1,251 research outputs found
Functional Bandits
We introduce the functional bandit problem, where the objective is to find an
arm that optimises a known functional of the unknown arm-reward distributions.
These problems arise in many settings such as maximum entropy methods in
natural language processing, and risk-averse decision-making, but current
best-arm identification techniques fail in these domains. We propose a new
approach, that combines functional estimation and arm elimination, to tackle
this problem. This method achieves provably efficient performance guarantees.
In addition, we illustrate this method on a number of important functionals in
risk management and information theory, and refine our generic theoretical
results in those cases
Simple regret for infinitely many armed bandits
We consider a stochastic bandit problem with infinitely many arms. In this
setting, the learner has no chance of trying all the arms even once and has to
dedicate its limited number of samples only to a certain number of arms. All
previous algorithms for this setting were designed for minimizing the
cumulative regret of the learner. In this paper, we propose an algorithm aiming
at minimizing the simple regret. As in the cumulative regret setting of
infinitely many armed bandits, the rate of the simple regret will depend on a
parameter characterizing the distribution of the near-optimal arms. We
prove that depending on , our algorithm is minimax optimal either up to
a multiplicative constant or up to a factor. We also provide
extensions to several important cases: when is unknown, in a natural
setting where the near-optimal arms have a small variance, and in the case of
unknown time horizon.Comment: in 32th International Conference on Machine Learning (ICML 2015
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