Student-$t$ processes have recently been proposed as an appealing alternative non-parameteric function prior. They feature enhanced flexibility and predictive variance. In this work the use of Student-$t$ processes are explored for multi-objective Bayesian optimization. In particular, an analytical expression for the hypervolume-based probability of improvement is developed for independent Student-$t$ process priors of the objectives. Its effectiveness is shown on a multi-objective optimization problem which is known to be difficult with traditional Gaussian processes.
We present an optimizer which uses Bayesian optimization to tune the system parameters of distributed stochastic gradient descent (SGD). Given a specific context, our goal is to quickly find efficient configurations which appropriately balance the load between the available machines to minimize the average SGD iteration time. Our experiments consider setups with over thirty parameters. Traditional Bayesian optimization, which uses a Gaussian process as its model, is not well suited to such high dimensional domains. To reduce convergence time, we exploit the available structure. We design a probabilistic model which simulates the behavior of distributed SGD and use it within Bayesian optimization. Our model can exploit many runtime measurements for inference per evaluation of the objective function. Our experiments show that our resulting optimizer converges to efficient configurations within ten iterations, the optimized configurations outperform those found by generic optimizer in thirty iterations by up to 2X.
The recently introduced Intelligent Trial-and-Error (IT&E) algorithm showed that robots can adapt to damage in a matter of a few trials. The success of this algorithm relies on two components: prior knowledge acquired through simulation with an intact robot, and Bayesian optimization (BO) that operates on-line, on the damaged robot. While IT&E leads to fast damage recovery, it does not incorporate any safety constraints that prevent the robot from attempting harmful behaviors. In this work, we address this limitation by replacing the BO component with a constrained BO procedure. We evaluate our approach on a simulated damaged humanoid robot that needs to crawl as fast as possible, while performing as few unsafe trials as possible. We compare our new "safety-aware IT&E" algorithm to IT&E and a multi-objective version of IT&E in which the safety constraints are dealt as separate objectives. Our results show that our algorithm outperforms the other approaches, both in crawling speed within the safe regions and number of unsafe trials.
Scarce data is a major challenge to scaling robot learning to truly complex tasks, as we need to generalize locally learned policies over different "contexts". Bayesian optimization approaches to contextual policy search (CPS) offer data-efficient policy learning that generalize over a context space. We propose to improve data-efficiency by factoring typically considered contexts into two components: target-type contexts that correspond to a desired outcome of the learned behavior, e.g. target position for throwing a ball; and environment type contexts that correspond to some state of the environment, e.g. initial ball position or wind speed. Our key observation is that experience can be directly generalized over target-type contexts. Based on that we introduce Factored Contextual Policy Search with Bayesian Optimization for both passive and active learning settings. Preliminary results show faster policy generalization on a simulated toy problem. A full paper extension is available at arXiv:1904.11761
Bayesian Optimization (BO) has become a core method for solving expensive black-box optimization problems. While much research focussed on the choice of the acquisition function, we focus on online length-scale adaption and the choice of kernel function. Instead of choosing hyperparameters in view of maximum likelihood on past data, we propose to use the acquisition function to decide on hyperparameter adaptation more robustly and in view of the future optimization progress. Further, we propose a particular kernel function that includes non-stationarity and local anisotropy and thereby implicitly integrates the efficiency of local convex optimization with global Bayesian optimization. Comparisons to state-of-the art BO methods underline the efficiency of these mechanisms on global optimization benchmarks.
The engineering of machine learning systems is still a nascent field; relying on a seemingly daunting collection of quickly evolving tools and best practices. It is our hope that this guidebook will serve as a useful resource for machine learning practitioners looking to take advantage of Bayesian optimization techniques. We outline four example machine learning problems that can be solved using open source machine learning libraries, and highlight the benefits of using Bayesian optimization in the context of these common machine learning applications.
A key requirement for the current generation of artificial decision-makers is that they should adapt well to changes in unexpected situations. This paper addresses the situation in which an AI for aerial dog fighting, with tunable parameters that govern its behavior, must optimize behavior with respect to an objective function that is evaluated and learned through simulations. Bayesian optimization with a Gaussian Process surrogate is used as the method for investigating the objective function. One key benefit is that during optimization, the Gaussian Process learns a global estimate of the true objective function, with predicted outcomes and a statistical measure of confidence in areas that haven't been investigated yet. Having a model of the objective function is important for being able to understand possible outcomes in the decision space; for example this is crucial for training and providing feedback to human pilots. However, standard Bayesian optimization does not perform consistently or provide an accurate Gaussian Process surrogate function for highly volatile objective functions. We treat these problems by introducing a novel sampling technique called Hybrid Repeat/Multi-point Sampling. This technique gives the AI ability to learn optimum behaviors in a highly uncertain environment. More importantly, it not only improves the reliability of the optimization, but also creates a better model of the entire objective surface. With this improved model the agent is equipped to more accurately/efficiently predict performance in unexplored scenarios.
