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Finding the bandit in a graph: Sequential search-and-stop

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Abstract

We consider the problem where an agent wants to find a hidden object that is randomly located in some vertex of a directed acyclic graph (DAG) according to a fixed but possibly unknown distribution. The agent can only examine vertices whose in-neighbors have already been examined. In this paper, we address a learning setting where we allow the agent to stop before having found the object and restart searching on a new independent instance of the same problem. Our goal is to maximize the total number of hidden objects found given a time budget. The agent can thus skip an instance after realizing that it would spend too much time on it. Our contributions are both to the search theory and multi-armed bandits. If the distribution is known, we provide a quasi-optimal and efficient stationary strategy. If the distribution is unknown, we additionally show how to sequentially approximate it and, at the same time, act near-optimally in order to collect as many hidden objects as possible.
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Dates and versions

hal-02387465 , version 1 (29-11-2019)

Identifiers

  • HAL Id : hal-02387465 , version 1

Cite

Pierre Perrault, Vianney Perchet, Michal Valko. Finding the bandit in a graph: Sequential search-and-stop. International Conference on Artificial Intelligence and Statistics, 2019, Okinawa, Japan. ⟨hal-02387465⟩
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