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Constructing skill trees
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Constructing skill trees : ウィキペディア英語版
Constructing skill trees

Constructing skill trees (CST) is a hierarchical reinforcement learning algorithm which can build skill trees from a set of sample solution trajectories obtained from demonstration. CST uses an incremental MAP(maximum a posteriori ) change point detection algorithm to segment each demonstration trajectory into skills and integrate the results into a skill tree. CST was introduced by George Konidaris, Scott Kuindersma, Andrew Barto and Roderic Grupen in 2010.
==Algorithm==
CST consists of mainly three parts;change point detection, alignment and merging. The main focus of CST is online change-point detection. The change-point detection algorithm is used to segment data into skills and uses the sum of discounted reward R_t^. A linear regression model with Gaussian noise is used to compute P(j,t,q)^, \frac). The prior for each weight follows Normal^ \delta) .
The fit probability P(j,t,q)^}}\left|(A+D)^\right|^}\frac}}}}\frac)}})}

Then, CST compute the probability of the changepoint at time j with model q, P^_j


P^_=\max_\frac, \forall j
The descriptions of the parameters and variables are as follows;

A=\sum^t_\Phi(x_i)\Phi(x_i)^T


\Phi(x_i)^R^2_)-b^T(A+D)^b


b=\sum^t_R_i\Phi(x_i)


R_i=\sum^T_\gamma^r_

\Gamma^_: The number of basis functions q has.
D^ on the diagonal and zeros else where
The skill length l is assumed to follow a Geometric distribution with parameter p

g^p


G^_

k^{}_{}: Expected skill length
Using the method above, CST can segment data into a skill chain. The time complexity of the change point detection is O(NL) and storage size is O(Nc), where N is the number of particles, L is the time of computing P(j,t,q), and there are O(c) change points.
Next step is alignment. CST needs to align the component skills because the change-point does not occur in the exactly same places. Thus, when segmenting second trajectory after segmenting the first trajectory, it has a bias on the location of change point in the second trajectory. This bias follows a mixture of gaussians.
The last step is merging. CST merges skill chains into a skill tree. CST merges a pair of trajectory segments by allocating the same skill. All trajectories have the same goal and it merges two chains by starting at their final segments. If two segments are statistically similar, it merges them. This procedure is repeated until it fails to merge a pair of skill segments. P(j,t,q) are used to determine whether a pair of trajectories are modeled better as one skill or as two different skills.

抄文引用元・出典: フリー百科事典『 ウィキペディア(Wikipedia)
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