In derivative pricing and hedging, the consistency between the price and Greek surfaces (i.e., the Greek surfaces can be obtained by differentiating the price surface) is important in stabilizing the balance sheet and reducing the hedging cost. To build consistent surfaces of the price and Greeks for real-time decisions, we propose to use the gradient-enhanced stochastic kriging method, based on the data collected through extensive simulation experiments conducted when the market is closed. In addition to the naturally guaranteed consistency, we prove that the constructed price and Greek surfaces are more accurate than those constructed separately using stochastic kriging. Besides the consistency between the price and Greeks, we show that the partial differential equation relation between the price and Greeks, implied by the famous Feynman-Kac formula, can also be used to further improve the accuracy of the constructed surfaces. The numerical studies show that our proposed metamodeling methods work well for derivative pricing and hedging. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the National Natural Science Foundation of China [Grants 72161160340, 72293562, 72121001, 72031006, and 72171060]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2023.0292 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2023.0292 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Many large-scale production networks include thousands of types of final products and tens to hundreds of thousands of types of raw materials and intermediate products. These networks face complicated inventory management decisions, which are often too complicated for inventory models and too large for simulation models. In this paper, by combining efficient computational tools of recurrent neural networks (RNNs) and the structural information of production networks, we propose an RNN-inspired simulation approach that may be thousands of times faster than the existing simulation approach and is capable of solving large-scale inventory optimization problems in a reasonable amount of time. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: This work was supported by the National Natural Science Foundation of China [Grant 72091211].

We consider a contextual online learning (multi-armed bandit) problem with high-dimensional covariate $x$ and decision $y$. The reward function to learn, $f(x,y)$, does not have a particular parametric form. The literature has shown that the optimal regret is $\tilde{O}(T^{(d_x\!+\!d_y\!+\!1)/(d_x\!+\!d_y\!+\!2)})$, where $d_x$ and $d_y$ are the dimensions of $x$ and $y$, and thus it suffers from the curse of dimensionality. In many applications, only a small subset of variables in the covariate affect the value of $f$, which is referred to as sparsity in statistics. To take advantage of the sparsity structure of the covariate, we propose a variable selection algorithm called BV-LASSO, which incorporates novel ideas such as binning and voting to apply LASSO to nonparametric settings. Using it as a subroutine, we can achieve the regret $\tilde{O}(T^{(d_x^*\!+\!d_y\!+\!1)/(d_x^*\!+\!d_y\!+\!2)})$, where $d_x^*$ is the effective covariate dimension. The regret matches the optimal regret when the covariate is $d^*_x$-dimensional and thus cannot be improved. Our algorithm may serve as a general recipe to achieve dimension reduction via variable selection in nonparametric settings.

In recent years, with the rapid development of computing technology, developing parallel procedures to solve large-scale ranking and selection (R&S) problems has attracted a lot of research attention. In this paper, we take fixed-budget R&S procedure as an example to investigate potential issues of developing parallel procedures. We argue that to measure the performance of a fixed-budget R&S procedure in solving large-scale problems, it is important to quantify the minimal growth rate of the total sampling budget such that as the number of alternatives increases, the probability of correct selection (PCS) would not decrease to zero. We call such a growth rate of the total sampling budget the rate for maintaining correct selection (RMCS). We show that a tight lower bound for the RMCS of a broad class of existing fixed-budget procedures is in the order of [Formula: see text], where k is the number of alternatives. Then, we propose a new type of fixed-budget procedure, namely the fixed-budget knockout-tournament ([Formula: see text]) procedure. We prove that, in terms of the RMCS, our procedure outperforms existing fixed-budget procedures and achieves the optimal order, that is, the order of k. Moreover, we demonstrate that our procedure can be easily implemented in parallel computing environments with almost no nonparallelizable calculations. Last, a comprehensive numerical study shows that our procedure is indeed suitable for solving large-scale problems in parallel computing environments. History: Accepted by Bruno Tuffin, Area Editor for Simulation. Funding: Y. Zhong was supported by the National Natural Science Foundation of China [Grant 72101047]. L. J. Hong was supported by the National Natural Science Foundation of China [Grants 72091211 and 72161160340]. G. Jiang was supported by the National Natural Science Foundation of China [Grants 72121001 and 72171060]. Supplemental Material: The online appendix is available at https://doi.org/10.1287/ijoc.2022.1221 .

