Stochastic Optimal Control of Spike Times in Single Neurons

TY - CHAP

T1 - Stochastic Optimal Control of Spike Times in Single Neurons

AU - Iolov, A.

AU - Ditlevsen, S.

AU - Longtin, A.

PY - 2016/9/29

Y1 - 2016/9/29

N2 - We consider the application of optimal control techniques to stochastic models of neural firing. There can be many goals for such control. Here we focus on the targeting of the spiking times of the cell, using a time-varying current applied additively to the current balance equation.We review the theory behind the maximum principle for stochastic optimal control, as well as the challenges posed by its numerical implementation. We then discuss dynamic programming methods for such control, and illustrate its implementation for spike time targeting in the leaky integrate-and-fire model with additive Gaussian white noise. The technique is described in the context where the controller has access to the ongoing voltage. The case where only spike times are available is briefly discussed, along with an outlook into future challenges in designing controls for threshold crossing in drift-diffusion processes.

AB - We consider the application of optimal control techniques to stochastic models of neural firing. There can be many goals for such control. Here we focus on the targeting of the spiking times of the cell, using a time-varying current applied additively to the current balance equation.We review the theory behind the maximum principle for stochastic optimal control, as well as the challenges posed by its numerical implementation. We then discuss dynamic programming methods for such control, and illustrate its implementation for spike time targeting in the leaky integrate-and-fire model with additive Gaussian white noise. The technique is described in the context where the controller has access to the ongoing voltage. The case where only spike times are available is briefly discussed, along with an outlook into future challenges in designing controls for threshold crossing in drift-diffusion processes.

KW - Morris-Lecar model

KW - Noise

KW - Ornstein-Uhlenbeck process

KW - Single neuron

KW - Spike times

KW - Stochastic optimal control

UR - http://www.scopus.com/inward/record.url?scp=85021963937&partnerID=8YFLogxK

U2 - 10.1016/b978-0-12-802452-2.00008-1

DO - 10.1016/b978-0-12-802452-2.00008-1

M3 - Book chapter

AN - SCOPUS:85021963937

SN - 9780128024522

SP - 101

EP - 111

BT - Closed Loop Neuroscience

PB - Elsevier Science Inc.

ER -