Regularizing Sampled Differential Dynamic Programming

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Abstract

Sampled Differential Dynamic Programming (SaDDP) is a recent Monte Carlo version of the widely used Differential Dynamic Programming (DDP). Very much like any algorithm based on DDP, the sampled version also requires regularization in order to work. The method makes heavy use of covariance matrices, for which we need to ensure positive definiteness. We present and compare different ways to regularize the covariance matrices. We also derive bounds for selecting the regularization parameters such that the condition number of each covariance matrix stays below a pre-chosen maximum. Our tests indicate that there is little difference in the convergence properties of the different algorithms. However, the possibility of divergence can be alleviated by two of the regularization techniques presented in this paper. Our tests furthermore show that the closed-loop regularization and rank-one updates in SaDDP are actually detrimental, when the covariance matrices are properly regularized.

Details

Original languageEnglish
Title of host publication2018 Annual American Control Conference, ACC 2018
Publication statusPublished - 9 Aug 2018
MoE publication typeA4 Article in a conference publication
EventAmerican Control Conference - Milwauke, United States
Duration: 27 Jun 201829 Jun 2018

Conference

ConferenceAmerican Control Conference
Abbreviated titleACC
CountryUnited States
CityMilwauke
Period27/06/201829/06/2018

ID: 28318474