A key drawback of the current generation of artificial decision-makers is that they do not adapt well to changes in unexpected situations. This paper addresses the situation in which an AI for aerial dog fighting, with tunable parameters that govern its behavior, will optimize behavior with respect to an objective function that must be evaluated and learned through simulations. Once this objective function has been modeled, the agent can then choose its desired behavior in different situations. Bayesian optimization with a Gaussian Process surrogate is used as the method for investigating the objective function. One key benefit is that during optimization the Gaussian Process learns a global estimate of the true objective function, with predicted outcomes and a statistical measure of confidence in areas that haven't been investigated yet. However, standard Bayesian optimization does not perform consistently or provide an accurate Gaussian Process surrogate function for highly volatile objective functions. We treat these problems by introducing a novel sampling technique called Hybrid Repeat/Multi-point Sampling. This technique gives the AI ability to learn optimum behaviors in a highly uncertain environment. More importantly, it not only improves the reliability of the optimization, but also creates a better model of the entire objective surface. With this improved model the agent is equipped to better adapt behaviors.
Kernelized Correlation Filter (KCF) is one of the state-of-the-art object trackers. However, it does not reasonably model the distribution of correlation response during tracking process, which might cause the drifting problem, especially when targets undergo significant appearance changes due to occlusion, camera shaking, and/or deformation. In this paper, we propose an Output Constraint Transfer (OCT) method that by modeling the distribution of correlation response in a Bayesian optimization framework is able to mitigate the drifting problem. OCT builds upon the reasonable assumption that the correlation response to the target image follows a Gaussian distribution, which we exploit to select training samples and reduce model uncertainty. OCT is rooted in a new theory which transfers data distribution to a constraint of the optimized variable, leading to an efficient framework to calculate correlation filters. Extensive experiments on a commonly used tracking benchmark show that the proposed method significantly improves KCF, and achieves better performance than other state-of-the-art trackers. To encourage further developments, the source code is made available https://github.com/bczhangbczhang/OCT-KCF.
In typical applications of Bayesian optimization, minimal assumptions are made about the objective function being optimized. This is true even when researchers have prior information about the shape of the function with respect to one or more argument. We make the case that shape constraints are often appropriate in at least two important application areas of Bayesian optimization: (1) hyperparameter tuning of machine learning algorithms and (2) decision analysis with utility functions. We describe a methodology for incorporating a variety of shape constraints within the usual Bayesian optimization framework and present positive results from simple applications which suggest that Bayesian optimization with shape constraints is a promising topic for further research.
Automatically searching for optimal hyperparameter configurations is of crucial importance for applying deep learning algorithms in practice. Recently, Bayesian optimization has been proposed for optimizing hyperparameters of various machine learning algorithms. Those methods adopt probabilistic surrogate models like Gaussian processes to approximate and minimize the validation error function of hyperparameter values. However, probabilistic surrogates require accurate estimates of sufficient statistics (e.g., covariance) of the error distribution and thus need many function evaluations with a sizeable number of hyperparameters. This makes them inefficient for optimizing hyperparameters of deep learning algorithms, which are highly expensive to evaluate. In this work, we propose a new deterministic and efficient hyperparameter optimization method that employs radial basis functions as error surrogates. The proposed mixed integer algorithm, called HORD, searches the surrogate for the most promising hyperparameter values through dynamic coordinate search and requires many fewer function evaluations. HORD does well in low dimensions but it is exceptionally better in higher dimensions. Extensive evaluations on MNIST and CIFAR-10 for four deep neural networks demonstrate HORD significantly outperforms the well-established Bayesian optimization methods such as GP, SMAC, and TPE. For instance, on average, HORD is more than 6 times faster than GP-EI in obtaining the best configuration of 19 hyperparameters.
Sophisticated gated recurrent neural network architectures like LSTMs and GRUs have been shown to be highly effective in a myriad of applications. We develop an un-gated unit, the statistical recurrent unit (SRU), that is able to learn long term dependencies in data by only keeping moving averages of statistics. The SRU's architecture is simple, un-gated, and contains a comparable number of parameters to LSTMs; yet, SRUs perform favorably to more sophisticated LSTM and GRU alternatives, often outperforming one or both in various tasks. We show the efficacy of SRUs as compared to LSTMs and GRUs in an unbiased manner by optimizing respective architectures' hyperparameters in a Bayesian optimization scheme for both synthetic and real-world tasks.
In practice, the parameters of control policies are often tuned manually. This is time-consuming and frustrating. Reinforcement learning is a promising alternative that aims to automate this process, yet often requires too many experiments to be practical. In this paper, we propose a solution to this problem by exploiting prior knowledge from simulations, which are readily available for most robotic platforms. Specifically, we extend Entropy Search, a Bayesian optimization algorithm that maximizes information gain from each experiment, to the case of multiple information sources. The result is a principled way to automatically combine cheap, but inaccurate information from simulations with expensive and accurate physical experiments in a cost-effective manner. We apply the resulting method to a cart-pole system, which confirms that the algorithm can find good control policies with fewer experiments than standard Bayesian optimization on the physical system only.
