New Additive OCBA Procedures for Robust Ranking and Selection (2412.06020v2)

Abstract: Robust ranking and selection (R&S) is an important and challenging variation of conventional R&S that seeks to select the best alternative among a finite set of alternatives. It captures the common input uncertainty in the simulation model by using an ambiguity set to include multiple possible input distributions and shifts to select the best alternative with the smallest worst-case mean performance over the ambiguity set. In this paper, we aim at developing new fixed-budget robust R&S procedures to minimize the probability of incorrect selection (PICS) under a limited sampling budget. Inspired by an additive upper bound of the PICS, we derive a new asymptotically optimal solution to the budget allocation problem. Accordingly, we design a new sequential optimal computing budget allocation (OCBA) procedure to solve robust R&S problems efficiently. We then conduct a comprehensive numerical study to verify the superiority of our robust OCBA procedure over existing ones. The numerical study also provides insights on the budget allocation behaviors that lead to enhanced efficiency.

• The paper introduces AR-OCBA, a new additive procedure that significantly reduces the probability of incorrect selection under input uncertainty.
• It transforms robust ranking and selection from km scenarios to a simpler k+m-1 scenario framework, optimizing resource allocation under fixed budgets.
• Extensive numerical studies validate AR-OCBA's superior performance, scalability, and statistical consistency compared to traditional OCBA methods.

Analysis of Additive OCBA Procedures in Robust Ranking and Selection

The paper "New Additive OCBA Procedures for Robust Ranking and Selection," presents a novel approach to addressing the challenge of robust ranking and selection (R&S) under uncertainty in input distributions. The authors focus on designing efficient procedures within a fixed budget to minimize the probability of incorrect selection (PICS), drawing insight from a refined additive approximation of PICS.

Overview

Robust R&S is a critical variant of classical R&S methods that incorporates input uncertainty within simulation models. This is achieved by using an ambiguity set of possible input distributions to account for variations in input data, which adds complexity through its two-layered minimax structure. The robust approach allows the selection of the best alternative by considering the worst-case performance, ensuring selections are resilient to uncertainty.

The difficulties presented by the input ambiguity and fixed-budget constraints necessitate novel procedures. This paper builds upon foundational work by providing a refined additive upper bound for PICS in robust R&S, adapting traditional OCBA (Optimal Computing Budget Allocation) frameworks from fixed-precision to fixed-budget approaches.

Methodology and Numerical Evaluation

The core methodological advancement is the adaptation of an additive upper bound for PICS derived originally by Fan et al. (2020) in a fixed-budget context. The authors formulate and solve the budget allocation problem by substantially transforming robust R&S problems with $km$ scenarios into traditional R&S problems with $k+m-1$ alternative scenarios. This transformation simplifies the complexity of the resource allocation task by focusing only on critical scenarios—those consisting of the best alternative's scenarios and the worst-case scenario for each non-best alternative.

The new procedure, termed AR-OCBA, employs a proportional allocation rule at each stage, diverging from traditional methods like the most-starving allocation rule. This choice is substantiated through comprehensive numerical studies demonstrating that AR-OCBA delivers superior performance compared to previous methods, especially as problem scales grow.

The numerical evaluation across various problem configurations validates the robustness and scalability of the AR-OCBA procedure. The results endorse that AR-OCBA efficiently approaches optimal performance, even under varying simulation budgets and scenario scales (varying $k$ and $m$). Interestingly, experiments highlight AR-OCBA's compelling display of statistical consistency, a desirable property in R&S methodologies.

Implications and Future Research

The advancements of AR-OCBA have both theoretical and practical implications. From a theoretical perspective, the simplification from $km$ to $k+m-1$ scenarios indicates a potential new classification or understanding of scenario interactions in robust R&S problems. Practically, being able to employ OCBA frameworks for robust R&S under budget constraints paves the way for resource-efficient decision-making tools in complex industrial applications, such as operations management and AI usage in uncertain environments.

Potential avenues for future research include formalizing the theoretical consistency of AR-OCBA and exploring its application beyond finite ambiguity sets to more intricate scenarios where ambiguity sets could comprise infinite distributions. Further understanding of the additive nature's implications in robust R&S might yield procedural insights, thereby enhancing policy development in this domain.

In summary, this paper contributes to a more nuanced understanding of robust R&S, blending theoretical refinement with practical implementation strategies, thereby offering advantages in settings where input uncertainty and budget limitations are predominant considerations.