In recent years, deep learning has achieved remarkable achievements in many fields, including computer vision, natural language processing, speech recognition and others. Adequate training data is the key to ensure the effectiveness of the deep models. However, obtaining valid data requires a lot of time and labor resources. Data augmentation (DA) is an effective alternative approach, which can generate new labeled data based on existing data using label-preserving transformations. Although we can benefit a lot from DA, designing appropriate DA policies requires a lot of expert experience and time consumption, and the evaluation of searching the optimal policies is costly. So we raise a new question in this paper: how to achieve automated data augmentation at as low cost as possible? We propose a method named BO-Aug for automating the process by finding the optimal DA policies using the Bayesian optimization approach. Our method can find the optimal policies at a relatively low search cost, and the searched policies based on a specific dataset are transferable across different neural network architectures or even different datasets. We validate the BO-Aug on three widely used image classification datasets, including CIFAR-10, CIFAR-100 and SVHN. Experimental results show that the proposed method can achieve state-of-the-art or near advanced classification accuracy. Code to reproduce our experiments is available at https://github.com/zhangxiaozao/BO-Aug.
Bayesian optimization has demonstrated impressive success in finding the optimum input x* and output f* = f(x*) = max f(x) of a black-box function f. In some applications, however, the optimum output f* is known in advance and the goal is to find the corresponding optimum input x*. In this paper, we consider a new setting in BO in which the knowledge of the optimum output f* is available. Our goal is to exploit the knowledge about f* to search for the input x* efficiently. To achieve this goal, we first transform the Gaussian process surrogate using the information about the optimum output. Then, we propose two acquisition functions, called confidence bound minimization and expected regret minimization. We show that our approaches work intuitively and give quantitatively better performance against standard BO methods. We demonstrate real applications in tuning a deep reinforcement learning algorithm on the CartPole problem and XGBoost on Skin Segmentation dataset in which the optimum values are publicly available.
Bayesian optimization is an effective method to efficiently optimize unknown objective functions with high evaluation costs. Traditional Bayesian optimization algorithms select one point per iteration for single objective function, whereas in recent years, Bayesian optimization for multi-objective optimization or multi-point search per iteration have been proposed. However, Bayesian optimization that can deal with them at the same time in non-heuristic way is not known at present. We propose a Bayesian optimization algorithm that can deal with multi-objective optimization and multi-point search at the same time. First, we define an acquisition function that considers both multi-objective and multi-point search problems. It is difficult to analytically maximize the acquisition function as the computational cost is prohibitive even when approximate calculations such as sampling approximation are performed; therefore, we propose an accurate and computationally efficient method for estimating gradient of the acquisition function, and develop an algorithm for Bayesian optimization with multi-objective and multi-point search. It is shown via numerical experiments that the performance of the proposed method is comparable or superior to those of heuristic methods.
Models often need to be constrained to a certain size for them to be considered interpretable. For example, a decision tree of depth 5 is much easier to understand than one of depth 50. Limiting model size, however, often reduces accuracy. We suggest a practical technique that minimizes this trade-off between interpretability and classification accuracy. This enables an arbitrary learning algorithm to produce highly accurate small-sized models. Our technique identifies the training data distribution to learn from that leads to the highest accuracy for a model of a given size. We represent the training distribution as a combination of sampling schemes. Each scheme is defined by a parameterized probability mass function applied to the segmentation produced by a decision tree. An Infinite Mixture Model with Beta components is used to represent a combination of such schemes. The mixture model parameters are learned using Bayesian Optimization. Under simplistic assumptions, we would need to optimize for $O(d)$ variables for a distribution over a $d$-dimensional input space, which is cumbersome for most real-world data. However, we show that our technique significantly reduces this number to a \emph{fixed set of eight variables} at the cost of relatively cheap preprocessing. The proposed technique is flexible: it is \emph{model-agnostic}, i.e., it may be applied to the learning algorithm for any model family, and it admits a general notion of model size. We demonstrate its effectiveness using multiple real-world datasets to construct decision trees, linear probability models and gradient boosted models with different sizes. We observe significant improvements in the F1-score in most instances, exceeding an improvement of $100\%$ in some cases.
