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w =
A
XTX
B−1
XTY (5.16)
where the matrix X and the vector Y are defined as follows:
X =
8
999999:
')p
?
u(1)
i |x(1)
i ; )
@T
, 1
... ...
')p
?
u(M)
i |x(M)
i ; )
@T
, 1
;
<<<<<<=
and Y =
8
999999:
CN−1
i=1 r(x(1)
i , u(1)
i )
...
CN−1
i=1 r(x(M)
i , u(M)
i )
;
<<<<<<=
To find the parameter vector w ! "n×1, there must be M > n number of trajectories
rollouts such that the matrix XTX is full rank and therefore invertible . With the episodic
Natural Actor Critic we will conclude our presentation of PG methods. In the next section
we discuss the application and comparison of PGs on a LQR optimal control problem.
5.5 Discussion
In this chapter we have reviewed the PG methods with the derivation of estimated corre-sponding
gradients. The work on PG methods for reinforcement learning was an impor-tant
advancement since it offered an alternative approach to optimal control problems
in which either no model is available, or if there is a model, it is a bad approximation.
Besides the their advantages, PG methods are in general, not easy to tune since they
are very sensitive to exploration noise as well as the cost function design. In the next
chapter we compare the PG methods with iterative path integral optimal control in via
point tasks.
179
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 193 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | w = A XTX B−1 XTY (5.16) where the matrix X and the vector Y are defined as follows: X = 8 999999: ')p ? u(1) i |x(1) i ; ) @T , 1 ... ... ')p ? u(M) i |x(M) i ; ) @T , 1 ; <<<<<<= and Y = 8 999999: CN−1 i=1 r(x(1) i , u(1) i ) ... CN−1 i=1 r(x(M) i , u(M) i ) ; <<<<<<= To find the parameter vector w ! "n×1, there must be M > n number of trajectories rollouts such that the matrix XTX is full rank and therefore invertible . With the episodic Natural Actor Critic we will conclude our presentation of PG methods. In the next section we discuss the application and comparison of PGs on a LQR optimal control problem. 5.5 Discussion In this chapter we have reviewed the PG methods with the derivation of estimated corre-sponding gradients. The work on PG methods for reinforcement learning was an impor-tant advancement since it offered an alternative approach to optimal control problems in which either no model is available, or if there is a model, it is a bad approximation. Besides the their advantages, PG methods are in general, not easy to tune since they are very sensitive to exploration noise as well as the cost function design. In the next chapter we compare the PG methods with iterative path integral optimal control in via point tasks. 179 |
