TY - JOUR

T1 - Discrete-Time Stochastic LQR via Path Integral Control and Its Sample Complexity Analysis

AU - Patil, Apurva

AU - Hanasusanto, Grani A.

AU - Tanaka, Takashi

N1 - Publisher Copyright:
© 2017 IEEE.

PY - 2024

Y1 - 2024

N2 - In this letter, we derive the path integral control algorithm to solve a discrete-time stochastic Linear Quadratic Regulator (LQR) problem and carry out its sample complexity analysis. While the stochastic LQR problem can be efficiently solved by the standard backward Riccati recursion, our primary focus in this letter is to establish the foundation for a sample complexity analysis of the path integral method when the analytical expressions of optimal control law and the cost are available. Specifically, we derive a bound on the error between the optimal LQR input and the input computed by the path integral method as a function of the sample size. Our analysis reveals that the sample size required exhibits a logarithmic dependence on the dimension of the control input. Lastly, we formulate a chance-constrained optimization problem whose solution quantifies the worst-case control performance of the path integral approach.

AB - In this letter, we derive the path integral control algorithm to solve a discrete-time stochastic Linear Quadratic Regulator (LQR) problem and carry out its sample complexity analysis. While the stochastic LQR problem can be efficiently solved by the standard backward Riccati recursion, our primary focus in this letter is to establish the foundation for a sample complexity analysis of the path integral method when the analytical expressions of optimal control law and the cost are available. Specifically, we derive a bound on the error between the optimal LQR input and the input computed by the path integral method as a function of the sample size. Our analysis reveals that the sample size required exhibits a logarithmic dependence on the dimension of the control input. Lastly, we formulate a chance-constrained optimization problem whose solution quantifies the worst-case control performance of the path integral approach.

KW - Path integral control

KW - sample complexity bound

KW - worst-case control performance

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U2 - 10.1109/LCSYS.2024.3413869

DO - 10.1109/LCSYS.2024.3413869

M3 - Article

AN - SCOPUS:85196073409

SN - 2475-1456

VL - 8

SP - 1595

EP - 1600

JO - IEEE Control Systems Letters

JF - IEEE Control Systems Letters

ER -