The current state-of-the-art Scrabble agents are not learning-based but depend on truncated Monte Carlo simulations and the quality of such agents is contingent upon the time available for running the simulations. This thesis takes steps towards building a learning-based Scrabble agent using self-play. Specifically, we try to find a better function approximation for the static evaluation function used in Scrabble which determines the move goodness at a given board configuration. In this work, we experimented with evolutionary algorithms and Bayesian Optimization to learn the weights for an approximate feature-based evaluation function. However, these optimization methods were not quite effective, which lead us to explore the given problem from an Imitation Learning point of view. We also tried to imitate the ranking of moves produced by the Quackle simulation agent using supervised learning with a neural network function approximator which takes the raw representation of the Scrabble board as the input instead of using only a fixed number of handcrafted features.
Bayesian optimization is a sample-efficient method for finding a global optimum of an expensive-to-evaluate black-box function. A global solution is found by accumulating a pair of query point and its function value, repeating these two procedures: (i) modeling a surrogate function; (ii) maximizing an acquisition function to determine where next to query. Convergence guarantees are only valid when the global optimizer of the acquisition function is found at each round and selected as the next query point. In practice, however, local optimizers of an acquisition function are also used, since searching for the global optimizer is often a non-trivial or time-consuming task. In this paper we consider three popular acquisition functions, PI, EI, and GP-UCB induced by Gaussian process regression. Then we present a performance analysis on the behavior of local optimizers of those acquisition functions, in terms of {\em instantaneous regrets} over global optimizers. We also introduce an analysis, allowing a local optimization method to start from multiple different initial conditions. Numerical experiments confirm the validity of our theoretical analysis.
In a standard setting of Bayesian optimization (BO), the objective function evaluation is assumed to be highly expensive. Multi-fidelity Bayesian optimization (MFBO) accelerates BO by incorporating lower fidelity observations available with a lower sampling cost. In this paper, we focus on the information-based approach, which is a popular and empirically successful approach in BO. For MFBO, however, existing information-based methods are plagued by difficulty in estimating the information gain. We propose an approach based on max-value entropy search (MES), which greatly facilitates computations by considering the entropy of the optimal function value instead of the optimal input point. We show that, in our multi-fidelity MES (MF-MES), most of additional computations, compared with usual MES, is reduced to analytical computations. Although an additional numerical integration is necessary for the information across different fidelities, this is only in one dimensional space, which can be performed efficiently and accurately. Further, we also propose parallelization of MF-MES. Since there exist a variety of different sampling costs, queries typically occur asynchronously in MFBO. We show that similar simple computations can be derived for asynchronous parallel MFBO. We demonstrate effectiveness of our approach by using benchmark datasets and a real-world application to materials science data.
Improving predictive understanding of Earth system variability and change requires data-model integration. Efficient data-model integration for complex models requires surrogate modeling to reduce model evaluation time. However, building a surrogate of a large-scale Earth system model (ESM) with many output variables is computationally intensive because it involves a large number of expensive ESM simulations. In this effort, we propose an efficient surrogate method capable of using a few ESM runs to build an accurate and fast-to-evaluate surrogate system of model outputs over large spatial and temporal domains. We first use singular value decomposition to reduce the output dimensions, and then use Bayesian optimization techniques to generate an accurate neural network surrogate model based on limited ESM simulation samples. Our machine learning based surrogate methods can build and evaluate a large surrogate system of many variables quickly. Thus, whenever the quantities of interest change such as a different objective function, a new site, and a longer simulation time, we can simply extract the information of interest from the surrogate system without rebuilding new surrogates, which significantly saves computational efforts. We apply the proposed method to a regional ecosystem model to approximate the relationship between 8 model parameters and 42660 carbon flux outputs. Results indicate that using only 20 model simulations, we can build an accurate surrogate system of the 42660 variables, where the consistency between the surrogate prediction and actual model simulation is 0.93 and the mean squared error is 0.02. This highly-accurate and fast-to-evaluate surrogate system will greatly enhance the computational efficiency in data-model integration to improve predictions and advance our understanding of the Earth system.
Bayesian optimization (BO) based on Gaussian process models is a powerful paradigm to optimize black-box functions that are expensive to evaluate. While several BO algorithms provably converge to the global optimum of the unknown function, they assume that the hyperparameters of the kernel are known in advance. This is not the case in practice and misspecification often causes these algorithms to converge to poor local optima. In this paper, we present the first BO algorithm that is provably no-regret and converges to the optimum without knowledge of the hyperparameters. During optimization we slowly adapt the hyperparameters of stationary kernels and thereby expand the associated function class over time, so that the BO algorithm considers more complex function candidates. Based on the theoretical insights, we propose several practical algorithms that achieve the empirical sample efficiency of BO with online hyperparameter estimation, but retain theoretical convergence guarantees. We evaluate our method on several benchmark problems.