Robot design is often a slow and difficult process requiring the iterative construction and testing of prototypes, with the goal of sequentially optimizing the design. For most robots, this process is further complicated by the need, when validating the capabilities of the hardware to solve the desired task, to already have an appropriate controller, which is in turn designed and tuned for the specific hardware. In this paper, we propose a novel approach, HPC-BBO, to efficiently and automatically design hardware configurations, and evaluate them by also automatically tuning the corresponding controller. HPC-BBO is based on a hierarchical Bayesian optimization process which iteratively optimizes morphology configurations (based on the performance of the previous designs during the controller learning process) and subsequently learns the corresponding controllers (exploiting the knowledge collected from optimizing for previous morphologies). Moreover, HPC-BBO can select a "batch" of multiple morphology designs at once, thus parallelizing hardware validation and reducing the number of time-consuming production cycles. We validate HPC-BBO on the design of the morphology and controller for a simulated 6-legged microrobot. Experimental results show that HPC-BBO outperforms multiple competitive baselines, and yields a $360\%$ reduction in production cycles over standard Bayesian optimization, thus reducing the hypothetical manufacturing time of our microrobot from 21 to 4 months.
Scarce data is a major challenge to scaling robot learning to truly complex tasks, as we need to generalize locally learned policies over different task contexts. Contextual policy search offers data-efficient learning and generalization by explicitly conditioning the policy on a parametric context space. In this paper, we further structure the contextual policy representation. We propose to factor contexts into two components: target contexts that describe the task objectives, e.g. target position for throwing a ball; and environment contexts that characterize the environment, e.g. initial position or mass of the ball. Our key observation is that experience can be directly generalized over target contexts. We show that this can be easily exploited in contextual policy search algorithms. In particular, we apply factorization to a Bayesian optimization approach to contextual policy search both in sampling-based and active learning settings. Our simulation results show faster learning and better generalization in various robotic domains. See our supplementary video: https://youtu.be/MNTbBAOufDY.
Graph structured data are abundant in the real world. Among different graph types, directed acyclic graphs (DAGs) are of particular interest to machine learning researchers, as many machine learning models are realized as computations on DAGs, including neural networks and Bayesian networks. In this paper, we study deep generative models for DAGs, and propose a novel DAG variational autoencoder (D-VAE). To encode DAGs into the latent space, we leverage graph neural networks. We propose an asynchronous message passing scheme that allows encoding the computations on DAGs, rather than using existing simultaneous message passing schemes to encode local graph structures. We demonstrate the effectiveness of our proposed DVAE through two tasks: neural architecture search and Bayesian network structure learning. Experiments show that our model not only generates novel and valid DAGs, but also produces a smooth latent space that facilitates searching for DAGs with better performance through Bayesian optimization.
In many high-throughput experimental design settings, such as those common in biochemical engineering, batched queries are more cost effective than one-by-one sequential queries. Furthermore, it is often not possible to directly choose items to query. Instead, the experimenter specifies a set of constraints that generates a library of possible items, which are then selected stochastically. Motivated by these considerations, we investigate \emph{Batched Stochastic Bayesian Optimization} (BSBO), a novel Bayesian optimization scheme for choosing the constraints in order to guide exploration towards items with greater utility. We focus on \emph{site-saturation mutagenesis}, a prototypical setting of BSBO in biochemical engineering, and propose a natural objective function for this problem. Importantly, we show that our objective function can be efficiently decomposed as a difference of submodular functions (DS), which allows us to employ DS optimization tools to greedily identify sets of constraints that increase the likelihood of finding items with high utility. Our experimental results show that our algorithm outperforms common heuristics on both synthetic and two real protein datasets.
Automated hyperparameter tuning aspires to facilitate the application of machine learning for non-experts. In the literature, different optimization approaches are applied for that purpose. This paper investigates the performance of Differential Evolution for tuning hyperparameters of supervised learning algorithms for classification tasks. This empirical study involves a range of different machine learning algorithms and datasets with various characteristics to compare the performance of Differential Evolution with Sequential Model-based Algorithm Configuration (SMAC), a reference Bayesian Optimization approach. The results indicate that Differential Evolution outperforms SMAC for most datasets when tuning a given machine learning algorithm - particularly when breaking ties in a first-to-report fashion. Only for the tightest of computational budgets SMAC performs better. On small datasets, Differential Evolution outperforms SMAC by 19% (37% after tie-breaking). In a second experiment across a range of representative datasets taken from the literature, Differential Evolution scores 15% (23% after tie-breaking) more wins than SMAC.
