In the automation of many kinds of processes, the observable outcome can often be described as the combined effect of an entire sequence of actions, or controls, applied throughout its execution. In these cases, strategies to optimise control policies for individual stages of the process might not be applicable, and instead the whole policy might have to be optimised at once. On the other hand, the cost to evaluate the policy's performance might also be high, being desirable that a solution can be found with as few interactions as possible with the real system. We consider the problem of optimising control policies to allow a robot to complete a given race track within a minimum amount of time. We assume that the robot has no prior information about the track or its own dynamical model, just an initial valid driving example. Localisation is only applied to monitor the robot and to provide an indication of its position along the track's centre axis. We propose a method for finding a policy that minimises the time per lap while keeping the vehicle on the track using a Bayesian optimisation (BO) approach over a reproducing kernel Hilbert space. We apply an algorithm to search more efficiently over high-dimensional policy-parameter spaces with BO, by iterating over each dimension individually, in a sequential coordinate descent-like scheme. Experiments demonstrate the performance of the algorithm against other methods in a simulated car racing environment.
In outdoor environments, mobile robots are required to navigate through terrain with varying characteristics, some of which might significantly affect the integrity of the platform. Ideally, the robot should be able to identify areas that are safe for navigation based on its own percepts about the environment while avoiding damage to itself. Bayesian optimisation (BO) has been successfully applied to the task of learning a model of terrain traversability while guiding the robot through more traversable areas. An issue, however, is that localisation uncertainty can end up guiding the robot to unsafe areas and distort the model being learnt. In this paper, we address this problem and present a novel method that allows BO to consider localisation uncertainty by applying a Gaussian process model for uncertain inputs as a prior. We evaluate the proposed method in simulation and in experiments with a real robot navigating over rough terrain and compare it against standard BO methods.
The paper presents a novel approach to direct covariance function learning for Bayesian optimisation, with particular emphasis on experimental design problems where an existing corpus of condensed knowledge is present. The method presented borrows techniques from reproducing kernel Banach space theory (specifically m-kernels) and leverages them to convert (or re-weight) existing covariance functions into new, problem-specific covariance functions. The key advantage of this approach is that rather than relying on the user to manually select (with some hyperparameter tuning and experimentation) an appropriate covariance function it constructs the covariance function to specifically match the problem at hand. The technique is demonstrated on two real-world problems - specifically alloy design and short-polymer fibre manufacturing - as well as a selected test function.
Bayesian optimization (BO) is a widely-used method for optimizing expensive (to evaluate) problems. At the core of most BO methods is the modeling of the objective function using a Gaussian Process (GP) whose covariance is selected from a set of standard covariance functions. From a weight-space view, this models the objective as a linear function in a feature space implied by the given covariance K, with an arbitrary Gaussian weight prior ${\bf w} \sim \mathcal{N} ({\bf 0}, {\bf I})$. In many practical applications there is data available that has a similar (covariance) structure to the objective, but which, having different form, cannot be used directly in standard transfer learning. In this paper we show how such auxiliary data may be used to construct a GP covariance corresponding to a more appropriate weight prior for the objective function. Building on this, we show that we may accelerate BO by modeling the objective function using this (learned) weight prior, which we demonstrate on both test functions and a practical application to short-polymer fibre manufacture.
Policy gradient methods ignore the potential value of adjusting environment variables: unobservable state features that are randomly determined by the environment in a physical setting, but are controllable in a simulator. This can lead to slow learning, or convergence to suboptimal policies, if the environment variable has a large impact on the transition dynamics. In this paper, we present fingerprint policy optimisation (FPO), which finds a policy that is optimal in expectation across the distribution of environment variables. The central idea is to use Bayesian optimisation (BO) to actively select the distribution of the environment variable that maximises the improvement generated by each iteration of the policy gradient method. To make this BO practical, we contribute two easy-to-compute low-dimensional fingerprints of the current policy. Our experiments show that FPO can efficiently learn policies that are robust to significant rare events, which are unlikely to be observable under random sampling, but are key to learning good policies.
Information-theoretic Bayesian optimisation techniques have demonstrated state-of-the-art performance in tackling important global optimisation problems. However, current information-theoretic approaches require many approximations in implementation, introduce often-prohibitive computational overhead and limit the choice of kernels available to model the objective. We develop a fast information-theoretic Bayesian Optimisation method, FITBO, that avoids the need for sampling the global minimiser, thus significantly reducing computational overhead. Moreover, in comparison with existing approaches, our method faces fewer constraints on kernel choice and enjoys the merits of dealing with the output space. We demonstrate empirically that FITBO inherits the performance associated with information-theoretic Bayesian optimisation, while being even faster than simpler Bayesian optimisation approaches, such as Expected Improvement.
Bayesian Optimisation (BO) refers to a class of methods for global optimisation of a function $f$ which is only accessible via point evaluations. It is typically used in settings where $f$ is expensive to evaluate. A common use case for BO in machine learning is model selection, where it is not possible to analytically model the generalisation performance of a statistical model, and we resort to noisy and expensive training and validation procedures to choose the best model. Conventional BO methods have focused on Euclidean and categorical domains, which, in the context of model selection, only permits tuning scalar hyper-parameters of machine learning algorithms. However, with the surge of interest in deep learning, there is an increasing demand to tune neural network \emph{architectures}. In this work, we develop NASBOT, a Gaussian process based BO framework for neural architecture search. To accomplish this, we develop a distance metric in the space of neural network architectures which can be computed efficiently via an optimal transport program. This distance might be of independent interest to the deep learning community as it may find applications outside of BO. We demonstrate that NASBOT outperforms other alternatives for architecture search in several cross validation based model selection tasks on multi-layer perceptrons and convolutional neural networks.