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Ranking and Selection with Simultaneous Input Data Collection

Yuhao Wang, Enlu Zhou

TL;DR

This work addresses ranking and selection under streaming input data by formulating two convex rate-optimization problems to allocate budgets for input data collection and simulations, respectively, while handling non-i.i.d. simulation outputs. A multi-stage simultaneous budget allocation (SBA) procedure is developed, with rigorous guarantees of consistency and asymptotic optimality, and estimators for input parameters, performance metrics, and gradients are integrated into a sequential, Balancing-based allocation rule. The framework accommodates multiple input data streams with differing budgets and applies to general input distributions beyond finite supports, demonstrating superior performance in both synthetic quadratic problems and multi-channel inventory control. The approach enables dynamic, data-driven, and resource-efficient decision-making in stochastic systems where inputs arrive in a streaming fashion, with practical implications for industries leveraging simulation-optimization under uncertainty.

Abstract

In this paper, we propose a general and novel formulation of ranking and selection with the existence of streaming input data. The collection of multiple streams of such data may consume different types of resources, and hence can be conducted simultaneously. To utilize the streaming input data, we aggregate simulation outputs generated under heterogeneous input distributions over time to form a performance estimator. By characterizing the asymptotic behavior of the performance estimators, we formulate two optimization problems to optimally allocate budgets for collecting input data and running simulations. We then develop a multi-stage simultaneous budget allocation procedure and provide its statistical guarantees such as consistency and asymptotic normality. We conduct several numerical studies to demonstrate the competitive performance of the proposed procedure.

Ranking and Selection with Simultaneous Input Data Collection

TL;DR

This work addresses ranking and selection under streaming input data by formulating two convex rate-optimization problems to allocate budgets for input data collection and simulations, respectively, while handling non-i.i.d. simulation outputs. A multi-stage simultaneous budget allocation (SBA) procedure is developed, with rigorous guarantees of consistency and asymptotic optimality, and estimators for input parameters, performance metrics, and gradients are integrated into a sequential, Balancing-based allocation rule. The framework accommodates multiple input data streams with differing budgets and applies to general input distributions beyond finite supports, demonstrating superior performance in both synthetic quadratic problems and multi-channel inventory control. The approach enables dynamic, data-driven, and resource-efficient decision-making in stochastic systems where inputs arrive in a streaming fashion, with practical implications for industries leveraging simulation-optimization under uncertainty.

Abstract

In this paper, we propose a general and novel formulation of ranking and selection with the existence of streaming input data. The collection of multiple streams of such data may consume different types of resources, and hence can be conducted simultaneously. To utilize the streaming input data, we aggregate simulation outputs generated under heterogeneous input distributions over time to form a performance estimator. By characterizing the asymptotic behavior of the performance estimators, we formulate two optimization problems to optimally allocate budgets for collecting input data and running simulations. We then develop a multi-stage simultaneous budget allocation procedure and provide its statistical guarantees such as consistency and asymptotic normality. We conduct several numerical studies to demonstrate the competitive performance of the proposed procedure.

Paper Structure

This paper contains 26 sections, 19 theorems, 111 equations, 4 figures, 1 algorithm.

Table of Contents

  1. Introduction
  2. Problem Statement
  3. Basic Setting
  4. A Multi-Stage Framework for Simultaneous Resource Allocation with Different Types of Input Data
  5. Rate Optimization
  6. Input Budget Allocation
  7. Simulation Budget Allocation
  8. Remark on Input Budget Allocation and Simulation Budget Allocation
  9. Multi-Stage Simultaneous Budget Allocation Procedure
  10. Parameter Estimation
  11. Sequential Allocation of Simulation Budget
  12. Consistency and Asymptotic Optimality
  13. Consistency
  14. Asymptotic Optimality
  15. Numerical Study
  16. ...and 11 more sections

Key Result

Lemma 1

Under Assumption assump: CLT active and supposing $\{n_{s,t}\}_{s\in\mathcal{S},t\ge1}$ are uniformly bounded and for each $s\in \mathcal{S}$, there exists $\Bar{n}_s >0$ such that $\lim_{t\rightarrow \infty} \frac{N_{s,t}}{t} = \Bar{n}_s$. Then, where

Figures (4)

  • Figure 1: Quadratic example with two types of input data
  • Figure 2: Quadratic example with given data
  • Figure 3: Inventory example with $2$ demand channels.
  • Figure 4: Inventory example with $4$ demand channels.

Theorems & Definitions (19)

  • Lemma 1
  • Lemma 2
  • Theorem 1
  • Theorem 2
  • Lemma 3
  • Theorem 3
  • Theorem 4
  • Lemma 4
  • Lemma 5
  • Lemma 6
  • ...and 9 more