Machine learning pipeline potentially consists of several stages of operations like data preprocessing, feature engineering and machine learning model training. Each operation has a set of hyper-parameters, which can become irrelevant for the pipeline when the operation is not selected. This gives rise to a hierarchical conditional hyper-parameter space. To optimize this mixed continuous and discrete conditional hierarchical hyper-parameter space, we propose an efficient pipeline search and configuration algorithm which combines the power of Reinforcement Learning and Bayesian Optimization. Empirical results show that our method performs favorably compared to state of the art methods like Auto-sklearn , TPOT, Tree Parzen Window, and Random Search.
High-speed and high-acceleration movements are inherently hard to control. Applying learning to the control of such motions on anthropomorphic robot arms can improve the accuracy of the control but might damage the system. The inherent exploration of learning approaches can lead to instabilities and the robot reaching joint limits at high speeds. Having hardware that enables safe exploration of high-speed and high-acceleration movements is therefore desirable. To address this issue, we propose to use robots actuated by Pneumatic Artificial Muscles (PAMs). In this paper, we present a four degrees of freedom (DoFs) robot arm that reaches high joint angle accelerations of up to 28000 deg/s^2 while avoiding dangerous joint limits thanks to the antagonistic actuation and limits on the air pressure ranges. With this robot arm, we are able to tune control parameters using Bayesian optimization directly on the hardware without additional safety considerations. The achieved tracking performance on a fast trajectory exceeds previous results on comparable PAM-driven robots. We also show that our system can be controlled well on slow trajectories with PID controllers due to careful construction considerations such as minimal bending of cables, lightweight kinematics and minimal contact between PAMs and PAMs with the links. Finally, we propose a novel technique to control the the co-contraction of antagonistic muscle pairs. Experimental results illustrate that choosing the optimal co-contraction level is vital to reach better tracking performance. Through the use of PAM-driven robots and learning, we do a small step towards the future development of robots capable of more human-like motions.
Multi-task learning (MTL) has achieved success over a wide range of problems, where the goal is to improve the performance of a primary task using a set of relevant auxiliary tasks. However, when the usefulness of the auxiliary tasks w.r.t. the primary task is not known a priori, the success of MTL models depends on the correct choice of these auxiliary tasks and also a balanced mixing ratio of these tasks during alternate training. These two problems could be resolved via manual intuition or hyper-parameter tuning over all combinatorial task choices, but this introduces inductive bias or is not scalable when the number of candidate auxiliary tasks is very large. To address these issues, we present AutoSeM, a two-stage MTL pipeline, where the first stage automatically selects the most useful auxiliary tasks via a Beta-Bernoulli multi-armed bandit with Thompson Sampling, and the second stage learns the training mixing ratio of these selected auxiliary tasks via a Gaussian Process based Bayesian optimization framework. We conduct several MTL experiments on the GLUE language understanding tasks, and show that our AutoSeM framework can successfully find relevant auxiliary tasks and automatically learn their mixing ratio, achieving significant performance boosts on several primary tasks. Finally, we present ablations for each stage of AutoSeM and analyze the learned auxiliary task choices.
Transferring knowledge across tasks to improve data-efficiency is one of the open key challenges in the field of global black-box optimization. Readily available algorithms are typically designed to be universal optimizers and, therefore, often suboptimal for specific tasks. We propose a novel transfer learning method to obtain customized optimizers within the well-established framework of Bayesian optimization, allowing our algorithm to utilize the proven generalization capabilities of Gaussian processes. Using reinforcement learning to meta-train an acquisition function (AF) on a set of related tasks, the proposed method learns to extract implicit structural information and to exploit it for improved data-efficiency. We present experiments on a simulation-to-real transfer task as well as on several synthetic functions and on two hyperparameter search problems. The results show that our algorithm (1) automatically identifies structural properties of objective functions from available source tasks or simulations, (2) performs favourably in settings with both scarse and abundant source data, and (3) falls back to the performance level of general AFs if no particular structure is present.
Online field experiments are the gold-standard way of evaluating changes to real-world interactive machine learning systems. Yet our ability to explore complex, multi-dimensional policy spaces - such as those found in recommendation and ranking problems - is often constrained by the limited number of experiments that can be run simultaneously. To alleviate these constraints, we augment online experiments with an offline simulator and apply multi-task Bayesian optimization to tune live machine learning systems. We describe practical issues that arise in these types of applications, including biases that arise from using a simulator and assumptions for the multi-task kernel. We measure empirical learning curves which show substantial gains from including data from biased offline experiments, and show how these learning curves are consistent with theoretical results for multi-task Gaussian process generalization. We find that improved kernel inference is a significant driver of multi-task generalization. Finally, we show several examples of Bayesian optimization efficiently tuning a live machine learning system by combining offline and online experiments.
