We propose a class of numerical integration methods for stochastic Poisson systems (SPSs) arbitrary dimensions. Based on the Darboux-Lie theorem, we transform SPSs to their canonical form, generalized Hamiltonian (SHSs), via coordinate transformations found by solving certain PDEs defined brackets SPSs. An a-generating function approach with \alpha\in [0,1] is then used create symplectic discre...

Adaptivity is an important yet under-studied property in modern optimization theory. The gap between the state-of-the-art theory and current practice striking that algorithms with desirable theoretical guarantees typically involve drastically different settings of hyperparameters, such as step size schemes batch sizes, regimes. Despite appealing results, divisive strategies provide little, if a...