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deterministic variable and therefore can be ignored since it is the same for all sampled
paths. We also absorbed, without loss of generality, the time step dt in cost terms. Con-sequently,
the fundamental result of the path integral stochastic optimal problem for the
case of DMPs is expressed as:
uti =
F
P (" i) u (" i) d" (c)
i (6.13)
where the probability P (" i) and local controls u (" i) are defined as
P (" i) =
e−1
"
˜ S(" i)
F
e−1
"
˜ S(" i)d" i
, u(" i) =
R−1g(c)
ti g(c)T
ti
g(c)T
ti R−1g(c)
ti
!ti (6.14)
and the path cost given as
˜ S(" i) = &tN +
N>−1
j=i
qtj +
1
2
N>−1
j=i
!Tt
jMTt
jRMtj !tj (6.15)
Note that ) = 0 in these equations, i.e., the parameters are initialized to zero. These
equations correspond to the case where the stochastic optimal control problem is solved
with one evaluation of the optimal controls (6.13) using dense sampling of the whole state
space under the “passive dynamics” (i.e., ) = 0), which requires a significant amount of
exploration noise. Such an approach was pursued in the original work by (Kappen 2007,
Broek et al. 2008), where a potentially large number of sample trajectories was needed
to achieve good results. Extending this sampling approach to high dimensional spaces,
however, is daunting, as with very high probablity, we would sample primarily rather
187
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 201 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | deterministic variable and therefore can be ignored since it is the same for all sampled paths. We also absorbed, without loss of generality, the time step dt in cost terms. Con-sequently, the fundamental result of the path integral stochastic optimal problem for the case of DMPs is expressed as: uti = F P (" i) u (" i) d" (c) i (6.13) where the probability P (" i) and local controls u (" i) are defined as P (" i) = e−1 " ˜ S(" i) F e−1 " ˜ S(" i)d" i , u(" i) = R−1g(c) ti g(c)T ti g(c)T ti R−1g(c) ti !ti (6.14) and the path cost given as ˜ S(" i) = &tN + N>−1 j=i qtj + 1 2 N>−1 j=i !Tt jMTt jRMtj !tj (6.15) Note that ) = 0 in these equations, i.e., the parameters are initialized to zero. These equations correspond to the case where the stochastic optimal control problem is solved with one evaluation of the optimal controls (6.13) using dense sampling of the whole state space under the “passive dynamics” (i.e., ) = 0), which requires a significant amount of exploration noise. Such an approach was pursued in the original work by (Kappen 2007, Broek et al. 2008), where a potentially large number of sample trajectories was needed to achieve good results. Extending this sampling approach to high dimensional spaces, however, is daunting, as with very high probablity, we would sample primarily rather 187 |
