Next Friday June 28, 2024:
Organized by: FAU DCN-AvH, Chair for Dynamics, Control, Machine Learning and Numerics – Alexander von Humboldt Professorship at FAU, Friedrich-Alexander-Universität Erlangen-Nürnberg (Germany)
14:00H
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
Slides
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.
14:30H
Title: Convergence of Consensus-Based Optimization (CBO) with Random Batch Interactions
Speaker: Prof. Dongnam Ko
Affiliation: The Catholic University of Korea
Slides
Abstract. In this talk, we analyze the convergence of the consensus-based optimization (CBO) algorithm. This includes the analysis with heterogeneous noise and general interaction network, for example, random batch method. Despite successful performance of CBO in many practical simulations, the analysis confined in kinetic level. This is the first result on the convergence of this algorithm. We start introducing previous formulations and results on CBO models, and then derive stochastic convergence of individual candidate positions to a common point in mean-squre and almost-sure sense under small noise assumption. The analysis uses the concept of ergodicity in stochastic matrix theory. Numerical simulations are also presented to compare convergence speed between different parameters.
WHEN
Fri. June 28, 2024 at 14:00H
WHERE
On-site: Room 0.151-115 Seminarraum
Elektrotechnik. Friedrich-Alexander-Universität Erlangen-Nürnberg
Cauerstraße 7/9, 91058 Erlangen
GPS-Koord. Raum: 49.573087N, 11.028468E
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