APM_52070_EP - Mathematical Foundations of Decision Theory in AI (2026-2027)

This course delves into the theoretical underpinnings of sequential decision-making in artificial intelligence (AI), focusing on the mathematical frameworks that govern online learning, multi-armed bandits, and Markov Decision Processes (MDPs). Starting from the game theoretic principles of decision-making, it moves to studying online learning through the lens of regret minimization, analyzing classical methods such as follow-the-regularized-leader and online (mirror) descent. It then transitions to the more challenging bandit setting, where it studies the trade-offs between exploration and exploitation and analyzes algorithms such as UCB and exp3. The final part covers MDPs, emphasizing dynamic programming, value iteration, and policy gradient methods with special attention to the theoretical guarantees of these approaches.