When is Particle Filtering Efficient for Planning in Partially Observed Linear Dynamical Systems?

• URL: http://arxiv.org/abs/2006.05975v2
• Date: Fri, 9 Jul 2021 01:28:42 GMT
• Title: When is Particle Filtering Efficient for Planning in Partially Observed Linear Dynamical Systems?
• Authors: Simon S. Du, Wei Hu, Zhiyuan Li, Ruoqi Shen, Zhao Song, Jiajun Wu
• Abstract summary: This paper initiates a study on the efficiency of particle filtering for sequential planning. 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. We believe this technique can be useful in other sequential decision-making problems.
• Score: 60.703816720093016
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: 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.

Related papers

• Learning Optimal Filters Using Variational Inference [0.3749861135832072]
  We present a framework for learning a parameterized analysis map - the map that takes a forecast distribution and observations to the filtering distribution. We show that this methodology can be used to learn gain matrices for filtering linear and nonlinear dynamical systems. Future work will apply this framework to learn new filtering algorithms.
  arXiv  Detail & Related papers  (2024-06-26T04:51:14Z)
• Closed-form Filtering for Non-linear Systems [83.91296397912218]
  We propose a new class of filters based on Gaussian PSD Models, which offer several advantages in terms of density approximation and computational efficiency. We show that filtering can be efficiently performed in closed form when transitions and observations are Gaussian PSD Models. Our proposed estimator enjoys strong theoretical guarantees, with estimation error that depends on the quality of the approximation and is adaptive to the regularity of the transition probabilities.
  arXiv  Detail & Related papers  (2024-02-15T08:51:49Z)
• Nonlinear Filtering with Brenier Optimal Transport Maps [4.745059103971596]
  This paper is concerned with the problem of nonlinear filtering, i.e., computing the conditional distribution of the state of a dynamical system. Conventional sequential importance resampling (SIR) particle filters suffer from fundamental limitations, in scenarios involving degenerate likelihoods or high-dimensional states. In this paper, we explore an alternative method, which is based on estimating the Brenier optimal transport (OT) map from the current prior distribution of the state to the posterior distribution at the next time step.
  arXiv  Detail & Related papers  (2023-10-21T01:34:30Z)
• An overview of differentiable particle filters for data-adaptive sequential Bayesian inference [19.09640071505051]
  Particle filters (PFs) provide an efficient mechanism for solving non-linear sequential state estimation problems. An emerging trend involves constructing components of particle filters using neural networks and optimising them by gradient descent. Differentiable particle filters are a promising computational tool for performing inference on sequential data in complex, high-dimensional tasks.
  arXiv  Detail & Related papers  (2023-02-19T18:03:53Z)
• Monte Carlo Neural PDE Solver for Learning PDEs via Probabilistic Representation [59.45669299295436]
  We propose a Monte Carlo PDE solver for training unsupervised neural solvers. We use the PDEs' probabilistic representation, which regards macroscopic phenomena as ensembles of random particles. Our experiments on convection-diffusion, Allen-Cahn, and Navier-Stokes equations demonstrate significant improvements in accuracy and efficiency.
  arXiv  Detail & Related papers  (2023-02-10T08:05:19Z)
• Particle-Based Score Estimation for State Space Model Learning in Autonomous Driving [62.053071723903834]
  Multi-object state estimation is a fundamental problem for robotic applications. We consider learning maximum-likelihood parameters using particle methods. We apply our method to real data collected from autonomous vehicles.
  arXiv  Detail & Related papers  (2022-12-14T01:21:05Z)
• Continuous-time Particle Filtering for Latent Stochastic Differential Equations [37.51802583388233]
  We propose continuous latent particle filters, an approach that extends particle filtering to the continuous-time domain. We demonstrate how continuous latent particle filters can be used as a generic plug-in replacement for inference techniques relying on a learned variational posterior.
  arXiv  Detail & Related papers  (2022-09-01T01:05:31Z)
• Computational Doob's h-transforms for Online Filtering of Discretely Observed Diffusions [65.74069050283998]
  We propose a computational framework to approximate Doob's $h$-transforms. The proposed approach can be orders of magnitude more efficient than state-of-the-art particle filters.
  arXiv  Detail & Related papers  (2022-06-07T15:03:05Z)
• Deep Learning for the Benes Filter [91.3755431537592]
  We present a new numerical method based on the mesh-free neural network representation of the density of the solution of the Benes model. We discuss the role of nonlinearity in the filtering model equations for the choice of the domain of the neural network.
  arXiv  Detail & Related papers  (2022-03-09T14:08:38Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.