......................................................................................................................... ii Acknowledgments ......................................................................................................... iii Vita ............................................................................................................................... iv List of Ta...

We give a short introduction to the stochastic calculus for Itô-Lévy processes, and review brie‡y the two main methods of optimal control of stochastic systems described by such processes, namely: (i) Dynamic programming and the Hamilton-Jacobi-Bellman (HJB) equation (ii) The stochastic maximum principle and its associated adjoint backward stochastic di¤erential equation (BSDE). The two methods...

Stochastic gradient Markov chain Monte Carlo (SG-MCMC) methods are Bayesian analogs to popular stochastic optimization methods; however, this connection is not well studied. We explore this relationship by applying simulated annealing to an SGMCMC algorithm. Furthermore, we extend recent SG-MCMC methods with two key components: i) adaptive preconditioners (as in ADAgrad or RMSprop), and ii) ada...