Adaptive Optimization algorithms for dependent data streams

The subject matter of this PhD study is Stochastic Gradient Descent Langevin (SGLD) and other data-driven MCMC algorithms for dependent data streams. In particular, the focus is on questions beyond Lipschitz gradients. Another important aim is to address well-known challenges on sampling from distributions on highdimensional spaces. Elements of stochastic approximations theory and numerical methods for stochastic differential equations are part of this study. This is also true for applications in the area of adaptive optimization and Bayesian inference.