Type: Research Paper (Lecture Notes)
Bibliographic Information:
Light, B. (2024). A Course in Dynamic Optimization. arXiv preprint arXiv:2408.03034v2.
To provide a comprehensive introduction to dynamic optimization, focusing on the theoretical underpinnings of dynamic programming, particularly for upper semi-continuous models, and their applications in various fields, including reinforcement learning.
The lecture notes present a theoretical framework for dynamic optimization, including a proof for the principle of optimality for upper semi-continuous dynamic programming. They also delve into the properties of value and policy functions, leveraging classical and recent results. Additionally, the notes offer an introduction to reinforcement learning, including a convergence proof for Q-learning algorithms and policy gradient methods for the average reward case.
The notes provide a novel approach to teaching dynamic optimization by focusing on upper semi-continuous dynamic programming, a middle ground between simpler and more complex cases. This approach allows for the inclusion of important examples like dynamic pricing, consumption-savings, and inventory management models. The notes also present a new convergence result for the policy gradient method in the tabular case for the average reward case.
The lecture notes offer a valuable resource for students and researchers interested in dynamic optimization. The focus on upper semi-continuous models and the inclusion of reinforcement learning make these notes particularly relevant for addressing real-world problems in various fields.
These lecture notes contribute significantly to the field of dynamic optimization by providing a rigorous yet accessible treatment of the subject, bridging the gap between theoretical foundations and practical applications. The inclusion of recent developments in reinforcement learning further enhances the relevance and value of these notes.
The lecture notes primarily focus on discrete-time dynamic programming models. Future iterations could expand on continuous-time models and explore more advanced topics in reinforcement learning, such as deep reinforcement learning.
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