Factored-reward bandits with intermediate observations: Regret minimization and best arm identification

IF 4.6 2区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Marco Mussi , Simone Drago , Marcello Restelli, Alberto Maria Metelli
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引用次数: 0

Abstract

In several real-world sequential decision problems, at every step, the learner is required to select different actions. Every action affects a specific part of the system and generates an observable intermediate effect. In this paper, we introduce the Factored-Reward Bandits (FRBs), a novel setting able to effectively capture and exploit the structure of this class of scenarios, where the reward is computed as the product of the action intermediate observations. We characterize the statistical complexity of the learning problem in the FRBs, by deriving worst-case and asymptotic instance-dependent regret lower bounds. Then, we devise and analyze two regret minimization algorithms. The former, F-UCB, is an anytime optimistic approach matching the worst-case lower bound (up to logarithmic factors) but fails to perform optimally from the instance-dependent perspective. The latter, F-Track, is a bound-tracking approach, that enjoys optimal asymptotic instance-dependent regret guarantees. Finally, we study the problem of performing best arm identification in this setting. We derive an error probability lower bound, and we develop F-SR, a nearly optimal rejection-based algorithm for identifying the best action vector, given a time budget.2
具有中间观察的因子奖励盗匪:后悔最小化和最佳武器识别
在一些现实世界的顺序决策问题中,在每一步,学习者都需要选择不同的动作。每个动作都会影响系统的特定部分,并产生可观察到的中间效应。在本文中,我们引入了因子奖励强盗(frb),这是一种能够有效捕获和利用这类场景结构的新设置,其中奖励是作为行动中间观察的产物计算的。我们通过推导最坏情况和渐近实例依赖的遗憾下界来表征frb中学习问题的统计复杂性。然后,我们设计并分析了两种遗憾最小化算法。前者,F-UCB,是一种随时乐观的方法,匹配最坏情况下界(直到对数因子),但从依赖实例的角度来看,它不能达到最佳效果。后者,F-Track,是一种边界跟踪方法,具有最优的渐近依赖实例的后悔保证。最后,我们研究了在这种情况下进行最佳手臂识别的问题。我们推导了错误概率下界,并开发了F-SR,这是一种基于几乎最优拒绝的算法,用于在给定时间预算的情况下识别最佳动作向量
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来源期刊
Artificial Intelligence
Artificial Intelligence 工程技术-计算机:人工智能
CiteScore
11.20
自引率
1.40%
发文量
118
审稿时长
8 months
期刊介绍: The Journal of Artificial Intelligence (AIJ) welcomes papers covering a broad spectrum of AI topics, including cognition, automated reasoning, computer vision, machine learning, and more. Papers should demonstrate advancements in AI and propose innovative approaches to AI problems. Additionally, the journal accepts papers describing AI applications, focusing on how new methods enhance performance rather than reiterating conventional approaches. In addition to regular papers, AIJ also accepts Research Notes, Research Field Reviews, Position Papers, Book Reviews, and summary papers on AI challenges and competitions.
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