This paper investigates lung nodule classification by using deep neural networks (DNNs). Hyperparameter optimization in DNNs is a computationally expensive problem, where evaluating a hyperparameter configuration may take several hours or even days. Bayesian optimization has been recently introduced for the automatically searching of optimal hyperparameter configurations of DNNs. It applies probabilistic surrogate models to approximate the validation error function of hyperparameter configurations, such as Gaussian processes, and reduce the computational complexity to a large extent. However, most existing surrogate models adopt stationary covariance functions to measure the difference between hyperparameter points based on spatial distance without considering its spatial locations. This distance-based assumption together with the condition of constant smoothness throughout the whole hyperparameter search space clearly violates the property that the points far away from optimal points usually get similarly poor performance even though each two of them have huge spatial distance between them. In this paper, a non-stationary kernel is proposed which allows the surrogate model to adapt to functions whose smoothness varies with the spatial location of inputs, and a multi-level convolutional neural network (ML-CNN) is built for lung nodule classification whose hyperparameter configuration is optimized by using the proposed non-stationary kernel based Gaussian surrogate model. Our algorithm searches the surrogate for optimal setting via hyperparameter importance based evolutionary strategy, and the experiments demonstrate our algorithm outperforms manual tuning and well-established hyperparameter optimization methods such as Random search, Gaussian processes with stationary kernels, and recently proposed Hyperparameter Optimization via RBF and Dynamic coordinate search.
This paper proposes an efficient neural network (NN) architecture design methodology called Chameleon that honors given resource constraints. Instead of developing new building blocks or using computationally-intensive reinforcement learning algorithms, our approach leverages existing efficient network building blocks and focuses on exploiting hardware traits and adapting computation resources to fit target latency and/or energy constraints. We formulate platform-aware NN architecture search in an optimization framework and propose a novel algorithm to search for optimal architectures aided by efficient accuracy and resource (latency and/or energy) predictors. At the core of our algorithm lies an accuracy predictor built atop Gaussian Process with Bayesian optimization for iterative sampling. With a one-time building cost for the predictors, our algorithm produces state-of-the-art model architectures on different platforms under given constraints in just minutes. Our results show that adapting computation resources to building blocks is critical to model performance. Without the addition of any bells and whistles, our models achieve significant accuracy improvements against state-of-the-art hand-crafted and automatically designed architectures. We achieve 73.8% and 75.3% top-1 accuracy on ImageNet at 20ms latency on a mobile CPU and DSP. At reduced latency, our models achieve up to 8.5% (4.8%) and 6.6% (9.3%) absolute top-1 accuracy improvements compared to MobileNetV2 and MnasNet, respectively, on a mobile CPU (DSP), and 2.7% (4.6%) and 5.6% (2.6%) accuracy gains over ResNet-101 and ResNet-152, respectively, on an Nvidia GPU (Intel CPU).
In multi-objective Bayesian optimization and surrogate-based evolutionary algorithms, Expected HyperVolume Improvement (EHVI) is widely used as the acquisition function to guide the search approaching the Pareto front. This paper focuses on the exact calculation of EHVI given a nondominated set, for which the existing exact algorithms are complex and can be inefficient for problems with more than three objectives. Integrating with different decomposition algorithms, we propose a new method for calculating the integral in each decomposed high-dimensional box in constant time. We develop three new exact EHVI calculation algorithms based on three region decomposition methods. The first grid-based algorithm has a complexity of $O(m\cdot n^m)$ with $n$ denoting the size of the nondominated set and $m$ the number of objectives. The Walking Fish Group (WFG)-based algorithm has a worst-case complexity of $O(m\cdot 2^n)$ but has a better average performance. These two can be applied for problems with any $m$. The third CLM-based algorithm is only for $m=3$ and asymptotically optimal with complexity $\Theta(n\log{n})$. Performance comparison results show that all our three algorithms are at least twice faster than the state-of-the-art algorithms with the same decomposition methods. When $m>3$, our WFG-based algorithm can be over $10^2$ faster than the corresponding existing algorithms. Our algorithm is demonstrated in an example involving efficient multi-objective material design with Bayesian optimization.
Bayesian optimization is proposed for automatic learning of optimal controller parameters from experimental data. A probabilistic description (a Gaussian process) is used to model the unknown function from controller parameters to a user-defined cost. The probabilistic model is updated with data, which is obtained by testing a set of parameters on the physical system and evaluating the cost. In order to learn fast, the Bayesian optimization algorithm selects the next parameters to evaluate in a systematic way, for example, by maximizing information gain about the optimum. The algorithm thus iteratively finds the globally optimal parameters with only few experiments. Taking throttle valve control as a representative industrial control example, the proposed auto-tuning method is shown to outperform manual calibration: it consistently achieves better performance with a low number of experiments. The proposed auto-tuning framework is flexible and can handle different control structures and objectives.
