Pure Exploration in Bandits with Linear Constraints
Paper i proceeding, 2024

We address the problem of identifying the optimal policy with a fixed confidence level in a multi-armed bandit setup, when the arms are subject to linear constraints. Unlike the standard best-arm identification problem which is well studied, the optimal policy in this case may not be deterministic and could mix between several arms. This changes the geometry of the problem which we characterize via an information-theoretic lower bound. We introduce two asymptotically optimal algorithms for this setting, one based on the Track-and-Stop method and the other based on a game-theoretic approach. Both these algorithms try to track an optimal allocation based on the lower bound and computed by a weighted projection onto the boundary of a normal cone. Finally, we provide empirical results that validate our bounds and visualize how constraints change the hardness of the problem.


Emil Carlsson

Chalmers, Data- och informationsteknik, Data Science och AI

Debabrota Basu

Université de Lille

Fredrik Johansson

Chalmers, Data- och informationsteknik, Data Science och AI

Devdatt Dubhashi

Chalmers, Data- och informationsteknik, Data Science och AI

Proceedings of the 38th Conference on Uncertainty in Artificial Intelligence, UAI 2022

26403498 (eISSN)

Vol. 238 334-342

27th International Conference on Artificial Intelligence and Statistics, AISTATS 2024
Valencia, Spain,



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