Particle Filtering for Stochastic Control and Global Optimization

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。该计划的目标是通过从粒子滤波和非线性滤波的最新结果中获得的见解，在随机控制和全局优化领域提供新的突破。重点是应用粒子滤波方法，提出的研究将导致(i)新的计算效率算法，用于连续状态部分可观察马尔可夫决策过程和全局优化，以及（ii）通过发展边界和收敛证明对算法进行严格分析。特别是，对于全局优化问题，粒子滤波框架可以通过提供坚实的分析基础来理解为什么算法工作良好，算法何时失效，如何比较算法，哪种算法在特定问题上比其他算法更好，以及如何开发适用于特定问题的新算法，从而证明具有变革性。部分可观察随机控制和全局优化是具有许多理论挑战和许多潜在应用的领域。要解决在大多数应用程序中发现的规模较大的难题，将需要重要的新方法。所提出的基于粒子滤波的方法将提供新的算法和严格的分析证明，而不是其他方法。更广泛的影响随机控制和优化可以应用于美国工业中许多关键问题，因此所得算法将具有广泛和变革性的适用性。在这个项目中，他们将在从电信到制造业到金融等行业的问题上接受测试。该项目将紧密结合博士生的培养。

Proposal Number: 0901543This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).Objective The objective of this program is to provide new breakthroughs in the areas of stochastic control and global optimization through insights gained from particle filtering and from additional recent results in nonlinear filtering. With a focus on applying the particle filtering methodology, the proposed research will result in (i) new computationally efficient algorithms for continuous-state partially observable Markov decision processes and global optimization, and (ii) rigorous analysis of the algorithms through the development of bounds and convergence proofs. In particular, for global optimization problems, the particle filtering framework can prove transformative by providing a firm analytical basis for understanding why algorithms work well, when algorithms break down, how to compare algorithms, which algorithm works better than the others for a specific problem, and how to develop new algorithms that should work well for particular problems.Intellectual meritPartially observable stochastic control and global optimization are areas with many theoretical challenges and many potential applications. To attack difficult problems of a size that are found in most applications will require significant new methodologies. The proposed approach based on particle filtering will provide new algorithms and rigorous analytical justification beyond that available with other methods.Broader impacts Stochastic control and optimization can be applied to many problems of critical concern in US industry, so the resulting algorithms will have broad and transformative applicability. In the project, they will be tested on problems in industries from telecommunications to manufacturing to finance. The project will closely integrate the training of PhD students.