Modified Index Policies for Multi-Armed Bandits with Network-like Markovian Dependencies

Sequential decision-making in dynamic and interconnected environments is a cornerstone of numerous applications, ranging from communication networks and finance to distributed blockchain systems and IoT frameworks. The multi-armed bandit (MAB) problem is a fundamental model in this domain that tradi...

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Main Authors: Abdalaziz Sawwan, Jie Wu
Format: Article
Language:English
Published: MDPI AG 2025-01-01
Series:Network
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Online Access:https://www.mdpi.com/2673-8732/5/1/3
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author Abdalaziz Sawwan
Jie Wu
author_facet Abdalaziz Sawwan
Jie Wu
author_sort Abdalaziz Sawwan
collection DOAJ
description Sequential decision-making in dynamic and interconnected environments is a cornerstone of numerous applications, ranging from communication networks and finance to distributed blockchain systems and IoT frameworks. The multi-armed bandit (MAB) problem is a fundamental model in this domain that traditionally assumes independent and identically distributed (iid) rewards, which limits its effectiveness in capturing the inherent dependencies and state dynamics present in some real-world scenarios. In this paper, we lay a theoretical framework for a modified MAB model in which each arm’s reward is generated by a hidden Markov process. In our model, each arm undergoes Markov state transitions independent of play in a way that results in varying reward distributions and heightened uncertainty in reward observations. The number of states for each arm can be up to three states. A key challenge arises from the fact that the underlying states governing each arm’s rewards remain hidden at the time of selection. To address this, we adapt traditional index-based policies and develop a modified index approach tailored to accommodate Markovian transitions and enhance selection efficiency for our model. Our proposed proposed Markovian Upper Confidence Bound (MC-UCB) policy achieves logarithmic regret. Comparative analysis with the classical UCB algorithm reveals that MC-UCB consistently achieves approximately a 15% reduction in cumulative regret. This work provides significant theoretical insights and lays a robust foundation for future research aimed at optimizing decision-making processes in complex, networked systems with hidden state dependencies.
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spelling doaj-art-c89ca8b19c6942319e1a06cfc41c21f02025-08-20T02:42:28ZengMDPI AGNetwork2673-87322025-01-0151310.3390/network5010003Modified Index Policies for Multi-Armed Bandits with Network-like Markovian DependenciesAbdalaziz Sawwan0Jie Wu1Department of Computer and Information Science, Temple University, Philadelphia, PA 19122, USADepartment of Computer and Information Science, Temple University, Philadelphia, PA 19122, USASequential decision-making in dynamic and interconnected environments is a cornerstone of numerous applications, ranging from communication networks and finance to distributed blockchain systems and IoT frameworks. The multi-armed bandit (MAB) problem is a fundamental model in this domain that traditionally assumes independent and identically distributed (iid) rewards, which limits its effectiveness in capturing the inherent dependencies and state dynamics present in some real-world scenarios. In this paper, we lay a theoretical framework for a modified MAB model in which each arm’s reward is generated by a hidden Markov process. In our model, each arm undergoes Markov state transitions independent of play in a way that results in varying reward distributions and heightened uncertainty in reward observations. The number of states for each arm can be up to three states. A key challenge arises from the fact that the underlying states governing each arm’s rewards remain hidden at the time of selection. To address this, we adapt traditional index-based policies and develop a modified index approach tailored to accommodate Markovian transitions and enhance selection efficiency for our model. Our proposed proposed Markovian Upper Confidence Bound (MC-UCB) policy achieves logarithmic regret. Comparative analysis with the classical UCB algorithm reveals that MC-UCB consistently achieves approximately a 15% reduction in cumulative regret. This work provides significant theoretical insights and lays a robust foundation for future research aimed at optimizing decision-making processes in complex, networked systems with hidden state dependencies.https://www.mdpi.com/2673-8732/5/1/3dynamic distributionslearning theoryMarkov chainmulti-armed bandit
spellingShingle Abdalaziz Sawwan
Jie Wu
Modified Index Policies for Multi-Armed Bandits with Network-like Markovian Dependencies
Network
dynamic distributions
learning theory
Markov chain
multi-armed bandit
title Modified Index Policies for Multi-Armed Bandits with Network-like Markovian Dependencies
title_full Modified Index Policies for Multi-Armed Bandits with Network-like Markovian Dependencies
title_fullStr Modified Index Policies for Multi-Armed Bandits with Network-like Markovian Dependencies
title_full_unstemmed Modified Index Policies for Multi-Armed Bandits with Network-like Markovian Dependencies
title_short Modified Index Policies for Multi-Armed Bandits with Network-like Markovian Dependencies
title_sort modified index policies for multi armed bandits with network like markovian dependencies
topic dynamic distributions
learning theory
Markov chain
multi-armed bandit
url https://www.mdpi.com/2673-8732/5/1/3
work_keys_str_mv AT abdalazizsawwan modifiedindexpoliciesformultiarmedbanditswithnetworklikemarkoviandependencies
AT jiewu modifiedindexpoliciesformultiarmedbanditswithnetworklikemarkoviandependencies