implemented in the POAP framework. We support the stochastic RBF method by Regis and Shoemaker along with various extensions of this method, and a general surrogate optimization strategy that covers most Bayesian optimization methods. We have implemented many different surrogate models, experimental designs, acquisition functions, and a large set of test problems. We make an extensive comparison between synchronous and asynchronous parallelism and find that the advantage of asynchronous computation increases as the variance of the evaluation time or number of processors increases. We observe a close to linear speed-up with 4, 8, and 16 processors in both the synchronous and asynchronous setting.
Bayesian Optimization (BO) is a framework for black-box optimization that is especially suitable for expensive cost functions. Among the main parts of a BO algorithm, the acquisition function is of fundamental importance, since it guides the optimization algorithm by translating the uncertainty of the regression model in a utility measure for each point to be evaluated. Considering such aspect, selection and design of acquisition functions are one of the most popular research topics in BO. Since no single acquisition function was proved to have better performance in all tasks, a well-established approach consists of selecting different acquisition functions along the iterations of a BO execution. In such an approach, the GP-Hedge algorithm is a widely used option given its simplicity and good performance. Despite its success in various applications, GP-Hedge shows an undesirable characteristic of accounting on all past performance measures of each acquisition function to select the next function to be used. In this case, good or bad values obtained in an initial iteration may impact the choice of the acquisition function for the rest of the algorithm. This fact may induce a dominant behavior of an acquisition function and impact the final performance of the method. Aiming to overcome such limitation, in this work we propose a variant of GP-Hedge, named No-PASt-BO, that reduce the influence of far past evaluations. Moreover, our method presents a built-in normalization that avoids the functions in the portfolio to have similar probabilities, thus improving the exploration. The obtained results on both synthetic and real-world optimization tasks indicate that No-PASt-BO presents competitive performance and always outperforms GP-Hedge.
Deep learning algorithms have achieved excellent performance lately in a wide range of fields (e.g., computer version). However, a severe challenge faced by deep learning is the high dependency on hyper-parameters. The algorithm results may fluctuate dramatically under the different configuration of hyper-parameters. Addressing the above issue, this paper presents an efficient Orthogonal Array Tuning Method (OATM) for deep learning hyper-parameter tuning. We describe the OATM approach in five detailed steps and elaborate on it using two widely used deep neural network structures (Recurrent Neural Networks and Convolutional Neural Networks). The proposed method is compared to the state-of-the-art hyper-parameter tuning methods including manually (e.g., grid search and random search) and automatically (e.g., Bayesian Optimization) ones. The experiment results state that OATM can significantly save the tuning time compared to the state-of-the-art methods while preserving the satisfying performance. The codes are open in GitHub (https://github.com/xiangzhang1015/OATM)
Robust machine learning is currently one of the most prominent topics which could potentially help shaping a future of advanced AI platforms that not only perform well in average cases but also in worst cases or adverse situations. Despite the long-term vision, however, existing studies on black-box adversarial attacks are still restricted to very specific settings of threat models (e.g., single distortion metric and restrictive assumption on target model's feedback to queries) and/or suffer from prohibitively high query complexity. To push for further advances in this field, we introduce a general framework based on an operator splitting method, the alternating direction method of multipliers (ADMM) to devise efficient, robust black-box attacks that work with various distortion metrics and feedback settings without incurring high query complexity. Due to the black-box nature of the threat model, the proposed ADMM solution framework is integrated with zeroth-order (ZO) optimization and Bayesian optimization (BO), and thus is applicable to the gradient-free regime. This results in two new black-box adversarial attack generation methods, ZO-ADMM and BO-ADMM. Our empirical evaluations on image classification datasets show that our proposed approaches have much lower function query complexities compared to state-of-the-art attack methods, but achieve very competitive attack success rates.
Learning robot controllers by minimizing a black-box objective cost using Bayesian optimization (BO) can be time-consuming and challenging. It is very often the case that some roll-outs result in failure behaviors, causing premature experiment detention. In such cases, the designer is forced to decide on heuristic cost penalties because the acquired data is often scarce, or not comparable with that of the stable policies. To overcome this, we propose a Bayesian model that captures exactly what we know about the cost of unstable controllers prior to data collection: Nothing, except that it should be a somewhat large number. The resulting Bayesian model, approximated with a Gaussian process, predicts high cost values in regions where failures are likely to occur. In this way, the model guides the BO exploration toward regions of stability. We demonstrate the benefits of the proposed model in several illustrative and statistical synthetic benchmarks, and also in experiments on a real robotic platform. In addition, we propose and experimentally validate a new BO method to account for unknown constraints. Such method is an extension of Max-Value Entropy Search, a recent information-theoretic method, to solve unconstrained global optimization problems.
The problem of a deep learning model losing performance on a previously learned task when fine-tuned to a new one is a phenomenon known as Catastrophic forgetting. There are two major ways to mitigate this problem: either preserving activations of the initial network during training with a new task; or restricting the new network activations to remain close to the initial ones. The latter approach falls under the denomination of lifelong learning, where the model is updated in a way that it performs well on both old and new tasks, without having access to the old task's training samples anymore. Recently, approaches like pruning networks for freeing network capacity during sequential learning of tasks have been gaining in popularity. Such approaches allow learning small networks while making redundant parameters available for the next tasks. The common problem encountered with these approaches is that the pruning percentage is hard-coded, irrespective of the number of samples, of the complexity of the learning task and of the number of classes in the dataset. We propose a method based on Bayesian optimization to perform adaptive compression/pruning of the network and show its effectiveness in lifelong learning. Our method learns to perform heavy pruning for small and/or simple datasets while using milder compression rates for large and/or complex data. Experiments on classification and semantic segmentation demonstrate the applicability of learning network compression, where we are able to effectively preserve performances along sequences of tasks of varying complexity.