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

Convergence Analysis of Stochastic Kriging-Assisted Simulation with Random Covariates

We consider performing simulation experiments in the presence of covariates. Here, covariates refer to some input information other than system designs to the simulation model that can also affect the system performance. To make decisions, decision makers need to know the covariate values of the problem. Traditionally in simulation-based decision making, simulation samples are collected after the covariate values are known; in contrast, as a new framework, simulation with covariates starts the simulation before the covariate values are revealed, and collects samples on covariate values that might appear later. Then, when the covariate values are revealed, the collected simulation samples are directly used to predict the desired results. This framework significantly reduces the decision time compared to the traditional way of simulation. In this paper, we follow this framework and suppose there are a finite number of system designs. We adopt the metamodel of stochastic kriging (SK) and use it to predict the system performance of each design and the best design. The goal is to study how fast the prediction errors diminish with the number of covariate points sampled. This is a fundamental problem in simulation with covariates and helps quantify the relationship between the offline simulation efforts and the online prediction accuracy. Particularly, we adopt measures of the maximal integrated mean squared error (IMSE) and integrated probability of false selection (IPFS) for assessing errors of the system performance and the best design predictions. Then, we establish convergence rates for the two measures under mild conditions. Last, these convergence behaviors are illustrated numerically using test examples

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

Improving the Knowledge Gradient Algorithm

The knowledge gradient (KG) algorithm is a popular policy for the best arm identification (BAI) problem. It is built on the simple idea of always choosing the measurement that yields the greatest expected one-step improvement in the estimate of the best mean of the arms. In this research, we show that this policy has limitations, causing the algorithm not asymptotically optimal. We next provide a remedy for it, by following the manner of one-step look ahead of KG, but instead choosing the measurement that yields the greatest one-step improvement in the probability of selecting the best arm. The new policy is called improved knowledge gradient (iKG). iKG can be shown to be asymptotically optimal. In addition, we show that compared to KG, it is easier to extend iKG to variant problems of BAI, with the $\epsilon$-good arm identification and feasible arm identification as two examples. The superior performances of iKG on these problems are further demonstrated using numerical examples.Comment: 32 pages, 42 figure

AdaTT: Adaptive Task-to-Task Fusion Network for Multitask Learning in Recommendations

Multi-task learning (MTL) aims at enhancing the performance and efficiency of machine learning models by training them on multiple tasks simultaneously. However, MTL research faces two challenges: 1) modeling the relationships between tasks to effectively share knowledge between them, and 2) jointly learning task-specific and shared knowledge. In this paper, we present a novel model Adaptive Task-to-Task Fusion Network (AdaTT) to address both challenges. AdaTT is a deep fusion network built with task specific and optional shared fusion units at multiple levels. By leveraging a residual mechanism and gating mechanism for task-to-task fusion, these units adaptively learn shared knowledge and task specific knowledge. To evaluate the performance of AdaTT, we conduct experiments on a public benchmark and an industrial recommendation dataset using various task groups. Results demonstrate AdaTT can significantly outperform existing state-of-the-art baselines

Research on the Design Method of a Bionic Suspension Workpiece Based on the Wing Structure of an Albatross

An air suspension platform uses air pressure to realize the suspension function during the suspension process, and it has the disadvantage of large air pressure and a small suspension force. In this study, an air suspension platform was built using bionic design to reduce the required air pressure and increase the suspension force. A suspension structure mapping model was established according to the physiological structure characteristics of albatross wings. A bionic model was established by using the theoretical calculation formula and structural size parameters of the structural design. A 3D printer was used to manufacture the physical prototype of the suspended workpiece. Based on this, a suspension test rig was built. Six sets of contrast experiments were designed. The experimental results of the suspension test bench were compared with the theoretical calculation results. The results show that the buoyancy of the suspended workpiece with a V-shaped surface at a 15-degree attack angle was optimal for the same air pressure as the other workpieces. The surface structure of the suspended workpiece was applied to the air static pressure guide rail. By comparing the experimental data, the air pressure of the original air suspension guide rail was reduced by 37%, and the validity of the theory and design method was verified