EAGER: Robust Reasoning using a Geometric Approach to SAT and PSAT

EAGER：使用几何方法进行 SAT 和 PSAT 的稳健推理

• 批准号: 2152454
• 负责人: Thomas Henderson
• 金额: $ 9.92万
• 依托单位: University of Utah
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-04-01 至 2023-09-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2152454&HistoricalAwards=false
• 关键词: EAGER; Robust; Reasoning; using; Geometric

The overarching goal of this EAGER project is to develop efficient and reliable methods for autonomous agents to produce plans for their safe operation in complex situations. For example, the development of large-scale unmanned aircraft system operation in urban areas for package delivery depends on such a capability. The fundamental issue is to determine if there is a viable solution in a specific situation; at the present time the complexity of this problem is too high to guarantee that a solution can be found. The team of researchers is developing a lower complexity approach with wide application in artificial intelligence. The project engages student researchers from underrepresented groups in computer science, and the research results are integrated into the classroom through courses like artificial intelligence, theory of computation, and autonomous agent systems.The project provides a new approach to agent planning at the cognitive level. The basic innovation is to convert the satisfiability problem into a geometric setting; in particular, the models of an n-variable logical sentence are viewed as the corners of an n-D hypercube, and interior points assign probabilities to the variables. Each conjunct in the conjunctive normal form sentence reduces the convex feasible solution region. Any non-empty feasible region indicates the existence of a solution to the probabilistic satisfiability problem and can also be probed with linear programming methods in polynomial time to seek an answer to the satisfiability problem. Particular approaches to be explored include: (1) modifications to the interior point method using barrier methods, (2) finding linear programming solutions in a non-Euclidean geometry, (3) applying random rotations to the feasible region to allow coordinate projects to determine if there is a solution, and (4) using Markov Chain Monte Carlo to get a point near a corner. Applications include probabilistic satisfiability inference, reinforcement policy optimization for autonomous agents, and probabilistic temporal logic.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

该 EAGER 项目的总体目标是为自主代理开发高效可靠的方法，以制定在复杂情况下安全运行的计划。例如，发展大型无人机系统在城市地区运行包裹投递就依赖于这样的能力。根本问题是确定在特定情况下是否有可行的解决方案；目前这个问题的复杂性太高，无法保证找到解决方案。研究人员团队正在开发一种复杂性较低的方法，可在人工智能领域广泛应用。该项目吸引了来自计算机科学领域代表性不足群体的学生研究人员，并将研究成果通过人工智能、计算理论和自主代理系统等课程融入课堂。该项目为认知层面的代理规划提供了一种新方法。基本创新是将可满足性问题转化为几何设置；特别是，n 变量逻辑句子的模型被视为 n 维超立方体的角，内部点将概率分配给变量。连接范式句子中的每个连接都会减少凸可行解区域。任何非空可行区域都表明存在概率可满足性问题的解，并且也可以在多项式时间内用线性规划方法进行探测，以寻求可满足性问题的答案。需要探索的具体方法包括：（1）使用障碍法对内点法进行修改，（2）在非欧几里得几何中寻找线性规划解决方案，（3）对可行区域应用随机旋转以允许坐标项目确定如果有解，（4）使用马尔可夫链蒙特卡罗得到靠近角点的点。应用包括概率可满足性推理、自主代理的强化策略优化和概率时序逻辑。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力优点和更广泛的影响审查标准进行评估，被认为值得支持。