← Research

Stochastic Approximation & Statistical Inference

When adaptive optimization algorithms are used to compute optimal solutions, an important question is how to characterize their convergence behavior and how to equip the resulting solutions with valid and computationally efficient confidence intervals. My research studies algorithmic inference by viewing learning algorithms as stochastic processes and leveraging their convergence dynamics and gradient noise for statistical inference.

A key theme is that carefully designed gradient estimators or algorithms can endow learned solutions with desirable statistical properties (such as valid uncertainty quantification, robustness, privacy, or fairness) without sacrificing computational efficiency. In particular, algorithmic randomness and gradient noise can be explicitly exploited to construct confidence intervals and enable principled statistical inference, offering a convenient pathway for understanding uncertainty in modern learning systems.

My recent work explores these ideas in a range of settings, including local SGD in federated learning, Q-learning in reinforcement learning, and operations research problems such as queueing systems and inventory control.

Stochastic Approximation
  • A Statistical Analysis of Polyak-Ruppert Averaged Q-Learning
    X. Li, W. Yang, J. Liang, Z. Zhang, and M. I. Jordan. AISTATS, 2023.
  • Convergence and Inference of Stream SGD, with Applications to Queueing Systems and Inventory Control
    X. Li*, J. Liang*, X. Chen, and Z. Zhang. Operations Research, 2026.
  • Online Statistical Inference for Nonlinear Stochastic Approximation with Markovian Data
    X. Li, J. Liang, and Z. Zhang. Technical report, arXiv preprint arXiv:2302.07690, 2023.
  • Asymptotic Behaviors of Projected Stochastic Approximation: A Jump Diffusion Perspective
    J. Liang, Y. Han, X. Li, and Z. Zhang. NeurIPS, 2022 (Spotlight).
  • Decoupled Functional Central Limit Theorems for Two-Time-Scale Stochastic Approximation
    Y. Han, X. Li, J. Liang, and Z. Zhang. Mathematics of Operations Research, 2026.
  • Finite-Time Decoupled Convergence in Nonlinear Two-Time-Scale Stochastic Approximation
    Y. Han, X. Li, and Z. Zhang. Journal of Machine Learning Research, 2026.
  • Do Subsampled Newton Methods Work for High-Dimensional Data?
    X. Li, S. Wang, and Z. Zhang. AAAI, 2020.