Multi-arm Bandits: Regret and Exploration

This lecture delves into the concept of regret in multi-arm bandit problems, exploring the trade-off between exploration and exploitation. The instructor explains how to calculate the expected regret over time steps, emphasizing the importance of the gap between optimal choices. The lecture covers the impact of time horizon on decision-making and introduces concentration bounds for tail probabilities. The discussion extends to Gaussian random variables, moment-generating functions, and the turn-off bound. The instructor highlights the challenges of balancing exploration and exploitation, showcasing the implications for real-world applications like internet advertising. The lecture concludes by hinting at future topics, including information-theoretic concepts and practical extensions of bandit algorithms.