To use simulation models to study the behaviors of stochastic systems, one needs to specify the distribution of the input random variables. However, specifying this distribution precisely is typically difficult and even impossible in practice. The issue is known as input uncertainty in the simulation literature, and it has been considered and studied extensively in recent years. In this paper, we model the uncertainty by an ambiguity set that is defined based on the likelihood ratio between the true (unknown) distribution and the nominal distribution (i.e., the best estimate), and develop a robust simulation (RS) approach that estimates the worst-case values of performance measures of the random simulation output when the true distribution varies in the ambiguity set. We show that the RS approach is computationally tractable, and the corresponding results reveal important information of the stochastic systems and help decision makers make better decisions.

We investigate a new approach to compute the gradients of artificial neural networks (ANNs), based on the so-called push-out likelihood ratio method. Unlike the widely used backpropagation (BP) method that requires continuity of the loss function and the activation function, our approach bypasses this requirement by injecting artificial noises into the signals passed along the neurons. We show how this approach has a similar computational complexity as BP, and moreover is more advantageous in terms of removing the backward recursion and eliciting transparent formulas. We also formalize the connection between BP, a pivotal technique for training ANNs, and infinitesimal perturbation analysis, a classic path-wise derivative estimation approach, so that both our new proposed methods and BP can be better understood in the context of stochastic gradient estimation. Our approach allows efficient training for ANNs with more flexibility on the loss and activation functions, and shows empirical improvements on the robustness of ANNs under adversarial attacks and corruptions of natural noises. Summary of Contribution: Stochastic gradient estimation has been studied actively in simulation for decades and becomes more important in the era of machine learning and artificial intelligence. The stochastic gradient descent is a standard technique for training the artificial neural networks (ANNs), a pivotal problem in deep learning. The most popular stochastic gradient estimation technique is the backpropagation method. We find that the backpropagation method lies in the family of infinitesimal perturbation analysis, a path-wise gradient estimation technique in simulation. Moreover, we develop a new likelihood ratio-based method, another popular family of gradient estimation technique in simulation, for training more general ANNs, and demonstrate that the new training method can improve the robustness of the ANN.

With the rapid development of computing technology, using parallel computing to solve large-scale ranking-and-selection (R&S) problems has emerged as an important research topic. However, direct implementation of traditionally fully sequential procedures in parallel computing environments may encounter various problems. First, the scheme of all-pairwise comparisons, which is commonly used in fully sequential procedures, requires a large amount of computation and significantly slows down the selection process. Second, traditional fully sequential procedures require frequent communication and coordination among processors, which are also not efficient in parallel computing environments. In this paper, we propose three modifications on one classical fully sequential procedure, Paulson’s procedure, to speed up its selection process in parallel computing environments. First, we show that if no common random numbers are used, then we can significantly reduce the computation spent on all-pairwise comparisons at each round. Second, by batching different alternatives, we show that we can reduce the communication cost among the processors, leading the procedure to achieve better performance. Third, to boost the procedure’s final-stage selection, when the number of surviving alternatives is less than the number of processors, we suggest to sample all surviving alternatives to the maximal number of observations that they should take. We show that, after these modifications, the procedure remains statistically valid and is more efficient compared with existing parallel procedures in the literature. Summary of Contribution: Ranking and selection (R&S) is a branch of simulation optimization, which is an important area of operations research. In recent years, using parallel computing to solve large-scale R&S problems has emerged as an important research topic, and this research topic is naturally situated in the intersection of computing and operations research. In this paper, we consider how to improve a fully sequential R&S procedure, namely, Paulson’s procedure, to reduce the high computational complexity of all-pairwise comparisons and the burden of frequent communications and coordination, so that the procedure is more suitable and more efficient in solving large-scale R&S problems using parallel computing environments that are becoming ubiquitous and accessible for ordinary users. The procedure designed in this paper appears more efficient than the ones available in the literature and is capable of solving R&S problems with over a million alternatives in a parallel computing environment with 96 processors. The paper also extended the theory of R&S by showing that the all-pairwise comparisons may be decomposed so that the computational complexity may be reduced significantly, which drastically improves the efficiency of all-pairwise comparisons as observed in numerical experiments.

