50 research outputs found
Asymptotic Optimality of Myopic Ranking and Selection Procedures
Ranking and selection (R&S) is a popular model for studying discrete-event
dynamic systems. It aims to select the best design (the design with the largest
mean performance) from a finite set, where the mean of each design is unknown
and has to be learned by samples. Great research efforts have been devoted to
this problem in the literature for developing procedures with superior
empirical performance and showing their optimality. In these efforts, myopic
procedures were popular. They select the best design using a 'naive' mechanism
of iteratively and myopically improving an approximation of the objective
measure. Although they are based on simple heuristics and lack theoretical
support, they turned out highly effective, and often achieved competitive
empirical performance compared to procedures that were proposed later and shown
to be asymptotically optimal. In this paper, we theoretically analyze these
myopic procedures and prove that they also satisfy the optimality conditions of
R&S, just like some other popular R&S methods. It explains the good performance
of myopic procedures in various numerical tests, and provides good insight into
the structure and theoretical development of efficient R&S procedures
Selecting the best stochastic systems for large scale engineering problems
Selecting a subset of the best solutions among large-scale problems is an important area of research. When the alternative solutions are stochastic in nature, then it puts more burden on the problem. The objective of this paper is to select a set that is likely to contain the actual best solutions with high probability. If the selected set contains all the best solutions, then the selection is denoted as correct selection. We are interested in maximizing the probability of this selection; P(CS). In many cases, the available computation budget for simulating the solution set in order to maximize P(CS) is limited. Therefore, instead of distributing these computational efforts equally likely among the alternatives, the optimal computing budget allocation (OCBA) procedure came to put more effort on the solutions that have more impact on the selected set. In this paper, we derive formulas of how to distribute the available budget asymptotically to find the approximation of P(CS). We then present a procedure that uses OCBA with the ordinal optimization (OO) in order to select the set of best solutions. The properties and performance of the proposed procedure are illustrated through a numerical example. Overall results indicate that the procedure is able to select a subset of the best systems with high probability of correct selection using small number of simulation samples under different parameter settings
Convergence Rate Analysis for Optimal Computing Budget Allocation Algorithms
Ordinal optimization (OO) is a widely-studied technique for optimizing
discrete-event dynamic systems (DEDS). It evaluates the performance of the
system designs in a finite set by sampling and aims to correctly make ordinal
comparison of the designs. A well-known method in OO is the optimal computing
budget allocation (OCBA). It builds the optimality conditions for the number of
samples allocated to each design, and the sample allocation that satisfies the
optimality conditions is shown to asymptotically maximize the probability of
correct selection for the best design. In this paper, we investigate two
popular OCBA algorithms. With known variances for samples of each design, we
characterize their convergence rates with respect to different performance
measures. We first demonstrate that the two OCBA algorithms achieve the optimal
convergence rate under measures of probability of correct selection and
expected opportunity cost. It fills the void of convergence analysis for OCBA
algorithms. Next, we extend our analysis to the measure of cumulative regret, a
main measure studied in the field of machine learning. We show that with minor
modification, the two OCBA algorithms can reach the optimal convergence rate
under cumulative regret. It indicates the potential of broader use of
algorithms designed based on the OCBA optimality conditions
Finite Simulation Budget Allocation for Ranking and Selection
We consider a simulation-based ranking and selection (R&S) problem under a
fixed budget setting. Existing budget allocation procedures focus either on
asymptotic optimality or on one-step-ahead allocation efficiency. Neither of
them depends on the fixed simulation budget, the ignorance of which could lead
to an inefficient allocation, especially when the simulation budget is finite.
In light of this, we develop a finite-budget allocation rule that is adaptive
to the simulation budget. Theoretical results show that the budget allocation
strategies are distinctively different between a finite budget and a
sufficiently large budget. Our proposed allocation rule can dynamically
determine the ratio of budget allocated to designs according to different
simulation budget and is optimal when the simulation budget goes to infinity,
indicating it not only possesses desirable finite-budget properties but also
achieves asymptotic optimality. Based on the proposed allocation rule, two
efficient finite simulation budget allocation algorithms are developed. In the
numerical experiments, we use both synthetic examples and a case study to show
the superior efficiency of our proposed allocation rule