TY - GEN

T1 - Deep FPF

T2 - 59th IEEE Conference on Decision and Control, CDC 2020

AU - Olmez, S. Yagiz

AU - Taghvaei, Amirhossein

AU - Mehta, Prashant G.

N1 - Funding Information:
Financial support from the NSF grant 1761622 and the ARO grant W911NF1810334 is gratefully acknowledged.

PY - 2020/12/14

Y1 - 2020/12/14

N2 - In this paper, we present a novel approach to approximate the gain function of the feedback particle filter (FPF). The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical problem is to approximate the exact gain function using only finitely many particles sampled from the probability distribution.Inspired by the recent success of the deep learning methods, we represent the gain function as a gradient of the output of a neural network. Thereupon considering a certain variational formulation of the Poisson equation, an optimization problem is posed for learning the weights of the neural network. A stochastic gradient algorithm is described for this purpose.The proposed approach has two significant properties/advantages: (i) The stochastic optimization algorithm allows one to process, in parallel, only a batch of samples (particles) ensuring good scaling properties with the number of particles; (ii) The remarkable representation power of neural networks means that the algorithm is potentially applicable and useful to solve high-dimensional problems. We numerically establish these two properties and provide extensive comparison to the existing approaches.

AB - In this paper, we present a novel approach to approximate the gain function of the feedback particle filter (FPF). The exact gain function is the solution of a Poisson equation involving a probability-weighted Laplacian. The numerical problem is to approximate the exact gain function using only finitely many particles sampled from the probability distribution.Inspired by the recent success of the deep learning methods, we represent the gain function as a gradient of the output of a neural network. Thereupon considering a certain variational formulation of the Poisson equation, an optimization problem is posed for learning the weights of the neural network. A stochastic gradient algorithm is described for this purpose.The proposed approach has two significant properties/advantages: (i) The stochastic optimization algorithm allows one to process, in parallel, only a batch of samples (particles) ensuring good scaling properties with the number of particles; (ii) The remarkable representation power of neural networks means that the algorithm is potentially applicable and useful to solve high-dimensional problems. We numerically establish these two properties and provide extensive comparison to the existing approaches.

UR - http://www.scopus.com/inward/record.url?scp=85099883736&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85099883736&partnerID=8YFLogxK

U2 - 10.1109/CDC42340.2020.9304260

DO - 10.1109/CDC42340.2020.9304260

M3 - Conference contribution

AN - SCOPUS:85099883736

T3 - Proceedings of the IEEE Conference on Decision and Control

SP - 4790

EP - 4795

BT - 2020 59th IEEE Conference on Decision and Control, CDC 2020

PB - Institute of Electrical and Electronics Engineers Inc.

Y2 - 14 December 2020 through 18 December 2020

ER -