Decentralized Multi-Armed Bandit Algorithm for Improved Regret Bounds over Strongly Connected Graphs

Основные понятия

Decentralized multi-armed bandit algorithms can significantly reduce regret in multi-agent networks.

Аннотация

This paper explores a decentralized multi-armed bandit problem in a network of agents facing the same set of arms. The proposed algorithm guarantees lower logarithmic asymptotic regret compared to classic UCB algorithms, especially in strongly connected graphs. Key insights include the roles of graph connectivity, maximum local degree, and network size in regret expression. The study extends conventional MAB problems to cooperative multi-agent frameworks with consensus processes among agents.
Structure:

Introduction to Multi-Armed Bandit Problems

Definition and applications.

Homogeneous Decentralized Multi-Armed Bandit Problem Formulation

Network structure and agent interactions.

Proposed Fully Decentralized UCB Algorithm

Design objectives and upper confidence bound functions.

Contributions and Results Analysis

Improved asymptotic regret bounds and comparison with existing algorithms.

Algorithm Design Details and Implementation Considerations

Initialization steps, decision-making process, and iterative updates.

Theoretical Analysis and Proof of Main Results

Exploration consistency lemma and estimation confidence lemma.

Lower Bound Analysis and Network Size Estimation Strategies

Flooding process for network size estimation and implications on regret bounds.

Conclusion and Future Directions

Статистика

A fully decentralized upper confidence bound (UCB) algorithm guarantees lower logarithmic asymptotic regret compared to classic UCB algorithms in strongly connected graphs.

Цитаты

"The proposed decentralized algorithm not only outperforms its classic single-agent counterpart but also guarantees improved asymptotic regret bounds."
"Collaboration among neighboring agents incentivizes improved performance within any strongly connected network."

Ключевые выводы из

Decentralized Multi-Armed Bandit Can Outperform Classic Upper Confidence Bound

by Jingxuan Zhu... в arxiv.org 03-26-2024

https://arxiv.org/pdf/2111.10933.pdf

Дополнительные вопросы

How does the proposed algorithm address challenges related to reward mean estimation accuracy

The proposed algorithm addresses challenges related to reward mean estimation accuracy by incorporating a decentralized approach that leverages information exchange among agents in the network. By utilizing a fully decentralized upper confidence bound (UCB) algorithm, each agent can update its reward mean estimate based on both local observations and information received from neighboring agents. This collaborative learning process allows for more accurate estimations by aggregating diverse perspectives and data points from multiple sources. Additionally, the algorithm introduces a novel method of push-sum based on a column stochastic matrix, which aids in distributed averaging over directed graphs without requiring global network-wide information. This approach ensures that each agent's confidence level in estimating arm rewards is appropriately calibrated, leading to improved accuracy in reward mean estimates.

What are the implications of the study's findings on real-world applications requiring multi-agent coordination

The findings of this study have significant implications for real-world applications that require multi-agent coordination, such as wireless communication systems, cognitive radio networks, adaptive routing algorithms, and online recommendation systems. By demonstrating the effectiveness of a homogeneous decentralized multi-armed bandit algorithm over strongly connected graphs, the research highlights the potential benefits of collaborative decision-making among agents facing similar sets of choices or arms. The improved asymptotic regret bounds achieved by the proposed algorithm underscore the advantages of network-wide cooperation in minimizing cumulative regret while maximizing overall performance. These results suggest that leveraging decentralized approaches for multi-agent coordination can lead to enhanced efficiency and effectiveness across various practical applications.

How might the concept of exploration consistency be extended to other decentralized learning paradigms

The concept of exploration consistency introduced in this study can be extended to other decentralized learning paradigms by emphasizing synchronization and alignment among agents' exploration strategies. In contexts where multiple autonomous entities interact within a shared environment or system, ensuring consistent levels of exploration across all agents is crucial for maintaining fairness and optimizing collective outcomes. By extending the principles of exploration consistency to different decentralized learning frameworks like reinforcement learning or distributed optimization algorithms, researchers can promote harmonized decision-making processes and prevent individual discrepancies from hindering overall progress towards common goals. This extension could enhance collaboration dynamics and facilitate smoother convergence towards optimal solutions in complex multi-agent scenarios.