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.

EAGER项目的首要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，在城市地区开发用于包裹递送的大规模无人驾驶飞机系统操作取决于这种能力。基本问题是确定在特定情况下是否存在可行的解决方案;目前这个问题的复杂性太高，无法保证可以找到解决方案。研究人员团队正在开发一种复杂性较低的方法，在人工智能中具有广泛的应用。该项目吸引了来自计算机科学领域代表性不足的学生研究人员，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。基本的创新是将可满足性问题转化为几何设置;特别是，将n变量逻辑句子的模型视为n维超立方体的角，内部点为变量分配概率。合取范式语句中的每一个合取都缩小了凸可行解区域。任何非空的可行域表明概率可满足性问题的解的存在，并且也可以用线性规划方法在多项式时间内探索以寻求可满足性问题的答案。要探索的具体方法包括：（1）使用障碍方法对内点方法进行修改，（2）在非欧几里德几何中找到线性规划解，（3）对可行区域应用随机旋转以允许坐标投影来确定是否存在解，以及（4）使用马尔可夫链蒙特卡罗来获得角附近的点。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态逻辑。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。