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dependent noise. This is computationally costly because second order derivatives have
to be calculated. An important aspect of stochastic optimal control theory is that, in
cases of additive noise, the optimal control u" and the optimal control gains L are both
independent of the noise and, therefore, the same with the corresponding deterministic
solution. In cases where the noise is control or state dependent, the resulting solutions
iLQG and SDDP differ from the solutions of the deterministic versions iLQR and DDP.
In the table 2.1 we provide the classification of the optimal control algorithms based on
the expansion of dynamics and cost function as well as the existence of noise.
2.3.1 Stochastic differential dynamic programming
We consider the class of nonlinear stochastic optimal control problems with cost
v#(x, t) =
!
h(x(T)) +
" T
t0
+ (', x(' ), ,(', x(' ))) d'
#
(2.29)
subject to the stochastic dynamics of the form:
dx = f(x, u)dt + F(x, u)dw (2.30)
where x ! "n×1 is the state, u ! "m×1 is the control and dw ! "p×1 is brownian
noise. The term h(x(T)) in the cost function (2.29), is the terminal cost while the
+ (', x(' ), ,(', x(' ))) is the instantaneous cost rate which is a function of the state x
and control policy ,(', x(' )). The cost-to - go v#(x, t) is defined as the expected cost
23
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 37 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | dependent noise. This is computationally costly because second order derivatives have to be calculated. An important aspect of stochastic optimal control theory is that, in cases of additive noise, the optimal control u" and the optimal control gains L are both independent of the noise and, therefore, the same with the corresponding deterministic solution. In cases where the noise is control or state dependent, the resulting solutions iLQG and SDDP differ from the solutions of the deterministic versions iLQR and DDP. In the table 2.1 we provide the classification of the optimal control algorithms based on the expansion of dynamics and cost function as well as the existence of noise. 2.3.1 Stochastic differential dynamic programming We consider the class of nonlinear stochastic optimal control problems with cost v#(x, t) = ! h(x(T)) + " T t0 + (', x(' ), ,(', x(' ))) d' # (2.29) subject to the stochastic dynamics of the form: dx = f(x, u)dt + F(x, u)dw (2.30) where x ! "n×1 is the state, u ! "m×1 is the control and dw ! "p×1 is brownian noise. The term h(x(T)) in the cost function (2.29), is the terminal cost while the + (', x(' ), ,(', x(' ))) is the instantaneous cost rate which is a function of the state x and control policy ,(', x(' )). The cost-to - go v#(x, t) is defined as the expected cost 23 |
