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

TL;DR

This paper introduces a sequential search-and-stop framework for finding hidden objects in a DAG, optimizing search strategies with unknown distributions and allowing early stopping to maximize total discoveries within a time budget.

Contribution

It develops a novel approach combining search theory and multi-armed bandits, providing efficient strategies for both known and unknown distributions in DAG search problems.

Findings

Quasi-optimal stationary strategy for known distributions

Sequential approximation of unknown distributions

Near-optimal collection of hidden objects within time constraints

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.