论文标题
在部分观察到的线性动态系统中，粒子过滤何时有效地计划？
When is Particle Filtering Efficient for Planning in Partially Observed Linear Dynamical Systems?
论文作者
论文摘要
粒子过滤是一种流行的方法，用于推断随机动力学系统中的潜在状态，其理论特性在机器学习和统计社区中进行了很好的研究。在许多控制问题中，例如，部分观察到的线性动力学系统（polds），通常会在每个步骤中进一步使用推断的潜在状态。本文启动了一项严格的研究粒子过滤效率以进行顺序规划，并给出了第一个粒子复杂性界限。尽管过去动作中的错误可能会影响未来，但我们能够绑定所需的粒子数量，以便基于粒子过滤的策略的长期奖励基于精确的推论接近该奖励。特别是，我们表明，在稳定的系统中，多个粒子就足够了。我们证明的关键是基于基于粒子过滤的近似计划而产生的理想序列的耦合。我们认为，该技术在其他顺序决策问题中很有用。
Particle filtering is a popular method for inferring latent states in stochastic dynamical systems, whose theoretical properties have been well studied in machine learning and statistics communities. In many control problems, e.g., partially observed linear dynamical systems (POLDS), oftentimes the inferred latent state is further used for planning at each step. This paper initiates a rigorous study on the efficiency of particle filtering for sequential planning, and gives the first particle complexity bounds. Though errors in past actions may affect the future, we are able to bound the number of particles needed so that the long-run reward of the policy based on particle filtering is close to that based on exact inference. In particular, we show that, in stable systems, polynomially many particles suffice. Key in our proof is a coupling of the ideal sequence based on the exact planning and the sequence generated by approximate planning based on particle filtering. We believe this technique can be useful in other sequential decision-making problems.
