Bandit Algorithms

Tor Lattimore is a research scientist at DeepMind. His research is focused on decision making in the face of uncertainty, including bandit algorithms and reinforcement learning. Before joining DeepMind he was an assistant professor at Indiana University and a postdoctoral fellow at the University of Alberta. Csaba Szepesvári is a Professor in the Department of Computing Science at the University of Alberta and a Principal Investigator of the Alberta Machine Intelligence Institute. He also leads the 'Foundations' team at DeepMind. He has co-authored a book on nonlinear approximate adaptive controllers and authored a book on reinforcement learning, in addition to publishing over 200 journal and conference papers. He is an action editor of the Journal of Machine Learning Research.

'This year marks the 68th anniversary of 'multi-armed bandits' introduced by Herbert Robbins in 1952, and the 35th anniversary of his 1985 paper with me that advanced multi-armed bandit theory in new directions via the concept of 'regret' and a sharp asymptotic lower bound for the regret. This vibrant subject has attracted important multidisciplinary developments and applications. Bandit Algorithms gives it a comprehensive and up-to-date treatment, and meets the need for such books in instruction and research in the subject, as in a new course on contextual bandits and recommendation technology that I am developing at Stanford.' Tze L. Lai, Stanford University

• 1. Introduction; 2. Foundations of probability; 3. Stochastic processes and Markov chains; 4. Finite-armed stochastic bandits; 5. Concentration of measure; 6. The explore-then-commit algorithm; 7. The upper confidence bound algorithm; 8. The upper confidence bound algorithm: asymptotic optimality; 9. The upper confidence bound algorithm: minimax optimality; 10. The upper confidence bound algorithm: Bernoulli noise; 11. The Exp3 algorithm; 12. The Exp3-IX algorithm; 13. Lower bounds: basic ideas; 14. Foundations of information theory; 15. Minimax lower bounds; 16. Asymptotic and instance dependent lower bounds; 17. High probability lower bounds; 18. Contextual bandits; 19. Stochastic linear bandits; 20. Confidence bounds for least squares estimators; 21. Optimal design for least squares estimators; 22. Stochastic linear bandits with finitely many arms; 23. Stochastic linear bandits with sparsity; 24. Minimax lower bounds for stochastic linear bandits; 25. Asymptotic lower bounds for stochastic linear bandits; 26. Foundations of convex analysis; 27. Exp3 for adversarial linear bandits; 28. Follow the regularized leader and mirror descent; 29. The relation between adversarial and stochastic linear bandits; 30. Combinatorial bandits; 31. Non-stationary bandits; 32. Ranking; 33. Pure exploration; 34. Foundations of Bayesian learning; 35. Bayesian bandits; 36. Thompson sampling; 37. Partial monitoring; 38. Markov decision processes.