Stochastic functional laws of the iterated logarithm with applications to learning and control

Xinjia Chen

doi:10.1117/12.2517390

13 May 2019 Stochastic functional laws of the iterated logarithm with applications to learning and control

Xinjia Chen

Proceedings Volume 11021, Unmanned Systems Technology XXI; 110210T (2019) https://doi.org/10.1117/12.2517390
Event: SPIE Defense + Commercial Sensing, 2019, Baltimore, MD, United States

Abstract

Modern intelligent systems highly depends on their capabilities to learn from experience and take control actions in uncertain environments. In this paper, we propose a random walk approach for analyzing the performance of learning and control of intelligent systems. We show that in many situations, the learning and control problem can be formulated as a random walk in a hyperspace with stopping boundary defined by parameters of learning and control policies. We show that the performance of the intelligent systems can be measured by a function of the stopping time and associated values of stochastic processes. Under some mild regularity conditions, we demonstrate that the performance measure follows stochastic functional laws of the iterated logarithm as the parameters of learning and control policies tend to certain values.

Citation Download Citation

Xinjia Chen "Stochastic functional laws of the iterated logarithm with applications to learning and control", Proc. SPIE 11021, Unmanned Systems Technology XXI, 110210T (13 May 2019); https://doi.org/10.1117/12.2517390

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