代理对世界的表示中的行动代数

IF 4.6 2区 计算机科学 Q1 COMPUTER SCIENCE, ARTIFICIAL INTELLIGENCE
Alexander Dean, Eduardo Alonso, Esther Mondragón
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引用次数: 0

摘要

学习高效表示允许对数据进行稳健处理,然后可以将数据推广到不同的任务和领域,因此它在人工智能的各个领域至关重要,包括计算机视觉、自然语言处理和强化学习等。在强化学习的背景下,我们在本文中提出了一个数学框架,通过从代理的角度提取世界变换的代数来学习表征。作为起点,我们使用我们的框架从[1]提出的基于对称的解纠缠表示学习(SBDRL)形式主义中再现表示,并证明尽管它们有用,但它们仅限于响应代数群性质的变换。然后,我们推广了SBDRL的两个重要结果——等方差条件和解纠集定义——从仅处理基于群的对称表示到处理捕获任何代数世界变换属性的表示,使用强化学习中常见的示例,并由计算相应Cayley表的算法生成。最后,我们将广义等方差条件和广义解纠缠定义结合起来,证明了解纠缠子代数可以有各自独立的等方差条件,这些条件可以用范畴论独立处理。通过这样做,我们的框架提供了一个丰富的形式化工具来表示强化学习中不同类型的对称变换,扩展了以前建议的范围,并为人工智能开发人员提供了实现高效应用的良好基础。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Algebras of actions in an agent's representations of the world
Learning efficient representations allows robust processing of data, data that can then be generalised across different tasks and domains, and it is thus paramount in various areas of Artificial Intelligence, including computer vision, natural language processing and reinforcement learning, among others. Within the context of reinforcement learning, we propose in this paper a mathematical framework to learn representations by extracting the algebra of the transformations of worlds from the perspective of an agent. As a starting point, we use our framework to reproduce representations from the symmetry-based disentangled representation learning (SBDRL) formalism proposed by [1] and prove that, although useful, they are restricted to transformations that respond to the properties of algebraic groups. We then generalise two important results of SBDRL –the equivariance condition and the disentangling definition– from only working with group-based symmetry representations to working with representations capturing the transformation properties of worlds for any algebra, using examples common in reinforcement learning and generated by an algorithm that computes their corresponding Cayley tables. Finally, we combine our generalised equivariance condition and our generalised disentangling definition to show that disentangled sub-algebras can each have their own individual equivariance conditions, which can be treated independently, using category theory. In so doing, our framework offers a rich formal tool to represent different types of symmetry transformations in reinforcement learning, extending the scope of previous proposals and providing Artificial Intelligence developers with a sound foundation to implement efficient applications.
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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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