During the development of AlphaGo, its many hyper-parameters were tuned with Bayesian optimization multiple times. This automatic tuning process resulted in substantial improvements in playing strength. For example, prior to the match with Lee Sedol, we tuned the latest AlphaGo agent and this improved its win-rate from 50% to 66.5% in self-play games. This tuned version was deployed in the final match. Of course, since we tuned AlphaGo many times during its development cycle, the compounded contribution was even higher than this percentage. It is our hope that this brief case study will be of interest to Go fans, and also provide Bayesian optimization practitioners with some insights and inspiration.
In this paper, we use a well-known Deep Learning technique called Long Short Term Memory (LSTM) recurrent neural networks to find sessions that are prone to code failure in applications that rely on telemetry data for system health monitoring. We also use LSTM networks to extract telemetry patterns that lead to a specific code failure. For code failure prediction, we treat the telemetry events, sequence of telemetry events and the outcome of each sequence as words, sentence and sentiment in the context of sentiment analysis, respectively. Our proposed method is able to process a large set of data and can automatically handle edge cases in code failure prediction. We take advantage of Bayesian optimization technique to find the optimal hyper parameters as well as the type of LSTM cells that leads to the best prediction performance. We then introduce the Contributors and Blockers concepts. In this paper, contributors are the set of events that cause a code failure, while blockers are the set of events that each of them individually prevents a code failure from happening, even in presence of one or multiple contributor(s). Once the proposed LSTM model is trained, we use a greedy approach to find the contributors and blockers. To develop and test our proposed method, we use synthetic (simulated) data in the first step. The synthetic data is generated using a number of rules for code failures, as well as a number of rules for preventing a code failure from happening. The trained LSTM model shows over 99% accuracy for detecting code failures in the synthetic data. The results from the proposed method outperform the classical learning models such as Decision Tree and Random Forest. Using the proposed greedy method, we are able to find the contributors and blockers in the synthetic data in more than 90% of the cases, with a performance better than sequential rule and pattern mining algorithms.
Probabilistic programming systems enable users to encode model structure and naturally reason about uncertainties, which can be leveraged towards improved Bayesian optimization (BO) methods. Here we present a probabilistic program embedding of BO that is capable of addressing main issues such as problematic domains (noisy, non-smooth, high-dimensional) and the neglected inner-optimization. Not only can we utilize programmable structure to incorporate domain knowledge to aid optimization, but dealing with uncertainties and implementing advanced BO techniques become trivial, crucial for use in practice (particularly for non-experts). We demonstrate the efficacy of the approach on optimization benchmarks and a real-world drug development scenario.
Purpose: Machine learning is broadly used for clinical data analysis. Before training a model, a machine learning algorithm must be selected. Also, the values of one or more model parameters termed hyper-parameters must be set. Selecting algorithms and hyper-parameter values requires advanced machine learning knowledge and many labor-intensive manual iterations. To lower the bar to machine learning, miscellaneous automatic selection methods for algorithms and/or hyper-parameter values have been proposed. Existing automatic selection methods are inefficient on large data sets. This poses a challenge for using machine learning in the clinical big data era. Methods: To address the challenge, this paper presents progressive sampling-based Bayesian optimization, an efficient and automatic selection method for both algorithms and hyper-parameter values. Results: We report an implementation of the method. We show that compared to a state of the art automatic selection method, our method can significantly reduce search time, classification error rate, and standard deviation of error rate due to randomization. Conclusions: This is major progress towards enabling fast turnaround in identifying high-quality solutions required by many machine learning-based clinical data analysis tasks.
Analog IC design relies on human experts to search for parameters that satisfy circuit specifications with their experience and intuitions, which is highly labor intensive, time consuming and suboptimal. Machine learning is a promising tool to automate this process. However, supervised learning is difficult for this task due to the low availability of training data: 1) Circuit simulation is slow, thus generating large-scale dataset is time-consuming; 2) Most circuit designs are propitiatory IPs within individual IC companies, making it expensive to collect large-scale datasets. We propose Learning to Design Circuits (L2DC) to leverage reinforcement learning that learns to efficiently generate new circuits data and to optimize circuits. We fix the schematic, and optimize the parameters of the transistors automatically by training an RL agent with no prior knowledge about optimizing circuits. After iteratively getting observations, generating a new set of transistor parameters, getting a reward, and adjusting the model, L2DC is able to optimize circuits. We evaluate L2DC on two transimpedance amplifiers. Trained for a day, our RL agent can achieve comparable or better performance than human experts trained for a quarter. It first learns to meet hard-constraints (eg. gain, bandwidth), and then learns to optimize good-to-have targets (eg. area, power). Compared with grid search-aided human design, L2DC can achieve $\mathbf{250}\boldsymbol{\times}$ higher sample efficiency with comparable performance. Under the same runtime constraint, the performance of L2DC is also better than Bayesian Optimization.
