5 papers
Tail-Sensitive KL and Rényi Convergence of Unadjusted Hamiltonian Monte Carlo via One-Shot Couplings
Nawaf Bou-Rabee, Siddharth Mitra, Andre Wibisono
Hamiltonian Monte Carlo (HMC) algorithms are among the most widely used sampling methods in high dimensional settings, yet their convergence properties are poorly understood in div…
A Symplectic Analysis of Alternating Mirror Descent
Jonas Katona, Xiuyuan Wang, Andre Wibisono
Motivated by understanding the behavior of the Alternating Mirror Descent (AMD) algorithm for bilinear zero-sum games, we study the discretization of continuous-time Hamiltonian fl…
On the Convergence of Min-Max Langevin Dynamics and Algorithm
Yang Cai, Siddharth Mitra, Xiuyuan Wang +1
We study zero-sum games in the space of probability distributions over the Euclidean space with entropy regularization, in the setting when the interaction function…
Characterizing Dependence of Samples along the Langevin Dynamics and Algorithms via Contraction of -Mutual Information
Jiaming Liang, Siddharth Mitra, Andre Wibisono
The mixing time of a Markov chain determines how fast the iterates of the Markov chain converge to the stationary distribution; however, it does not control the dependencies betwee…
Fast Convergence of -Divergence Along the Unadjusted Langevin Algorithm and Proximal Sampler
Siddharth Mitra, Andre Wibisono
We study the mixing time of two popular discrete-time Markov chains in continuous space, the Unadjusted Langevin Algorithm and the Proximal Sampler, which are discretizations of th…