Stochastic Control with Partial Information: Regularity, Optimality, Approximations, and Learning

Explore a comprehensive seminar on stochastic control with partial information, covering regularity, optimality, approximations, and learning. Delve into the complexities of partially observed stochastic control models and their applications. Examine the reduction of partially observed problems to fully observed ones using probability measure valued filter states and filtering equations. Investigate regularity results for Markovian kernels, including weak continuity and Wasserstein regularity. Learn about existence results for optimal solutions under discounted cost and average cost criteria. Discover approximation techniques using quantized filter approximations and finite sliding window methods. Understand the concept of filter stability and its role in near-optimal finite-window control policies. Explore the convergence of reinforcement learning algorithms for control policies using finite approximations or finite windows of past observations. Gain insights into the asymptotic convergence and near optimality of finite-memory Q-learning algorithms. Examine extensions to average cost criteria and non-Markovian systems in this in-depth exploration of stochastic control theory and applications.