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investigates the underlying control strategies and studies their sensitivity with respect to
model changes.
Since reinforcement learning and stochastic optimal control are the main frameworks
of this thesis, a complete presentation should incorporate views coming from different
communities of science and engineering. For this reason, in the next two sections we dis-cuss
the optimal control and reinforcement learning frameworks from the control theoretic
and machine learning point of view. In the last section of this introductory chapter we
provide an outline of this work with a short description of the structure and the contents
of each chapter.
1.2 Stochastic optimal control theory
Among the areas of control theory, optimal control is one of the most significant, with
a plethora of applications from the very early development of aerospace engineering, to
robotics, traffic control, biology and computational motor control. With respect to other
control theoretic frameworks, optimal control was the first to introduce optimization as
a method to find controls. In fact, optimal control can be thought as a constrained
optimization problem that has the characteristic that the constraints are not static, in
the sense of algebraic equations, but they correspond to dynamical systems and therefore
they are represented by differential equations. The addition of differential equations as
constraints in the optimization problem leads to the property that in optimal control
theory the minimum is not represented by one point x" in state space but by a trajectory
" " = (x"1
, x"2
..., x"N), which is the optimal trajectory.
3
Object Description
| Title | Iterative path integral stochastic optimal control: theory and applications to motor control |
| Author | Theodorou, Evangelos A. |
| Author email | etheodor@usc.edu; theo0027@umn.edu |
| Degree | Doctor of Philosophy |
| Document type | Dissertation |
| Degree program | Computer Science |
| School | Viterbi School of Engineering |
| Date defended/completed | 2011-01-11 |
| Date submitted | 2011 |
| Restricted until | Unrestricted |
| Date published | 2011-04-29 |
| Advisor (committee chair) | Schaal, Stefan |
| Advisor (committee member) |
Valero-Cuevas, Francisco Sukhatme, Gaurav S. Todorov, Emo Schweighofer, Nicolas |
| Abstract | Motivated by the limitations of current optimal control and reinforcement learning methods in terms of their efficiency and scalability, this thesis proposes an iterative stochastic optimal control approach based on the generalized path integral formalism. More precisely, we suggest the use of the framework of stochastic optimal control with path integrals to derive a novel approach to RL with parameterized policies. While solidly grounded in value function estimation and optimal control based on the stochastic Hamilton Jacobi Bellman (HJB) equation, policy improvements can be transformed into an approximation problem of a path integral which has no open algorithmic parameters other than the exploration noise. The resulting algorithm can be conceived of as model-based, semi-model-based, or even model free, depending on how the learning problem is structured. The new algorithm, Policy Improvement with Path Integrals (PI2), demonstrates interesting similarities with previous RL research in the framework of probability matching and provides intuition why the slightly heuristically motivated probability matching approach can actually perform well. Applications to high dimensional robotic systems are presented for a variety of tasks that require optimal planning and gain scheduling.; In addition to the work on generalized path integral stochastic optimal control, in this thesis we extend model based iterative optimal control algorithms to the stochastic setting. More precisely we derive the Differential Dynamic Programming algorithm for stochastic systems with state and control multiplicative noise. Finally, in the last part of this thesis, model based iterative optimal control methods are applied to bio-mechanical models of the index finger with the goal to find the underlying tendon forces applied for the movements of, tapping and flexing. |
| Keyword | stochastic optimal control; reinforcement learning,; robotics |
| Language | English |
| Part of collection | University of Southern California dissertations and theses |
| Publisher (of the original version) | University of Southern California |
| Place of publication (of the original version) | Los Angeles, California |
| Publisher (of the digital version) | University of Southern California. Libraries |
| Provenance | Electronically uploaded by the author |
| Type | texts |
| Legacy record ID | usctheses-m3804 |
| Contributing entity | University of Southern California |
| Rights | Theodorou, Evangelos A. |
| Repository name | Libraries, University of Southern California |
| Repository address | Los Angeles, California |
| Repository email | cisadmin@lib.usc.edu |
| Filename | etd-Theodorou-4581 |
| Archival file | uscthesesreloadpub_Volume14/etd-Theodorou-4581.pdf |
Description
| Title | Page 17 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | investigates the underlying control strategies and studies their sensitivity with respect to model changes. Since reinforcement learning and stochastic optimal control are the main frameworks of this thesis, a complete presentation should incorporate views coming from different communities of science and engineering. For this reason, in the next two sections we dis-cuss the optimal control and reinforcement learning frameworks from the control theoretic and machine learning point of view. In the last section of this introductory chapter we provide an outline of this work with a short description of the structure and the contents of each chapter. 1.2 Stochastic optimal control theory Among the areas of control theory, optimal control is one of the most significant, with a plethora of applications from the very early development of aerospace engineering, to robotics, traffic control, biology and computational motor control. With respect to other control theoretic frameworks, optimal control was the first to introduce optimization as a method to find controls. In fact, optimal control can be thought as a constrained optimization problem that has the characteristic that the constraints are not static, in the sense of algebraic equations, but they correspond to dynamical systems and therefore they are represented by differential equations. The addition of differential equations as constraints in the optimization problem leads to the property that in optimal control theory the minimum is not represented by one point x" in state space but by a trajectory " " = (x"1 , x"2 ..., x"N), which is the optimal trajectory. 3 |
