Large deviations perspective on ordinal optimization of heavy-tailed systems

Blanchet, José; Liu, Jingchen; Zwart, Bert

doi:10.1109/wsc.2008.4736104

Cited by 5 publications

(2 citation statements)

References 12 publications

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“…, p d ) under the constraint d i=1 p i = 1 to determine the optimal allocations as n → ∞ even for non-Gausssian distributions. Significant liter-ature since then has appeared that relies on large deviations analysis (e.g., Hunter and Pasupathy 2013, Szechtman and Yucesan 2008, Broadie, Han, Zeevi 2007, Blanchet, Liu, Zwart 2008, Shin, Broadie and Zeevi 2016.…”

Section: Introductionmentioning

confidence: 99%

Selecting the best system and multi-armed bandits

Juneja¹

2015

Preprint

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Consider the problem of finding a population or a probability distribution amongst many with the largest mean when these means are unknown but population samples can be simulated or otherwise generated. Typically, by selecting largest sample mean population, it can be shown that false selection probability decays at an exponential rate. Lately, researchers have sought algorithms that guarantee that this probability is restricted to a small δ in order log(1/δ) computational time by estimating the associated large deviations rate function via simulation. We show that such guarantees are misleading when populations have unbounded support even when these may be light-tailed. Specifically, we show that any policy that identifies the correct population with probability at least 1 − δ for each problem instance requires infinite number of samples in expectation in making such a determination in any problem instance. This suggests that some restrictions are essential on populations to devise O(log(1/δ)) algorithms with 1 − δ correctness guarantees. We note that under restriction on population moments, such methods are easily designed, and that sequential methods from stochastic multi-armed bandit literature can be adapted to devise such algorithms.

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Section: Introductionmentioning

confidence: 99%

Selecting the best system and multi-armed bandits

Juneja¹

2015

Preprint

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“…Therefore, we compare the performance of the SCORE allocation with equal allocation. (In the unconstrained case, optimal allocation in the case of heavy-tailed distributions was explored in Broadie et al [2007] and Blanchet et al [2008].) As in Section 7.3, we retain all parameters of Algorithm 1 used in previous numerical examples.…”

Section: Robustness To Violation Of Assumptions 5 Andmentioning

confidence: 99%

Stochastically Constrained Ranking and Selection via SCORE

Pasupathy

Hunter

Pujowidianto

et al. 2014

ACM Trans. Model. Comput. Simul.

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Consider the context of constrained Simulation Optimization (SO); that is, optimization problems where the objective and constraint functions are known through dependent Monte Carlo estimators. For solving such problems on large finite spaces, we provide an easily implemented sampling framework called SCORE (Sampling Criteria for Optimization using Rate Estimators) that approximates the optimal simulation budget allocation. We develop a general theory, but, like much of the existing literature on ranking and selection, our focus is on SO problems where the distribution of the simulation observations is Gaussian. We first characterize the nature of the optimal simulation budget as a bi-level optimization problem. We then show that under a certain asymptotic limit, the solution to the bi-level optimization problem becomes surprisingly tractable and is expressed through a single intuitive measure, the score. We provide an iterative SO algorithm that repeatedly estimates the score and determines how the available simulation budget should be expended across contending systems. Numerical experience with the algorithm resulting from the proposed sampling approximation is very encouraging-in numerous examples of constrained SO problems having 1,000 to 10,000 systems, the optimal allocation is identified to negligible error within a few seconds to 1 minute on a typical laptop computer. Corresponding times to solve the full bi-level optimization problem range from tens of minutes to several hours.

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