New battery technology will be crucial to the electrification of transportation and aviation 1, 2 , but battery innovations can take years to deliver. For battery electrolytes, the many design variables present in selecting multiple solvents, salts, and their relative ratios [3][4][5][6][7] mean that optimization studies are slow and laborious, even those restricted to small search spaces. The key challenge is to lower the number and time-cost of experiments needed to formulate an electrolyte for a given objective.
In many scientific and engineering applications, we are tasked with the maximisation of an expensive to evaluate black box function f . Traditional settings for this problem assume just the availability of this single function. However, in many cases, cheap approximations to f may be obtainable. For example, the expensive real world behaviour of a robot can be approximated by a cheap computer simulation. We can use these approximations to eliminate low function value regions cheaply and use the expensive evaluations of f in a small but promising region and speedily identify the optimum. We formalise this task as a multi-fidelity bandit problem where the target function and its approximations are sampled from a Gaussian process. We develop MF-GP-UCB, a novel method based on upper confidence bound techniques. In our theoretical analysis we demonstrate that it exhibits precisely the above behaviour and achieves better bounds on the regret than strategies which ignore multi-fidelity information. Empirically, MF-GP-UCB outperforms such naive strategies and other multi-fidelity methods on several synthetic and real experiments. KANDASAMY, DASARATHY, OLIVA, SCHNEIDER, P脫CZOS n=300 n=3000 1. We present a formalism for multi-fidelity bandit optimisation using Gaussian process (GP) assumptions on f and its approximations. We develop a novel algorithm, Multi-Fidelity Gaussian Process Upper Confidence Bound (MF-GP-UCB) for this setting.2. Our theoretical analysis proves that MF-GP-UCB explores the space X at lower fidelities and uses the high fidelities in successively smaller regions to converge on the optimum. As lower fidelity queries are cheaper, MF-GP-UCB has better upper bounds on the regret than single fidelity strategies which have to rely on the expensive function to explore the entire space.3. We demonstrate that MF-GP-UCB outperforms single fidelity methods and other alternatives empirically, via a series of synthetic examples, three hyper-parameter tuning tasks and one inference problem in astrophysics. Our matlab implementation and experiments are available at github.com/kirthevasank/mf-gp-ucb. Related WorkSince the seminal work by Robbins [1952], the multi-armed bandit problem has been studied extensively in the K-armed setting. Recently, there has been a surge of interest in the optimism under uncertainty principle for K-armed bandits, typified by upper confidence bound (UCB) methods Cesa-Bianchi, 2012, Auer, 2003]. UCB strategies have also been used in bandit
A common problem in disciplines of applied Statistics research such as Astrostatistics is of estimating the posterior distribution of relevant parameters. Typically, the likelihoods for such models are computed via expensive experiments such as cosmological simulations of the universe. An urgent challenge in these research domains is to develop methods that can estimate the posterior with few likelihood evaluations.In this paper, we study active posterior estimation in a Bayesian setting when the likelihood is expensive to evaluate. Existing techniques for posterior estimation are based on generating samples representative of the posterior. Such methods do not consider efficiency in terms of likelihood evaluations. In order to be query efficient we treat posterior estimation in an active regression framework. We propose two myopic query strategies to choose where to evaluate the likelihood and implement them using Gaussian processes. Via experiments on a series of synthetic and real examples we demonstrate that our approach is significantly more query efficient than existing techniques and other heuristics for posterior estimation.
Bayesian Optimisation (BO), refers to a suite of techniques for global optimisation of expensive black box functions, which use introspective Bayesian models of the function to efficiently find the optimum. While BO has been applied successfully in many applications, modern optimisation tasks usher in new challenges where conventional methods fail spectacularly. In this work, we present Dragonfly, an open source Python library for scalable and robust BO. Dragonfly incorporates multiple recently developed methods that allow BO to be applied in challenging real world settings; these include better methods for handling higher dimensional domains, methods for handling multi-fidelity evaluations when cheap approximations of an expensive function are available, methods for optimising over structured combinatorial spaces, such as the space of neural network architectures, and methods for handling parallel evaluations. Additionally, we develop new methodological improvements in BO for selecting the Bayesian model, selecting the acquisition function, and optimising over complex domains with different variable types and additional constraints. We compare Dragonfly to a suite of other packages and algorithms for global optimisation and demonstrate that when the above methods are integrated, they enable significant improvements in the performance of BO. The Dragonfly library is available at dragonfly.github.io.
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