Sampling-based motion planning (SBMP) is a major algorithmic trajectory planning approach in autonomous driving given its high efficiency and outstanding performance in practice. However, driving safety still calls for further refinement of SBMP. In this article we organically integrate algorithmic motion planning with learning models to improve SBMP in highway traffic scenarios from the following two perspectives. First, given the number of points to be sampled, we develop a new model to sample “important” points for SBMP by predicting the intention of surrounding vehicles and learning the distribution of human drivers’ trajectory. Second, we empirically study the relationship between the number of sample points and the environment, which is largely ignored in conventional SBMP. Then, we provide a guideline to select the appropriate number of points to be sampled under different scenarios to guarantee efficiency. The simulation experiments are conducted based on the vehicle trajectory dataset NGSIM. The results show that the proposed sampling strategy outperforms existing sampling strategies in terms of the computing time, traveling time, and smoothness of the trajectory.

We consider a problem of ranking and selection via simulation in the context of personalized decision making, in which the best alternative is not universal, but varies as a function of some observable covariates. The goal of ranking and selection with covariates (R&S-C) is to use simulation samples to obtain a selection policy that specifies the best alternative with a certain statistical guarantee for subsequent individuals upon observing their covariates. A linear model is proposed to capture the relationship between the mean performance of an alternative and the covariates. Under the indifference-zone formulation, we develop two-stage procedures for both homoscedastic and heteroscedastic simulation errors, respectively, and prove their statistical validity in terms of average probability of correct selection. We also generalize the well-known slippage configuration and prove that the generalized slippage configuration is the least favorable configuration for our procedures. Extensive numerical experiments are conducted to investigate the performance of the proposed procedures, the experimental design issue, and the robustness to the linearity assumption. Finally, we demonstrate the usefulness of R&S-C via a case study of selecting the best treatment regimen in the prevention of esophageal cancer. We find that by leveraging disease-related personal information, R&S-C can substantially improve patients’ expected quality-adjusted life years by providing a patient-specific treatment regimen.

Sampling-based motion planning (SBMP) is a major trajectory planning approach in autonomous driving given its high efficiency in practice. As the core of SBMP schemes, sampling strategy holds the key to whether a smooth and collision-free trajectory can be found in real-time. Although some bias sampling strategies have been explored in the literature to accelerate SBMP, the trajectory generated under existing bias sampling strategies may lead to sharp lane changing. To address this issue, we propose a new learning framework for SBMP. Specifically, we develop a novel automatic labeling scheme and a 2-Stage prediction model to improve the accuracy in predicting the intention of surrounding vehicles. We then develop an imitation learning scheme to generate sample points based on the experience of human drivers. Using the prediction results, we design a new bias sampling strategy to accelerate the SBMP algorithm by strategically selecting necessary sample points that can generate a smooth and collision-free trajectory and avoid sharp lane changing. Data-driven experiments show that the proposed sampling strategy outperforms existing sampling strategies, in terms of the computing time, traveling time, and smoothness of the trajectory. The results also show that our scheme is even better than human drivers.

Estimating portfolio risk measures and classifying portfolio risk levels in real time are important yet challenging tasks. In this paper, we propose to build a logistic regression model using data generated in past simulation experiments and to use the model to predict portfolio risk measures and classify risk levels at any time. We further explore regularization techniques, simulation model structure, and additional simulation budget to enhance the estimators of the logistic regression model to make its predictions more precise. Our numerical results show that the proposed methods work well. Our work may be viewed as an example of the recently proposed idea of simulation analytics, which treats a simulation model as a data generator and proposes to apply data analytics tools to the simulation outputs to uncover conditional statements. Our work shows that the simulation analytics idea is viable and promising in the field of financial risk management.

