Finding the bandit in a graph: Sequential search-and-stop
This addresses a sequential search-and-stop problem for agents in graph-based environments, offering incremental improvements by combining search theory and multi-armed bandits.
The paper tackles the problem of sequentially searching for hidden objects in a directed acyclic graph with a time budget, where the agent can stop and restart on new instances to maximize the total objects found. It provides a quasi-optimal strategy for known distributions and a method to approximate unknown distributions while acting near-optimally.
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.