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a) b)
c) d)
Figure 6.1: Comparison of reinforcement learning of an optimized movement with mo-tor
primitives. a) Position trajectories of the initial trajectory (before learning) and the
results of all algorithms after learning – the different algorithms are essentially indistu-ighishable.
b) The same as a), just using the velocity trajectories. c) Average learning
curves for the different algorithms with 1 std error bars from averaging 10 runs for each
of the algorithms. d) Learning curves for the different algorithms when only two roll-outs
are used per update (note that the eNAC cannot work in this case and is omitted).
learning results of the four different algorithms after learning – essentially, all algorithms
achieve the same result such that all trajectories lie on top of each other. In Figure 6.1c,
however, it can be seen that PI2 outperforms the gradient algorithms by an order of
magnitude. Figure 6.1d illustrates learning curves for the same task as in Figure 6.1c,
just that parameter updates are computed already after two roll-outs – the eNAC was
excluded from this evaluation as it would be too heuristic to stablize its ill-conditioned
matrix inversion that results from such few roll-outs. PI2 continues to converge much
faster than the other algorithms even in this special scenario. However, there are some
195
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 209 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | 0 500000 1000000 1500000 2000000 2500000 3000000 1 10 100 1000 10000 15000 Cost Number of Roll-Outs -0.2 0 0.2 0.4 0.6 0.8 1 0 0.1 0.2 0.3 0.4 0.5 Position [rad] Time [s] Initial PI^2 REINFORCE PG NAC -1 0 1 2 3 4 5 6 0 0.1 0.2 0.3 0.4 0.5 Velocity [rad/s] Time [s] 0 500000 1000000 1500000 2000000 2500000 3000000 1 10 100 1000 2000 Cost Number of Roll-Outs a) b) c) d) Figure 6.1: Comparison of reinforcement learning of an optimized movement with mo-tor primitives. a) Position trajectories of the initial trajectory (before learning) and the results of all algorithms after learning – the different algorithms are essentially indistu-ighishable. b) The same as a), just using the velocity trajectories. c) Average learning curves for the different algorithms with 1 std error bars from averaging 10 runs for each of the algorithms. d) Learning curves for the different algorithms when only two roll-outs are used per update (note that the eNAC cannot work in this case and is omitted). learning results of the four different algorithms after learning – essentially, all algorithms achieve the same result such that all trajectories lie on top of each other. In Figure 6.1c, however, it can be seen that PI2 outperforms the gradient algorithms by an order of magnitude. Figure 6.1d illustrates learning curves for the same task as in Figure 6.1c, just that parameter updates are computed already after two roll-outs – the eNAC was excluded from this evaluation as it would be too heuristic to stablize its ill-conditioned matrix inversion that results from such few roll-outs. PI2 continues to converge much faster than the other algorithms even in this special scenario. However, there are some 195 |
