Continuous multi-task Bayesian Optimisation with correlation

Pearce, Michael; Branke, Juergen

doi:10.1016/j.ejor.2018.03.017

Cited by 34 publications

(19 citation statements)

References 20 publications

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“…In this section, we adapt the IKG algorithm to our setting, and compare it with GP-C-OCBA. IKG offers a strong benchmark for our method, since it is based on the same GP model and has demonstrated superior sampling efficiency in prior work [21,22]. Knowledge Gradient (KG) [10] is a value-of-information type policy that was originally proposed for the R&S problem and later expanded to global optimization of black-box functions.…”

Section: Integrated Knowledge Gradientmentioning

confidence: 99%

“…In the classical R&S setting, where 𝑐 and 𝑐 ′ are redundant (i.e., there is only a single context), the KG policy operates by evaluating the alternative 𝑘 * = arg max 𝑘 KG(𝑘, 𝑐; 𝑐). To extend this to the contextual Bayesian optimization problem, [8,21,22] each study an integrated (or summed) version of KG, under slightly different problem settings, where either the context space or both alternative-context spaces are continuous. The main differences between these three works are in how they approximate and optimize the integrated KG factor in their respective problem settings.…”

Section: Integrated Knowledge Gradientmentioning

confidence: 99%

“…• Finally, we demonstrate the performance of GP-C-OCBA in numerical experiments. We see that GP-C-OCBA achieves significantly improved sampling efficiency when compared with C-OCBA [11], DSCO [17], TS, and TS+ [23]; and is highly competitive against the integrated knowledge gradient (IKG) algorithm [21], which uses the same GP model but requires significantly larger computational effort to decide on the next alternative-context to evaluate.…”

Section: Introductionmentioning

confidence: 99%

“…The main difficulty with using the IKG policy is its computational cost. In the finite alternative-context setting that we are working with, the KG(𝑘; 𝑐) can be computed exactly using Algorithm 1 from [21], which has a cost of O (𝐾 log 𝐾) for any pair (𝑘, 𝑐), given 𝜇 𝑛 (•, •) and Σ 𝑛 (•, •). This translates to an O (|C|𝐾 log 𝐾) cost for calculating the IKG factor for a given (𝑘, 𝑐).…”

mentioning

confidence: 99%

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Contextual Ranking and Selection with Gaussian Processes

Cakmak¹,

Gao²,

Zhou³

2022

Preprint

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In many real world problems, we are faced with the problem of selecting the best among a finite number of alternatives, where the best alternative is determined based on context specific information. In this work, we study the contextual Ranking and Selection problem under a finite-alternative-finite-context setting, where we aim to find the best alternative for each context. We use a separate Gaussian process to model the reward for each alternative, and derive the large deviations rate function for both the expected and worst-case contextual probability of correct selection. We propose the GP-C-OCBA sampling policy, which uses the Gaussian process posterior to iteratively allocate observations to maximize the rate function. We prove its consistency and show that it achieves the optimal convergence rate under the assumption of a non-informative prior. Numerical experiments show that our algorithm is highly competitive in terms of sampling efficiency, while having significantly smaller computational overhead.

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Section: Integrated Knowledge Gradientmentioning

confidence: 99%

Section: Integrated Knowledge Gradientmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

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Contextual Ranking and Selection with Gaussian Processes

Cakmak¹,

Gao²,

Zhou³

2022

Preprint

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“…Rastringin and Ackley function) and no explicit information from the distance between the tasks is exploited. Multi-task Bayesian optimization focuses on solving multiple correlated tasks when the fitness function is expensive [32], for instance when tuning a machine learning algorithm to several datasets or to tune a policy for a robot that depends on the context [13], like a walking controller that depends on the slope. The general idea of Bayesian optimization [3] is to use the previous fitness evaluations to predict the location of the most promising candidate solution, evaluate it, update the predictor, and repeat.…”

Section: Multitask Optimization and Learningmentioning

confidence: 99%

Quality diversity for multi-task optimization

Mouret

Maguire

2020

Proceedings of the 2020 Genetic and Evolutionary Computation Conference

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Quality Diversity (QD) algorithms are a recent family of optimization algorithms that search for a large set of diverse but highperforming solutions. In some specific situations, they can solve multiple tasks at once. For instance, they can find the joint positions required for a robotic arm to reach a set of points, which can also be solved by running a classic optimizer for each target point. However, they cannot solve multiple tasks when the fitness needs to be evaluated independently for each task (e.g., optimizing policies to grasp many different objects). In this paper, we propose an extension of the MAP-Elites algorithm, called Multi-task MAP-Elites, that solves multiple tasks when the fitness function depends on the task. We evaluate it on a simulated parametrized planar arm (10-dimensional search space; 5000 tasks) and on a simulated 6-legged robot with legs of different lengths (36-dimensional search space; 2000 tasks). The results show that in both cases our algorithm outperforms the optimization of each task separately with the CMA-ES algorithm.

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Technical note—Knowledge gradient for selection with covariates: Consistency and computation

Ding

Shen

et al. 2021

Naval Research Logistics

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Knowledge gradient is a design principle for developing Bayesian sequential sampling policies to solve optimization problems. In this paper, we consider the ranking and selection problem in the presence of covariates, where the best alternative is not universal but depends on the covariates. In this context, we prove that under minimal assumptions, the sampling policy based on knowledge gradient is consistent, in the sense that following the policy the best alternative as a function of the covariates will be identified almost surely as the number of samples grows. We also propose a stochastic gradient ascent algorithm for computing the sampling policy and demonstrate its performance via numerical experiments.

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Continuous multi-task Bayesian Optimisation with correlation

Cited by 34 publications

References 20 publications

Contextual Ranking and Selection with Gaussian Processes

Contextual Ranking and Selection with Gaussian Processes

Quality diversity for multi-task optimization

Technical note—Knowledge gradient for selection with covariates: Consistency and computation

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