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6. A PC-Kriging-HDMR integrated with an adaptive sequential sampling strategy for high-dimensional approximate modeling

Author

Zhang, Yili, Huang, Hanyan, Xiong, Mei, and Yao, Zengquan

Subjects
Statistics - Methodology
Abstract

High-dimensional complex multi-parameter problems are prevalent in engineering, exceeding the capabilities of traditional surrogate models designed for low/medium-dimensional problems. These models face the curse of dimensionality, resulting in decreased modeling accuracy as the design parameter space expands. Furthermore, the lack of a parameter decoupling mechanism hinders the identification of couplings between design variables, particularly in highly nonlinear cases. To address these challenges and enhance prediction accuracy while reducing sample demand, this paper proposes a PC-Kriging-HDMR approximate modeling method within the framework of Cut-HDMR. The method leverages the precision of PC-Kriging and optimizes test point placement through a multi-stage adaptive sequential sampling strategy. This strategy encompasses a first-stage adaptive proportional sampling criterion and a second-stage central-based maximum entropy criterion. Numerical tests and a practical application involving a cantilever beam demonstrate the advantages of the proposed method. Key findings include: (1) The performance of traditional single-surrogate models, such as Kriging, significantly deteriorates in high-dimensional nonlinear problems compared to combined surrogate models under the Cut-HDMR framework (e.g., Kriging-HDMR, PCE-HDMR, SVR-HDMR, MLS-HDMR, and PC-Kriging-HDMR); (2) The number of samples required for PC-Kriging-HDMR modeling increases polynomially rather than exponentially as the parameter space expands, resulting in substantial computational cost reduction; (3) Among existing Cut-HDMR methods, no single approach outperforms the others in all aspects. However, PC-Kriging-HDMR exhibits improved modeling accuracy and efficiency within the desired improvement range compared to PCE-HDMR and Kriging-HDMR, demonstrating robustness., Comment: 17 pages with 7 figures and 9 tables

Published
2023
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10. Learning-based Optimal Admission Control in a Single Server Queuing System

Author

Cohen, Asaf, Subramanian, Vijay G., and Zhang, Yili

Subjects
Mathematics - Optimization and Control, Statistics - Machine Learning
Abstract

We consider a long-term average profit maximizing admission control problem in an M/M/1 queuing system with unknown service and arrival rates. With a fixed reward collected upon service completion and a cost per unit of time enforced on customers waiting in the queue, a dispatcher decides upon arrivals whether to admit the arriving customer or not based on the full history of observations of the queue-length of the system. (Naor 1969, Econometrica) showed that if all the parameters of the model are known, then it is optimal to use a static threshold policy -- admit if the queue-length is less than a predetermined threshold and otherwise not. We propose a learning-based dispatching algorithm and characterize its regret with respect to optimal dispatch policies for the full information model of Naor (1969). We show that the algorithm achieves an $O(1)$ regret when all optimal thresholds with full information are non-zero, and achieves an $O(\ln^{1+\epsilon}(N))$ regret for any specified $\epsilon>0$, in the case that an optimal threshold with full information is $0$ (i.e., an optimal policy is to reject all arrivals), where $N$ is the number of arrivals.

Published
2022

46. On the asymptotic optimality of the comb strategy for prediction with expert advice

Author

Bayraktar, Erhan, Ekren, Ibrahim, and Zhang, Yili

Subjects
Mathematics - Probability, Computer Science - Machine Learning, Mathematics - Optimization and Control
Abstract

For the problem of prediction with expert advice in the adversarial setting with geometric stopping, we compute the exact leading order expansion for the long time behavior of the value function. Then, we use this expansion to prove that as conjectured in Gravin et al. [12], the comb strategies are indeed asymptotically optimal for the adversary in the case of 4 experts., Comment: To appear in Annals of Applied Probabilty

Published
2019

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