Particle Filtering for Stochastic Control and Global Optimization

提案编号：0901543该奖项由2009年美国复苏和再投资法案(公法111-5)资助。该项目的目标是通过从粒子滤波和非线性滤波的其他最新成果中获得的见解，在随机控制和全局优化领域提供新的突破。以粒子滤波方法的应用为重点，本研究将产生(I)计算高效的连续状态部分可观测马尔可夫决策过程和全局优化的新算法，以及(Ii)通过发展界和收敛证明对算法进行严格的分析。特别是，对于全局优化问题，粒子过滤框架可以通过提供坚实的分析基础来理解算法为什么工作得很好，算法何时崩溃，如何比较算法，哪种算法对特定问题比其他算法工作得更好，以及如何开发应该对特定问题工作得更好的新算法。要解决在大多数应用程序中发现的如此规模的难题，将需要重大的新方法。基于粒子滤波的方法将提供比其他方法更新的算法和严格的分析论证。Broader Impact随机控制和优化可以应用于美国工业中许多关键关注的问题，因此所得到的算法将具有广泛和变革性的适用性。在该项目中，它们将在从电信到制造业再到金融等行业的问题上进行测试。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.