Bridging Rested and Restless Bandits with Graph-Triggering: Rising and Rotting
Gianmarco Genalti, Marco Mussi, Nicola Gatti, Marcello, Restelli, Matteo Castiglioni, Alberto Maria Metelli

TL;DR
This paper introduces Graph-Triggered Bandits (GTBs), a unified framework that models the evolution of arm rewards through a graph, encompassing rested and restless bandits, and explores optimal policies for rising and rotting reward behaviors.
Contribution
The work proposes GTBs as a generalization of rested and restless bandits, providing algorithms and theoretical analysis for specific monotonic reward cases.
Findings
GTBs unify rested and restless bandits via graph modeling.
Algorithms with theoretical guarantees are developed for rising and rotting cases.
The complexity of learning depends on the underlying graph structure.
Abstract
Rested and Restless Bandits are two well-known bandit settings that are useful to model real-world sequential decision-making problems in which the expected reward of an arm evolves over time due to the actions we perform or due to the nature. In this work, we propose Graph-Triggered Bandits (GTBs), a unifying framework to generalize and extend rested and restless bandits. In this setting, the evolution of the arms' expected rewards is governed by a graph defined over the arms. An edge connecting a pair of arms represents the fact that a pull of arm triggers the evolution of arm , and vice versa. Interestingly, rested and restless bandits are both special cases of our model for some suitable (degenerated) graph. As relevant case studies for this setting, we focus on two specific types of monotonic bandits: rising, where the expected reward of an arm grows as the number of…
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Taxonomy
TopicsAdvanced Bandit Algorithms Research · Mind wandering and attention · Smart Grid Energy Management
MethodsFocus
