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noticable fluctuation after convergence. This noise around the convergence baseline is
caused by using only two noisy roll-outs to continue updating the parameters, which
causes continuous parameter fluctuations around the optimal parameters. Annealing the
exploration noise, or just adding the optimal trajectory from the previous parameter
update as one of the roll-outs for the next parameter update can alleviate this issue – we
do not illustrate such little “tricks” in this paper as they really only affect fine tuning of
the algorithm.
6.4.2 Learning optimal performance of a 1 DOF via-point task
The second evaluation was identical to the first evaluation, just that the cost function
now forced the movement to pass through an intermediate via-point at t = 300ms. This
evaluation is an abstract approximation of hitting a target, e.g., as in playing tennis, and
requires a significant change in how the movement is performed relative to the initial
trajectory (Figure 6.2a). The cost function was
r300ms = 100000000(G − yt300ms)2 &tN = 0 (6.29)
with G = 0.25. Only this single reward was given. For this cost function, the PoWER
algorithm can be applied, too, with cost function ˜r300ms = exp(−1/% r300ms) and ˜rti =
0 otherwise. This transformed cost function has the same optimum as r300ms. The
resulting learning curves are given in Figure 6.2 and resemble the previous evaluation:
PI2 outperforms the gradient algorithms by roughly an order of magnitude, while all
the gradient algorithms have almost identical learning curves. As was expected from the
196
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 210 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | noticable fluctuation after convergence. This noise around the convergence baseline is caused by using only two noisy roll-outs to continue updating the parameters, which causes continuous parameter fluctuations around the optimal parameters. Annealing the exploration noise, or just adding the optimal trajectory from the previous parameter update as one of the roll-outs for the next parameter update can alleviate this issue – we do not illustrate such little “tricks” in this paper as they really only affect fine tuning of the algorithm. 6.4.2 Learning optimal performance of a 1 DOF via-point task The second evaluation was identical to the first evaluation, just that the cost function now forced the movement to pass through an intermediate via-point at t = 300ms. This evaluation is an abstract approximation of hitting a target, e.g., as in playing tennis, and requires a significant change in how the movement is performed relative to the initial trajectory (Figure 6.2a). The cost function was r300ms = 100000000(G − yt300ms)2 &tN = 0 (6.29) with G = 0.25. Only this single reward was given. For this cost function, the PoWER algorithm can be applied, too, with cost function ˜r300ms = exp(−1/% r300ms) and ˜rti = 0 otherwise. This transformed cost function has the same optimum as r300ms. The resulting learning curves are given in Figure 6.2 and resemble the previous evaluation: PI2 outperforms the gradient algorithms by roughly an order of magnitude, while all the gradient algorithms have almost identical learning curves. As was expected from the 196 |
