Summer Term 2026

Lecture by Dr. Dave Jacobi

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Time and place

• Lecture: Monday, 14:00--16:00h, SR 119, Arnimallee 3 
• Exam: TBA

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Prerequisits: Stochastics I and II. For continuous RL: Stochastics III. The knowledge of advanced measure theoretic probability is required to follow this course.
Target Group: BMS Students, Master students of Mathematics, advanced Bachelor students of Mathematics, PhDs, Postdocs.

• FU students only need to register for the course via CM (Campus Management).
• Non-FU students are required to register via MyCampus/Whiteboard.

Course Overview/ Content:

This lecture provides a rigorous introduction to the mathematical foundations of reinforcement learning (RL), focusing on theoretical guarantees underlying modern RL methods. Reinforcement learning lies at the core of many state-of-the-art artificial intelligence algorithms, enabling agents to solve complex optimal control tasks in robotics, finance, physical AI, drug discovery, computer games and many other applications.
Students will develop a thorough understanding of how agents learn to make optimal sequential decisions in uncertain environments, with an emphasis on the interplay between probability theory, optimization, and stochastic control. Via mathematically rigorous treatment, this course enables students to analyze RL algorithms beyond empirical performance, evaluate their theoretical intricacies, and understand current research.

Topics include:
- Markov decision processes (MDPs),
- Value functions and Bellman equations,
- Stochastic approximation,
- Value function based methods,
- Policy gradient methods,
- Actor critic methods,
- Deep reinforcement learning,
- Continuous time and state-action space RL,
- Entropy regularized RL.

References

Literature will be announced during the course.