Title: RBM-SVRG: A random-sampling based solver for optimal control problems with variance reduction
Speaker: Prof. Byungjoon Lee
Affiliation: The Catholic University of Korea

Abstract. In this talk, we introduce a new random-sampling based solver for optimal control problems with variance reduction technique, so called RBM-SVRG, inspired by Random Batch Method (RBM) and stochastic variance reduced gradient (SVRG). The proposed algorithm is based on the gradient descent method with adjoint states from Pontryagin’s maximum principle, which requires the computation of the controlled trajectory (forward dynamics) and its adjoint system. To reduce the computational costs on dynamics, we apply a random sampling on the forward dynamics, splitting into simpler randomized ones. Then, from the initial guess of the control, the update of the control function follows the gradient of the randomized cost function as in the stochastic gradient system. Then the variance reduction technique is applied to handle random error from approximation by random sampling. We showed that this optimization process converges to the optimal control of the original system for simple cases, i.e., linear-quadratic optimal control problems. Numerical simulations are also presented to validate the performance of the proposed method.
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