Selecting the solution with the largest or smallest mean of a primary performance measure from a finite set of solutions while requiring secondary performance measures to satisfy certain constraints is called constrained selection of the best (CSB) in the simulation ranking and selection literature. In this paper, we consider CSB problems with secondary performance measures that must satisfy probabilistic constraints, and we call such problems chance constrained selection of the best (CCSB). We design procedures that first check the feasibility of all solutions and then select the best among all the sample feasible solutions. We prove the statistical validity of these procedures for variations of the CCSB problem under the indifference-zone formulation. Numerical results show that the proposed procedures can efficiently handle CCSB problems with up to 100 solutions, each with five chance constraints.

We study optimization problems with value-at-risk (VaR) constraints. Because it lacks subadditivity, VaR is not a coherent risk measure and does not necessarily preserve the convexity. Thus, the problems we consider are typically not provably convex. As such, the conditional value-at-risk (CVaR) approximation is often used to handle such problems. Even though the CVaR approximation is known as the best convex conservative approximation, it sometimes leads to solutions with poor performance. In this paper, we investigate the CVaR approximation from a different perspective and demonstrate what is lost in this approximation. We then show that the lost part of this approximation can be remedied using a sequential convex approximation approach, in which each iteration only requires solving a CVaR-like approximation via certain Monte Carlo techniques. We show that the solution found by this approach generally makes the VaR constraints binding and is guaranteed to be better than the solution found by the CVaR approximation and moreover is empirically often globally optimal for the target problem. The numerical experiments show the effectiveness of our approach.

Estimating the sensitivities of portfolio credit risk with respect to the underlying model parameters is an important problem for credit risk management. In this paper, we consider performance measures that may be expressed as an expectation of a performance function of the portfolio credit loss and derive closed-form expressions of its sensitivities to the underlying parameters. Our results are applicable to both idiosyncratic and macroeconomic parameters and to performance functions that may or may not be continuous. Based on the closed-form expressions, we first develop an estimator for sensitivities, in a general framework, that relies on the kernel method for estimation. The unified estimator allows us to further derive two general forms of the estimators by using conditioning techniques on either idiosyncratic or macroeconomic factors. We then specialize our results to develop faster estimators for three popular classes of models used for portfolio credit risk: latent variable models, Bernoulli mixture models, and doubly stochastic models.

Response surface methodology (RSM) is a widely used method for simulation optimization. Its strategy is to explore small subregions of the decision space in succession instead of attempting to explore the entire decision space in a single attempt. This method is especially suitable for complex stochastic systems where little knowledge is available. Although RSM is popular in practice, its current applications in simulation optimization treat simulation experiments the same as real experiments. However, the unique properties of simulation experiments make traditional RSM inappropriate in two important aspects: (1) It is not automated; human involvement is required at each step of the search process; (2) RSM is a heuristic procedure without convergence guarantee; the quality of the final solution cannot be quantified. We propose the stochastic trust-region response-surface method (STRONG) for simulation optimization in attempts to solve these problems. STRONG combines RSM with the classic trust-region method developed for deterministic optimization to eliminate the need for human intervention and to achieve the desired convergence properties. The numerical study shows that STRONG can outperform the existing methodologies, especially for problems that have grossly noisy response surfaces, and its computational advantage becomes more obvious when the dimension of the problem increases.

We propose an adaptive hyperbox algorithm (AHA), which is an instance of a locally convergent, random search algorithm for solving discrete optimization via simulation problems. Compared to the COMPASS algorithm, AHA is more efficient in high-dimensional problems. By analyzing models of the behavior of COMPASS and AHA, we show why COMPASS slows down significantly as dimension increases, whereas AHA is less affected. Both AHA and COMPASS can be used as the local search algorithm within the Industrial Strength COMPASS framework, which consists of a global search phase, a local search phase, and a final cleanup phase. We compare the performance of AHA to COMPASS within the framework of Industrial Strength COMPASS and as stand-alone algorithms. Numerical experiments demonstrate that AHA scales up well in high-dimensional problems and has similar performance to COMPASS in low-dimensional problems.