Differential dynamic programming: Difference between revisions

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Sampled differential dynamic programming (SaDDP) is a Monte Carlo variant of differential dynamic programming.<ref>{{Cite journal|title=Sampled differential dynamic programming - IEEE Conference Publication|language=en-US|doi=10.1109/IROS.2016.7759229|s2cid=1338737}}</ref><ref>{{Cite journal|url=https://ieeexplore.ieee.org/document/8430799|title=Regularizing Sampled Differential Dynamic Programming - IEEE Conference Publication|website=ieeexplore.ieee.org|date=June 2018 |pages=2182–2189 |doi=10.23919/ACC.2018.8430799 |s2cid=243932441 |language=en-US|access-date=2018-10-19}}</ref><ref>{{Cite book|last=Joose|first=Rajamäki|date=2018|title=Random Search Algorithms for Optimal Control|url=http://urn.fi/URN:ISBN:978-952-60-8156-4|language=en|issn=1799-4942|isbn=9789526081564|publisher=Aalto University}}</ref> It is based on treating the quadratic cost of differential dynamic programming as the energy of a [[Boltzmann distribution]]. This way the quantities of DDP can be matched to the statistics of a [[Multivariate normal distribution|multidimensional normal distribution]]. The statistics can be recomputed from sampled trajectories without differentiation.

Sampled differential dynamic programming has been extended to Path Integral Policy Improvement with Differential Dynamic Programming.<ref>{{Cite journalbook|last1=Lefebvre|first1=Tom|last2=Crevecoeur|first2=Guillaume|datetitle=July 2019 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM) |titlechapter=Path Integral Policy Improvement with Differential Dynamic Programming |date=July 2019|chapter-url=https://ieeexplore.ieee.org/document/8868359|journal=2019 IEEE/ASME International Conference on Advanced Intelligent Mechatronics (AIM)|pages=739–745|doi=10.1109/AIM.2019.8868359|hdl=1854/LU-8623968|isbn=978-1-7281-2493-3|s2cid=204816072|url=https://biblio.ugent.be/publication/8623968 |hdl-access=free}}</ref> This creates a link between differential dynamic programming and path integral control,<ref>{{Cite journalbook|last1=Theodorou|first1=Evangelos|last2=Buchli|first2=Jonas|last3=Schaal|first3=Stefan|datetitle=May 2010 IEEE International Conference on Robotics and Automation |titlechapter=Reinforcement learning of motor skills in high dimensions: A path integral approach |date=May 2010|chapter-url=https://ieeexplore.ieee.org/document/5509336|journal=2010 IEEE International Conference on Robotics and Automation|pages=2397–2403|doi=10.1109/ROBOT.2010.5509336|isbn=978-1-4244-5038-1|s2cid=15116370}}</ref> which is a framework of stochastic optimal control.

== Constrained problems ==