论文标题

对一类多工具的匪徒问题,具有对数遗憾的分散政策,具有选项不可用的约束和随机通信协议

A Decentralized Policy with Logarithmic Regret for a Class of Multi-Agent Multi-Armed Bandit Problems with Option Unavailability Constraints and Stochastic Communication Protocols

论文作者

Pankayaraj, Pathmanathan, Maithripala, D. H. S., Berg, J. M.

论文摘要

本文考虑了一个多臂强盗(MAB)问题,其中多种移动代理通过从空间分散的随机过程中采样(称为匪徒)获得奖励。目的是为每个代理制定分散的政策,以最大程度地利用所有代理商的总累积奖励,但要受期权可用性和主体间通信约束。问题表达是由应用程序团队在不确定环境中完成探索和剥削任务的应用程序进行的。匪徒位置由空间图的顶点表示。在任何时候,代理商的选项包括在当前位置对土匪进行采样,或沿着空间图的边缘移动到新的强盗位置。通信约束由定向的,非平稳的随机通信图描述。在任何时候,代理商只能从其邻居内的通信图中收到数据。对于完全连接的空间图上的单个代理的情况,众所周知,任何最佳策略的预期遗憾必然在下面由成长为时间对数的函数限制。一类称为上置信度结合(UCB)算法的政策渐近地对对数遗憾了古典mAb问题。在本文中,我们提出了一个基于UCB的分散运动和期权选择策略以及一个非平稳随机通信协议,以保证对数遗憾。据我们所知,这是针对具有通信约束的非紧密连接的空间图的第一个分散策略。当空间图完全连接并且通信图是静止的时,我们的分散算法匹配或超过文献中报告的最佳先前结果。

This paper considers a multi-armed bandit (MAB) problem in which multiple mobile agents receive rewards by sampling from a collection of spatially dispersed stochastic processes, called bandits. The goal is to formulate a decentralized policy for each agent, in order to maximize the total cumulative reward over all agents, subject to option availability and inter-agent communication constraints. The problem formulation is motivated by applications in which a team of autonomous mobile robots cooperates to accomplish an exploration and exploitation task in an uncertain environment. Bandit locations are represented by vertices of the spatial graph. At any time, an agent's option consist of sampling the bandit at its current location, or traveling along an edge of the spatial graph to a new bandit location. Communication constraints are described by a directed, non-stationary, stochastic communication graph. At any time, agents may receive data only from their communication graph in-neighbors. For the case of a single agent on a fully connected spatial graph, it is known that the expected regret for any optimal policy is necessarily bounded below by a function that grows as the logarithm of time. A class of policies called upper confidence bound (UCB) algorithms asymptotically achieve logarithmic regret for the classical MAB problem. In this paper, we propose a UCB-based decentralized motion and option selection policy and a non-stationary stochastic communication protocol that guarantee logarithmic regret. To our knowledge, this is the first such decentralized policy for non-fully connected spatial graphs with communication constraints. When the spatial graph is fully connected and the communication graph is stationary, our decentralized algorithm matches or exceeds the best reported prior results from the literature.

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