Robust Sensitivity Analysis for Stochastic Systems

Lam, Henry

doi:10.1287/moor.2015.0776

Cited by 130 publications

(132 citation statements)

References 58 publications

Supporting

Mentioning

126

Contrasting

Order By: Relevance

“…In recent years there has been increasing interest in robust analysis of queueing systems. We consider uncertainty in the diffusion scale of the QCP in a way that is often referred to as model uncertainty or Knightian uncertainty, see e.g., [35,26,25,9] and in the context of queueing systems see [28,13,34], see also [38] in a discrete time setup. This is not to be confused with the terminology robust queueing theory, which is often referred to an optimization based performance analysis, see e.g., [7,44].…”

Section: Introductionmentioning

confidence: 99%

Asymptotic Analysis of a Multiclass Queueing Control Problem Under Heavy Traffic with Model Uncertainty

Cohen

2019

Stochastic Systems

View full text Add to dashboard Cite

We study a multiclass M/M/1 queueing control problem with finite buffers under heavytraffic where the decision maker is uncertain about the rates of arrivals and service of the system and by scheduling and admission/rejection decisions acts to minimize a discounted cost that accounts for the uncertainty. The main result is the asymptotic optimality of a cµ-type of policy derived via underlying stochastic differential games studied in [20]. Under this policy, with high probability, rejections are not performed when the workload lies below some cut-off that depends on the ambiguity level. When the workload exceeds this cut-off, rejections are carried out and only from the buffer with the cheapest rejection cost weighted with the mean service rate. The allocation part of the policy is the same for all the ambiguity levels. This is the first work to address a heavy-traffic queueing control problem with model uncertainty.AMS subject classifications. 60K25, 60J60, 93E20, 60F05, 68M20, 91A15.

show abstract

Section: Introductionmentioning

confidence: 99%

Asymptotic Analysis of a Multiclass Queueing Control Problem Under Heavy Traffic with Model Uncertainty

Cohen

2019

Stochastic Systems

View full text Add to dashboard Cite

show abstract

“…For example, Hu and Hong [19] suggests removing ambiguity by the Lagrangian dual when the divergence measure associated with the ambiguity set is the Kullback-Leibler (KL) divergence. On the other hand, one can remove ambiguity by considering series expansion similar to Henry Lam's approach [23] for the KL divergence and the approach used by Gotoh et al [17] for more general divergence measure on objective function with a penalty term.…”

Section: Introductionmentioning

confidence: 99%

Understanding Distributional Ambiguity via Non-robust Chance Constraint

Leung

et al. 2019

SSRN Journal

View full text Add to dashboard Cite

The choice of the ambiguity radius is critical when an investor uses the distributionally robust approach to address the issue that the portfolio optimization problem is sensitive to the uncertainties of the asset return distribution. It cannot be set too large because the larger the size of the ambiguity set the worse the portfolio return. It cannot be too small either; otherwise, one loses the robust protection. This tradeoff demands a financial understanding of the ambiguity set. In this paper, we propose a non-robust interpretation of the distributionally robust optimization (DRO) problem. By relating the impact of an ambiguity set to the impact of a non-robust chance constraint, our interpretation allows investors to understand the size of the ambiguity set through parameters that are directly linked to investment performance. We first show that for general φ-divergences, a DRO problem is asymptotically equivalent to a class of mean-deviation problem, where the ambiguity radius controls investor's risk preference. Based on this non-robust reformulation, we then show that when a boundedness constraint is added to the investment strategy, the DRO problem can be cast as a chance-constrained optimization (CCO) problem without distributional uncertainties. If the boundedness constraint is removed, the CCO problem is shown to perform uniformly better than the DRO problem, irrespective of the radius of the ambiguity set, the choice of the divergence measure, or the tail heaviness of the center distribution. Our results apply to both the widely-used Kullback-Leibler (KL) divergence which requires the distribution of the objective function to be exponentially bounded, as well as those more general divergence measures which allow heavy tail ones such as student t and lognormal distributions. * The corresponding author.Preprint. Under review.

show abstract

“…Qian (2016, 2017) study the use of empirical likelihood, and Xie et al (2018) studies nonparametric Bayesian methods to construct CIs. Glasserman and Xu (2014), Hu et al (2012), Lam (2016b) and Ghosh and Lam (2015) study input uncertainty from a robust optimization viewpoint. In the parametric regime, Barton et al (2013) and Xie et al (2016) investigate the basic bootstrap with a metamodel built in advance, a technique known as the metamodel-assisted bootstrap.…”

Section: Introductionmentioning

confidence: 99%

Subsampling Variance for Input Uncertainty Quantification

Lam¹,

Qian²

2018

2018 Winter Simulation Conference (WSC)

Self Cite

View full text Add to dashboard Cite

In stochastic simulation, input uncertainty refers to the output variability arising from the statistical noise in specifying the input models. This uncertainty can be measured by a variance contribution in the output, which, in the nonparametric setting, is commonly estimated via the bootstrap. However, due to the convolution of the simulation noise and the input noise, the bootstrap consists of a two-layer sampling and typically requires substantial simulation effort. This paper investigates a subsampling framework to reduce the required effort, by leveraging the form of the variance and its estimation error in terms of the data size and the sampling requirement in each layer. We show how the total required effort can be reduced from an order bigger than the data size in the conventional approach to an order independent of the data size in subsampling. We explicitly identify the procedural specifications in our framework that guarantees relative consistency in the estimation, and the corresponding optimal simulation budget allocations. We substantiate our theoretical results with numerical examples.

show abstract

Robust Sensitivity Analysis for Stochastic Systems

Cited by 130 publications

References 58 publications

Asymptotic Analysis of a Multiclass Queueing Control Problem Under Heavy Traffic with Model Uncertainty

Asymptotic Analysis of a Multiclass Queueing Control Problem Under Heavy Traffic with Model Uncertainty

Understanding Distributional Ambiguity via Non-robust Chance Constraint

Subsampling Variance for Input Uncertainty Quantification

Contact Info

Product

Resources

About