Selecting the Optimal System Design under Covariates

Gao, Siyang; Du, Jianzhong; Chen, Chun‐Hung

doi:10.1109/coase.2019.8842957

Cited by 26 publications

(35 citation statements)

References 15 publications

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“…More importantly, they provided a theoretical analysis of the asymptotic behavior of the KG based policy and proved that the best alternative as a function of the covariates will be identified almost surely as the number of samples grows. Gao et al (2019b) considered the case where the covariates only take discrete values and designed an OCBA-based sampling policy that converges to the asymptotic optimal budget allocation rule.…”

Section: Rands With Covariatesmentioning

confidence: 99%

Review on ranking and selection: A new perspective

2021

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In this paper, we briefly review the development of ranking and selection (R&S) in the past 70 years, especially the theoretical achievements and practical applications in the past 20 years. Different from the frequentist and Bayesian classifications adopted by Kim and Nelson (2006b) and Chick (2006) in their review articles, we categorize existing R&S procedures into fixed-precision and fixed-budget procedures, as in Hunter and Nelson (2017). We show that these two categories of procedures essentially differ in the underlying methodological formulations, i.e., they are built on hypothesis testing and dynamic programming, respectively. In light of this variation, we review in detail some well-known procedures in the literature and show how they fit into these two formulations. In addition, we discuss the use of R&S procedures in solving various practical problems and propose what we think are the important research questions in the field.

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Section: Rands With Covariatesmentioning

confidence: 99%

Review on ranking and selection: A new perspective

2021

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“…In this work, we consider two approaches to aggregate 𝑃𝐶𝑆 (𝑐)'s to a scalar objective. The first one is the expected 𝑃𝐶𝑆 [11,23], denoted as 𝑃𝐶𝑆 𝐸 , which is the expectation or the weighted average of 𝑃𝐶𝑆 (𝑐) given a set of normalized weights, and the second one is the worst-case 𝑃𝐶𝑆 [17], denoted as 𝑃𝐶𝑆 𝑀 , which is the minimum 𝑃𝐶𝑆 (𝑐) obtained across all contexts.…”

Section: Introductionmentioning

confidence: 99%

“…The contextual R&S problem has seen an increasing interest in past few years. Notable works that study this problem under finite alternative-context setting include but not limited to [11,15,17,23]. [17] focuses on worst-case 𝑃𝐶𝑆, uses independent normal random variables to model rewards, and proposes a one-step look-ahead policy with an efficient value function approximation scheme to maximize 𝑃𝐶𝑆 𝑀 .…”

Section: Introductionmentioning

confidence: 99%

“…[23] assumes that the reward for each alternative is a linear function of the context and proposes a two-stage algorithm based on the indifference zone formulation for optimizing the expected 𝑃𝐶𝑆. The most closely related work to ours is [11]. They model the rewards using independent normal random variables, extend the analysis in [12] to derive the large deviations rate function for the contextual 𝑃𝐶𝑆, and propose an algorithm that obtains the asymptotically optimal allocation ratio for both the worst-case and expected 𝑃𝐶𝑆.…”

Section: Introductionmentioning

confidence: 99%

“…In contrast, we use a Gaussian process, model correlations between contexts, and extend the large deviations approach to leverage the efficient inference brought in by our statistical model. [15] also follows a large deviations approach similar to that of [11]; however, their algorithm does not perform well when only the observed data is used to make decisions.…”

Section: Introductionmentioning

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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A Simulation Optimization Approach forPrecision Medicine

Gao

Chen

2022

Springer Proceedings in Business and Economics

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Selecting the Optimal System Design under Covariates

Cited by 26 publications

References 15 publications

Review on ranking and selection: A new perspective

Review on ranking and selection: A new perspective

Contextual Ranking and Selection with Gaussian Processes

A Simulation Optimization Approach forPrecision Medicine

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