Symmetry reduction for dynamic programming and application to MRI

John Maidens , Axel Barrau (1) , Silvère Bonnabel (2) , Murat Arcak

1 Safran Tech
2 CAOR - Centre de Robotique

— We present a method of exploiting symmetries of discrete-time optimal control problems to reduce the dimen-sionality of dynamic programming iterations. The results are derived for systems with continuous state variables, and can be applied to systems with continuous or discrete symmetry groups. We prove that symmetries of the state update equation and stage costs induce corresponding symmetries of the optimal cost function and the optimal policies. Thus symmetries can be exploited to allow dynamic programming iterations to be performed in a reduced state space. The application of these results is illustrated using a model of spin dynamics for magnetic resonance imaging (MRI). For this application problem, the symmetry reduction introduced leads to a significant speedup, reducing computation time by a factor of 75×.

Domaines: Sciences de l'ingénieur [physics]; Sciences de l'ingénieur [physics]; Automatique / Robotique; Sciences de l'ingénieur [physics]; Traitement du signal et de l'image [eess.SP]

John Maidens, Axel Barrau, Silvère Bonnabel, Murat Arcak. Symmetry reduction for dynamic programming and application to MRI. 2017 American Control Conference (ACC), May 2017, Seattle, France. ⟨10.23919/ACC.2017.7963669⟩. ⟨hal-01695778⟩