Deep generative models have been wildly successful at learning coherent latent representations for continuous data such as video and audio. However, generative modeling of discrete data such as arithmetic expressions and molecular structures still poses significant challenges. Crucially, state-of-the-art methods often produce outputs that are not valid. We make the key observation that frequently, discrete data can be represented as a parse tree from a context-free grammar. We propose a variational autoencoder which encodes and decodes directly to and from these parse trees, ensuring the generated outputs are always valid. Surprisingly, we show that not only does our model more often generate valid outputs, it also learns a more coherent latent space in which nearby points decode to similar discrete outputs. We demonstrate the effectiveness of our learned models by showing their improved performance in Bayesian optimization for symbolic regression and molecular synthesis.
Bayesian optimization has become a successful tool for hyperparameter optimization of machine learning algorithms, such as support vector machines or deep neural networks. Despite its success, for large datasets, training and validating a single configuration often takes hours, days, or even weeks, which limits the achievable performance. To accelerate hyperparameter optimization, we propose a generative model for the validation error as a function of training set size, which is learned during the optimization process and allows exploration of preliminary configurations on small subsets, by extrapolating to the full dataset. We construct a Bayesian optimization procedure, dubbed Fabolas, which models loss and training time as a function of dataset size and automatically trades off high information gain about the global optimum against computational cost. Experiments optimizing support vector machines and deep neural networks show that Fabolas often finds high-quality solutions 10 to 100 times faster than other state-of-the-art Bayesian optimization methods or the recently proposed bandit strategy Hyperband.
We present mlrMBO, a flexible and comprehensive R toolbox for model-based optimization (MBO), also known as Bayesian optimization, which addresses the problem of expensive black-box optimization by approximating the given objective function through a surrogate regression model. It is designed for both single- and multi-objective optimization with mixed continuous, categorical and conditional parameters. Additional features include multi-point batch proposal, parallelization, visualization, logging and error-handling. mlrMBO is implemented in a modular fashion, such that single components can be easily replaced or adapted by the user for specific use cases, e.g., any regression learner from the mlr toolbox for machine learning can be used, and infill criteria and infill optimizers are easily exchangeable. We empirically demonstrate that mlrMBO provides state-of-the-art performance by comparing it on different benchmark scenarios against a wide range of other optimizers, including DiceOptim, rBayesianOptimization, SPOT, SMAC, Spearmint, and Hyperopt.
In this work, we utilize a Trust Region based Derivative Free Optimization (DFO-TR) method to directly maximize the Area Under Receiver Operating Characteristic Curve (AUC), which is a nonsmooth, noisy function. We show that AUC is a smooth function, in expectation, if the distributions of the positive and negative data points obey a jointly normal distribution. The practical performance of this algorithm is compared to three prominent Bayesian optimization methods and random search. The presented numerical results show that DFO-TR surpasses Bayesian optimization and random search on various black-box optimization problem, such as maximizing AUC and hyperparameter tuning.
We consider the problem of a robot learning the mechanical properties of objects through physical interaction with the object, and introduce a practical, data-efficient approach for identifying the motion models of these objects. The proposed method utilizes a physics engine, where the robot seeks to identify the inertial and friction parameters of the object by simulating its motion under different values of the parameters and identifying those that result in a simulation which matches the observed real motions. The problem is solved in a Bayesian optimization framework. The same framework is used for both identifying the model of an object online and searching for a policy that would minimize a given cost function according to the identified model. Experimental results both in simulation and using a real robot indicate that the proposed method outperforms state-of-the-art model-free reinforcement learning approaches.
We propose a general approach to modeling semi-supervised learning (SSL) algorithms. Specifically, we present a declarative language for modeling both traditional supervised classification tasks and many SSL heuristics, including both well-known heuristics such as co-training and novel domain-specific heuristics. In addition to representing individual SSL heuristics, we show that multiple heuristics can be automatically combined using Bayesian optimization methods. We experiment with two classes of tasks, link-based text classification and relation extraction. We show modest improvements on well-studied link-based classification benchmarks, and state-of-the-art results on relation-extraction tasks for two realistic domains.
Bayesian optimization (BO) has emerged during the last few years as an effective approach to optimizing black-box functions where direct queries of the objective are expensive. In this paper we consider the case where direct access to the function is not possible, but information about user preferences is. Such scenarios arise in problems where human preferences are modeled, such as A/B tests or recommender systems. We present a new framework for this scenario that we call Preferential Bayesian Optimization (PBO) which allows us to find the optimum of a latent function that can only be queried through pairwise comparisons, the so-called duels. PBO extends the applicability of standard BO ideas and generalizes previous discrete dueling approaches by modeling the probability of the winner of each duel by means of a Gaussian process model with a Bernoulli likelihood. The latent preference function is used to define a family of acquisition functions that extend usual policies used in BO. We illustrate the benefits of PBO in a variety of experiments, showing that PBO needs drastically fewer comparisons for finding the optimum. According to our experiments, the way of modeling correlations in PBO is key in obtaining this advantage.