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Gaussian Approximation in Wasserstein-p: Markovian Martingale Differences and Stochastic Approximation
Yixuan Zhang, Qiaomin Xie
We establish nonasymptotic Gaussian approximation bounds in higher-order Wasserstein distance , , for deterministic matrix-weighted sums of multivariate Poisson martin…
On the Peril of (Even a Little) Nonstationarity in Satisficing Regret Minimization
Yixuan Zhang, Ruihao Zhu, Qiaomin Xie
Motivated by the principle of satisficing in decision-making, we study satisficing regret guarantees for nonstationary -armed bandits. We show that in the general realizable, pi…
Optimization with Parametric Variational Inequality Constraints on a Moving Set Based on a Smoothing Method
Xiaojun Chen, Jin Zhang, Yixuan Zhang
This paper focuses on optimization problems constrained by Parametric Variational Inequalities (PVI) defined on a moving set. Unlike most existing works on mathematical programs wi…
Wasserstein-p Central Limit Theorem Rates: From Local Dependence to Markov Chains
Yixuan Zhang, Qiaomin Xie
Non-asymptotic central limit theorem (CLT) rates play a central role in modern machine learning and operations research. In this paper, we study CLT rates for multivariate dependen…