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Explore constrained best arm identification in bandit problems through this research seminar presented by Prof. Wouter M. Koolen from the Centrum Wiskunde & Informatica and University of Twente. Learn about real-world decision-making scenarios where you must select the optimal policy while respecting economic constraints, focusing on bandit problems where each arm represents a joint distribution of reward and cost. Discover how to identify the arm with the highest mean reward among all arms whose mean cost falls below a specified threshold, particularly when reward and cost are dependent. Examine information-theoretic lower bounds on sample complexity across three distinct models: Gaussian with fixed covariance, Gaussian with unknown covariance, and non-parametric distributions with rectangular support. Understand the proposed combination of sampling and stopping rules that accurately identifies the constrained best arm while matching optimal sample complexities for each model. Review simulation results demonstrating the empirical performance of these algorithms and gain insights into applications in machine learning theory, game theory, information theory, statistics, and optimization from an expert in multi-armed bandit models and accelerated learning methods.
