7 papers
Near-Linear Accuracy Bounds for Moreau--Yosida Unadjusted Langevin Sampling
Yuchen Xin, Zhihua Zhang
We establish near-linear accuracy bounds for the classical Moreau--Yosida unadjusted Langevin algorithm (MYULA). The target is , where i…
Rényi Tracking Bounds for Langevin Dynamics with Moving Targets
Yuchen Xin, Jingxin Zhan, Zhihua Zhang
We study Langevin diffusion and Langevin Monte Carlo (LMC) when the target distribution changes over time. Under a log-Sobolev inequality (LSI), we derive non-asymptotic Rényi-dive…
Conditionally Resampled Sliding-Window Count Kernels: Spectral-Gap Bounds and Poincaré Inequalities
Yanjin Xiang, Yuchen Xin, Zhihua Zhang
We study the conditionally resampled sliding-window count kernel associated with the empirical counts of length- windows from a stationary finite-state reversible Markov chain.…
Active-Trace Complexity Bounds for Moreau--Yosida Unadjusted Langevin Sampling
Yuchen Xin, Zhihua Zhang
We study the Moreau--Yosida unadjusted Langevin algorithm (MYULA) for the nonsmooth composite target \[ π(dx)\propto \exp\{-f(x)-g(x)\}\,dx, \qquad x\in\mathbb R^d, \] where \(f\)…
Matrix Moment and Concentration Inequalities for Martingales and Ergodic Markov Chains with Applications in Statistical Learning
Yang Peng, Yuchen Xin, Zhihua Zhang
In this paper, we study moment and concentration inequalities for the spectral norm of sums of dependent random matrices. We establish novel Rosenthal-Burkholder inequalities for t…
Follow-the-Perturbed-Leader Approaches Best-of-Both-Worlds for the m-Set Semi-Bandit Problems
Jingxin Zhan, Yuchen Xin, Chenjie Sun +1
We consider a common case of the combinatorial semi-bandit problem, the -set semi-bandit, where the learner exactly selects arms from the total arms. In the adversarial…
A Regularized Online Newton Method for Stochastic Convex Bandits with Linear Vanishing Noise
Jingxin Zhan, Yuchen Xin, Kaicheng Jin +1
We study a stochastic convex bandit problem where the subgaussian noise parameter is assumed to decrease linearly as the learner selects actions closer and closer to the minimizer…