An energy based approach for stabilizing a mechanical system has offered a simple yet powerful control scheme. However, since it does not impose such strong constraints on parameter space of the controller, finding appropriate parameter values for an optimal controller is known to be hard. This paper intends to generate an optimal energy-based controller for swinging up a rotary inverted pendulum, also known as the Furuta pendulum, by applying the Bayesian optimization called Entropy Search. Simulations and experiments show that the optimal controller has an improved performance compared to a nominal controller for various initial conditions.
To solve a machine learning problem, one typically needs to perform data preprocessing, modeling, and hyperparameter tuning, which is known as model selection and hyperparameter optimization.The goal of automated machine learning (AutoML) is to design methods that can automatically perform model selection and hyperparameter optimization without human interventions for a given dataset. In this paper, we propose a meta-learning method that can search for a high-performance machine learning pipeline from the predefined set of candidate pipelines for supervised classification datasets in an efficient way by leveraging meta-data collected from previous experiments. More specifically, our method combines an adaptive Bayesian regression model with a neural network basis function and the acquisition function from Bayesian optimization. The adaptive Bayesian regression model is able to capture knowledge from previous meta-data and thus make predictions of the performances of machine learning pipelines on a new dataset. The acquisition function is then used to guide the search of possible pipelines based on the predictions.The experiments demonstrate that our approach can quickly identify high-performance pipelines for a range of test datasets and outperforms the baseline methods.
Optical scatterometry is a method to measure the size and shape of periodic micro- or nanostructures on surfaces. For this purpose the geometry parameters of the structures are obtained by reproducing experimental measurement results through numerical simulations. We compare the performance of Bayesian optimization to different local minimization algorithms for this numerical optimization problem. Bayesian optimization uses Gaussian-process regression to find promising parameter values. We examine how pre-computed simulation results can be used to train the Gaussian process and to accelerate the optimization.
We present Acquisition Thompson Sampling (ATS), a novel technique for batch Bayesian Optimization (BO) based on the idea of sampling multiple acquisition functions from a stochastic process. We define this process through the dependency of the acquisition functions on a set of model hyper-parameters. ATS is conceptually simple, straightforward to implement and, unlike other batch BO methods, it can be employed to parallelize any sequential acquisition function or to make existing parallel methods scale further. We present experiments on a variety of benchmark functions and on the hyper-parameter optimization of a popular gradient boosting tree algorithm. These demonstrate the advantages of ATS with respect to classical parallel Thompson Sampling for BO, its competitiveness with two state-of-the-art batch BO methods, and its effectiveness if applied to existing parallel BO algorithms.
Multi-fidelity methods are prominently used when cheaply-obtained, but possibly biased and noisy, observations must be effectively combined with limited or expensive true data in order to construct reliable models. This arises in both fundamental machine learning procedures such as Bayesian optimization, as well as more practical science and engineering applications. In this paper we develop a novel multi-fidelity model which treats layers of a deep Gaussian process as fidelity levels, and uses a variational inference scheme to propagate uncertainty across them. This allows for capturing nonlinear correlations between fidelities with lower risk of overfitting than existing methods exploiting compositional structure, which are conversely burdened by structural assumptions and constraints. We show that the proposed approach makes substantial improvements in quantifying and propagating uncertainty in multi-fidelity set-ups, which in turn improves their effectiveness in decision making pipelines.
Echo State Networks (ESNs) are recurrent neural networks that only train their output layer, thereby precluding the need to backpropagate gradients through time, which leads to significant computational gains. Nevertheless, a common issue in ESNs is determining its hyperparameters, which are crucial in instantiating a well performing reservoir, but are often set manually or using heuristics. In this work we optimize the ESN hyperparameters using Bayesian optimization which, given a limited budget of function evaluations, outperforms a grid search strategy. In the context of large volumes of time series data, such as light curves in the field of astronomy, we can further reduce the optimization cost of ESNs. In particular, we wish to avoid tuning hyperparameters per individual time series as this is costly; instead, we want to find ESNs with hyperparameters that perform well not just on individual time series but rather on groups of similar time series without sacrificing predictive performance significantly. This naturally leads to a notion of clusters, where each cluster is represented by an ESN tuned to model a group of time series of similar temporal behavior. We demonstrate this approach both on synthetic datasets and real world light curves from the MACHO survey. We show that our approach results in a significant reduction in the number of ESN models required to model a whole dataset, while retaining predictive performance for the series in each cluster.