2026 Theses Doctoral

Efficient Computation and Uncertainty Quantification for Stochastic Dynamics and Optimization

Yan, Yunhao

This dissertation studies computational and statistical methods for sequential decision-making under stochastic dynamics. In many realistic settings, stochastic systems are high-dimensional, time-inhomogeneous, and calibrated from finite data, while even evaluating the performance of a fixed policy may already be computationally expensive. These features make both policy optimization and uncertainty quantification difficult when one relies on classical exact methods or naive Monte Carlo procedures. A central theme of the dissertation is that structural properties of the underlying problem can be exploited to improve tractability without sacrificing the quality of optimization or inference.

The dissertation develops three related approaches. First, for the control of nonstationary queueing systems, it introduces QPLEX Decision Processes (QDPs), which embed QPLEX-based transient approximations into a nonlinear Markov decision framework. This leads to efficient deterministic schemes for policy evaluation and gradient computation, together with a natural-gradient-inspired optimization method. The resulting approach enables the fast computation of high-quality policies for challenging control problems in nonstationary queueing systems with features such as nonstationary arrivals, general service-time distributions, and service-level chance constraints.

Second, when stochastic models are fitted from finite real-world data, uncertainty in the input distributions can materially affect subsequent performance evaluation and decision quality. Quantifying this input uncertainty is often computationally demanding, since bootstrap-based methods require repeated evaluation of stochastic systems that may involve expensive simulation or other black-box computations. To address this challenge, the dissertation develops the studentized cheap bootstrap (SCB), which retains the higher-order coverage accuracy of studentization while using only a very small number of inner resamples, thereby reconciling statistical accuracy with computational tractability.

Third, for policy assessment in multistage stochastic optimization under stagewise independence, it develops the Multi-Sample Average Approximation (MSAA) framework. This provides a preliminary approach to the highly challenging problem of statistically assessing optimality gaps in multistage stochastic optimization. By connecting MSAA to multisample U-statistics and U-processes, the dissertation establishes consistency and related convergence results, and uses these ideas to derive statistical bounds on the optimality gaps of candidate solutions.

Overall, the dissertation shows how careful use of structure can support both efficient computation and rigorous uncertainty quantification in stochastic decision problems.