Learning by integrating multiple heterogeneous data sources is a common requirement in many tasks. Collective Matrix Factorization (CMF) is a technique to learn shared latent representations from arbitrary collections of matrices. It can be used to simultaneously complete one or more matrices, for predicting the unknown entries. Classical CMF methods assume linearity in the interaction of latent factors which can be restrictive and fails to capture complex non-linear interactions. In this paper, we develop the first deep-learning based method, called dCMF, for unsupervised learning of multiple shared representations, that can model such non-linear interactions, from an arbitrary collection of matrices. We address optimization challenges that arise due to dependencies between shared representations through Multi-Task Bayesian Optimization and design an acquisition function adapted for collective learning of hyperparameters. Our experiments show that dCMF significantly outperforms previous CMF algorithms in integrating heterogeneous data for predictive modeling. Further, on two tasks - recommendation and prediction of gene-disease association - dCMF outperforms state-of-the-art matrix completion algorithms that can utilize auxiliary sources of information.
Bayesian optimization usually assumes that a Bayesian prior is given. However, the strong theoretical guarantees in Bayesian optimization are often regrettably compromised in practice because of unknown parameters in the prior. In this paper, we adopt a variant of empirical Bayes and show that, by estimating the Gaussian process prior from offline data sampled from the same prior and constructing unbiased estimators of the posterior, variants of both GP-UCB and probability of improvement achieve a near-zero regret bound, which decreases to a constant proportional to the observational noise as the number of offline data and the number of online evaluations increase. Empirically, we have verified our approach on challenging simulated robotic problems featuring task and motion planning.
The performance of modern machine learning methods highly depends on their hyperparameter configurations. One simple way of selecting a configuration is to use default settings, often proposed along with the publication and implementation of a new algorithm. Those default values are usually chosen in an ad-hoc manner to work good enough on a wide variety of datasets. To address this problem, different automatic hyperparameter configuration algorithms have been proposed, which select an optimal configuration per dataset. This principled approach usually improves performance but adds additional algorithmic complexity and computational costs to the training procedure. As an alternative to this, we propose learning a set of complementary default values from a large database of prior empirical results. Selecting an appropriate configuration on a new dataset then requires only a simple, efficient and embarrassingly parallel search over this set. We demonstrate the effectiveness and efficiency of the approach we propose in comparison to random search and Bayesian Optimization.
We present a novel algorithm utilizing a deep Siamese neural network as a general object similarity function in combination with a Bayesian optimization (BO) framework to encode spatio-temporal information for efficient object tracking in video. In particular, we treat the video tracking problem as a dynamic (i.e. temporally-evolving) optimization problem. Using Gaussian Process priors, we model a dynamic objective function representing the location of a tracked object in each frame. By exploiting temporal correlations, the proposed method queries the search space in a statistically principled and efficient way, offering several benefits over current state of the art video tracking methods.
Cooking typically involves a plethora of decisions about ingredients and tools that need to be chosen in order to write a good cooking recipe. Cooking can be modelled in an optimization framework, as it involves a search space of ingredients, kitchen tools, cooking times or temperatures. If we model as an objective function the quality of the recipe, several problems arise. No analytical expression can model all the recipes, so no gradients are available. The objective function is subjective, in other words, it contains noise. Moreover, evaluations are expensive both in time and human resources. Bayesian Optimization (BO) emerges as an ideal methodology to tackle problems with these characteristics. In this paper, we propose a methodology to suggest recipe recommendations based on a Machine Learning (ML) model that fits real and simulated data and BO. We provide empirical evidence with two experiments that support the adequacy of the methodology.
The performance of deep neural networks crucially depends on good hyperparameter configurations. Bayesian optimization is a powerful framework for optimizing the hyperparameters of DNNs. These methods need sufficient evaluation data to approximate and minimize the validation error function of hyperparameters. However, the expensive evaluation cost of DNNs leads to very few evaluation data within a limited time, which greatly reduces the efficiency of Bayesian optimization. Besides, the previous researches focus on using the complete evaluation data to conduct Bayesian optimization, and ignore the intermediate evaluation data generated by early stopping methods. To alleviate the insufficient evaluation data problem, we propose a fast hyperparameter optimization method, HOIST, that utilizes both the complete and intermediate evaluation data to accelerate the hyperparameter optimization of DNNs. Specifically, we train multiple basic surrogates to gather information from the mixed evaluation data, and then combine all basic surrogates using weighted bagging to provide an accurate ensemble surrogate. Our empirical studies show that HOIST outperforms the state-of-the-art approaches on a wide range of DNNs, including feed forward neural networks, convolutional neural networks, recurrent neural networks, and variational autoencoder.