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it increases gains when needed, but tries to maintain low gain control otherwise. The
optimal reference trajectory always fulfilled the task goal. Learning speed was rather fast,
i.e., within at most a few hun- dred trials, the task objective was accomplished. From a
machine learning point of view, this performance of a reinforcement learning algorithm
is very fast. The PI2 algorithms inherits the properties of all trajectory-based learning
algorithms in that it only finds locally optimal solutions. For high dimensional robotic
system, this is unfortunately all one can hope for, as exploring the entire state- action
space in search for a globally optimal solution is impossible.
We continue our discussion in the next subsections with some issues that deserve more
detailed discussions.
6.8.1 Simplifications of PI2.
In this section we discuss simplifications of PI2. The discussions starts with research
directions that may allows us to remove the assumption between control weight matrix
and variance of the noise. Moreover, we show how PI2 could be used as model based,
semi model based of model free way. Finally, we discuss some rules for cost function
design as well as how PI2 handles hidden states in the state vector and arbitrary states
in the cost function.
6.8.2 The assumption !R−1 = "!
In order to obtain linear 2nd order differential equations for the exponentially transformed
HJB equations, the simplification %R−1 = !! was applied. Essentially, this assumption
couples the control cost to the stochasticity of the system dynamics, i.e., a control with
219
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 233 |
| Contributing entity | University of Southern California |
| Repository email | cisadmin@lib.usc.edu |
| Full text | it increases gains when needed, but tries to maintain low gain control otherwise. The optimal reference trajectory always fulfilled the task goal. Learning speed was rather fast, i.e., within at most a few hun- dred trials, the task objective was accomplished. From a machine learning point of view, this performance of a reinforcement learning algorithm is very fast. The PI2 algorithms inherits the properties of all trajectory-based learning algorithms in that it only finds locally optimal solutions. For high dimensional robotic system, this is unfortunately all one can hope for, as exploring the entire state- action space in search for a globally optimal solution is impossible. We continue our discussion in the next subsections with some issues that deserve more detailed discussions. 6.8.1 Simplifications of PI2. In this section we discuss simplifications of PI2. The discussions starts with research directions that may allows us to remove the assumption between control weight matrix and variance of the noise. Moreover, we show how PI2 could be used as model based, semi model based of model free way. Finally, we discuss some rules for cost function design as well as how PI2 handles hidden states in the state vector and arbitrary states in the cost function. 6.8.2 The assumption !R−1 = "! In order to obtain linear 2nd order differential equations for the exponentially transformed HJB equations, the simplification %R−1 = !! was applied. Essentially, this assumption couples the control cost to the stochasticity of the system dynamics, i.e., a control with 219 |
