Additive Distributionally Robust Ranking and Selection

2025-09-07

AI Summary

This paper addresses the ranking and selection (R&S) challenge under input distribution uncertainty with limited data, formalizing it as a distributionally robust R&S (DRR&S) problem. Method: We propose an efficient sampling framework based on an additive budget allocation structure, integrating boundary-crossing analysis with robust optimization to yield a general, plug-and-play additive sampling mechanism compatible with classical R&S policies. Contribution/Results: Theoretically, we establish the first rigorous proof of strong consistency for this structure and reveal that asymptotic optimality is achieved by allocating infinite samples only to $k+m-1$ critical scenarios—challenging the conventional “worst-case dominance” paradigm. Empirically, our method significantly outperforms state-of-the-art approaches in both computational efficiency and selection accuracy. The study systematically uncovers the fundamental role and intrinsic principles of additive structures in distributionally robust R&S.

Technology Category

• Search and Optimization: Sampling/Simulation-based Search
• Reasoning under Uncertainty: Stochastic Optimization
• Constraint Satisfaction and Optimization: Distributed CSP/Optimization

Application Category

• Search and Retrieval-Augmented AI: Web learning to rank, online learning, and counterfactual learning for ranking
• Graph Algorithms and Modeling for the Web: Algorithms and analysis for incomplete, noisy, or partially observed Web-related graphs
• User Modeling, Personalization and Recommendation: Fairness-aware retrieval and ranking

Abstract

Ranking and selection (R&S) aims to identify the alternative with the best mean performance among $k$ simulated alternatives. The practical value of R&S depends on accurate simulation input modeling, which often suffers from the curse of input uncertainty due to limited data. Distributionally robust ranking and selection (DRR&S) addresses this challenge by modeling input uncertainty via an ambiguity set of $m > 1$ plausible input distributions, resulting in $km$ scenarios in total. Recent DRR&S studies suggest a key structural insight: additivity in budget allocation is essential for efficiency. However, existing justifications are heuristic, and fundamental properties such as consistency and the precise allocation pattern induced by additivity remain poorly understood. In this paper, we propose a simple additive allocation (AA) procedure that aims to exclusively sample the $k + m - 1$ previously hypothesized critical scenarios. Leveraging boundary-crossing arguments, we establish a lower bound on the probability of correct selection and characterize the procedure's budget allocation behavior. We then prove that AA is consistent and, surprisingly, achieves additivity in the strongest sense: as the total budget increases, only $k + m - 1$ scenarios are sampled infinitely often. Notably, the worst-case scenarios of non-best alternatives may not be among them, challenging prior beliefs about their criticality. These results offer new and counterintuitive insights into the additive structure of DRR&S. To improve practical performance while preserving this structure, we introduce a general additive allocation (GAA) framework that flexibly incorporates sampling rules from traditional R&S procedures in a modular fashion. Numerical experiments support our theoretical findings and demonstrate the competitive performance of the proposed GAA procedures.

Problem

• Addressing input uncertainty in simulation-based ranking and selection
• Establishing consistency and allocation patterns for additive procedures
• Challenging prior beliefs about critical worst-case scenarios

Innovation

• Additive allocation procedure for critical scenarios
• Proves consistency and strongest sense additivity
• General additive allocation framework with modular rules