 A Course in Dynamic OptimizationBar Light Abstract: These lecture notes are derived from a graduate-level course in dynamic optimization, offering an introduction to techniques and models extensively used in management science, economics, operations research, engineering, and computer science. The course emphasizes the theoretical underpinnings of discrete-time dynamic programming models and advanced algorithmic strategies for solving these models. Unlike typical treatments, it provides a proof for the principle of optimality for upper semi-continuous dynamic programming, a middle ground between the simpler countable state space case \cite{bertsekas2012dynamic}, and the involved universally measurable case \cite{bertsekas1996stochastic}. This approach is sufficiently rigorous to include important examples such as dynamic pricing, consumption-savings, and inventory management models. The course also delves into the properties of value and policy functions, leveraging classical results \cite{topkis1998supermodularity} and recent developments. Additionally, it offers an introduction to reinforcement learning, including a formal proof of the convergence of Q-learning algorithms. Furthermore, the notes delve into policy gradient methods for the average reward case, presenting a convergence result for the tabular case in this context. This result is simple and similar to the discounted case but appears to be new. Date: 2024-08, Revised 2024-10 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:arx:papers:2408.03034 Access Statistics for this paper More papers in Papers from arXiv.org |
Is your work missing from RePEc? Here is how to contribute.
Questions or problems? Check the EconPapers FAQ or send mail to .
EconPapers is hosted by the
School of Business at Örebro University.