25:
765:
1998:
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
2002:
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.
535:
113:
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
1139:
421:
760:{\displaystyle P(j,t,q)={\frac {\pi ^{-{\frac {n}{2}}}}{\delta ^{m}}}\left|(A+D)^{-1}\right|^{\frac {1}{2}}{\frac {u^{\frac {v}{2}}}{(y+u)^{\frac {u+v}{2}}}}{\frac {\Gamma ({\frac {n+v}{2}})}{\Gamma ({\frac {v}{2}})}}}
989:
1409:
1234:
1561:
483:
2243:
CTS assume that the demonstrated skills form a tree, the domain reward function is known and the best model for merging a pair of skills is the model selected for representing both individually.
1483:
2182:
p.A := zero matrix(p.m, p.m) p.b := zero vector(p.m) p.z := zero vector(p.m) p.sum r := 0 p.tr1 := 0 p.tr2 := 0
2255:. CST can be applied to learning higher dimensional policies. Even unsuccessful episode can improve skills. Skills acquired using agent-centric features can be used for other problems.
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p_tjq := (1 â G(t â p.pos â 1)) Ă p.fit_prob Ă model_prior(p.model) Ă p.prev_MAP p.MAP := p_tjq Ă g(tâp.pos) / (1 â G(t â p.pos â 1))
89:) change point detection algorithm to segment each demonstration trajectory into skills and integrate the results into a skill tree. CST was introduced by
338:
94:
90:
2281:
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85:
algorithm which can build skill trees from a set of sample solution trajectories obtained from demonstration. CST uses an incremental MAP (
862:
2307:
1308:
1150:
1489:
426:
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Using the method above, CST can segment data into a skill chain. The time complexity of the change point detection is
2134:
new_p := create_particle(model=q, pos=t, prev_MAP=max_MAP, path=max_path) p := p ∪ new_p
65:
2120:
p.MAP max_path := max_particle.path ∪ max_particle max_MAP := max_particle.MAP
2044:
are used to determine whether a pair of trajectories are modeled better as one skill or as two different skills.
1731:
1659:
47:
1806:
823:
2338:(2010). "Constructing Skill Trees for Reinforcement Learning Agents from Demonstration Trajectories".
250:
1134:{\displaystyle P_{j}^{\text{MAP}}=\max _{i,q}{\frac {P_{j}(i,q)g(j-i)}{1-G(j-i-1)}},\forall j<t}
43:
2267:
domain. It has been also used to acquire skills from human demonstration on a mobile manipulator.
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2353:(2009). "Skill discovery in continuous reinforcement learning domains using skill chaining".
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as the target regression variable. Each skill is assigned an appropriate abstraction. A
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2308:"Underrated But Fascinating ML Concepts #5 â CST, PBWM, SARSA, & Sammon Mapping"
2329:
148:
The change point detection algorithm is implemented as follows. The data for times
416:{\displaystyle \mathrm {InverseGamma} \left({\frac {v}{2}},{\frac {u}{2}}\right)}
142:
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particles := update_particle(current_state, current_reward, p)
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2003:
This procedure is repeated until it fails to merge a pair of skill segments.
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213:
are given. The algorithm is assumed to be able to fit a segment from time
98:
2053:
984:{\displaystyle P_{t}(j,q)=(1-G(t-j-1))P(j,t,q)p(q)P_{j}^{\text{MAP}}}
335:. The Gaussian noise prior has mean zero, and variance which follows
2263:
CST has been used to acquire skills from human demonstration in the
294:. A linear regression model with Gaussian noise is used to compute
2367:; Zhen Liu (2007). "On-line Inference for Multiple Change Points".
2235:
p.tr1 p.fit_prob := compute_fit_prob(p, v, u, delta, đŸ)
2218:
p.z p.tr1 := 1 + đŸ p.tr1 p.sum r := sum p.r + r
2264:
1144:
The descriptions of the parameters and variables are as follows;
1650:
is assumed to follow a
Geometric distribution with parameter
1404:{\displaystyle y=(\sum _{i=j}^{t}R_{i}^{2})-b^{T}(A+D)^{-1}b}
1229:{\displaystyle A=\sum _{i=j}^{t}\Phi (x_{i})\Phi (x_{i})^{T}}
770:
Then, CST compute the probability of the changepoint at time
2187:// Compute the basis function vector for the current state
2167:
update_particle(current_state, current_reward, particle)
2067://Compute fit probabilities for all particles
145:
is used to control the computational complexity of CST.
1556:{\displaystyle R_{i}=\sum _{j=i}^{T}\gamma ^{j-i}r_{j}}
478:{\displaystyle \mathrm {Normal} (0,\sigma ^{2}\delta )}
2171:p := particle r_t := current_reward
2348:
2059:
particles := ; Process each incoming data point
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2103:max_path := max_MAP := 1/|Q|
2125:// Create new particles for a changepoint at time t
1277:: a vector of m basis functions evaluated at state
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1478:{\displaystyle b=\sum _{i=j}^{t}R_{i}\Phi (x_{i})}
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2156:// Return the most likely path to the final point
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2089:particles := particle_filter(p.MAP, M)
2056:describes the change point detection algorithm:
1020:
2277:Prefrontal cortex basal ganglia working memory
46:. There might be a discussion about this on
2305:
2251:CST is much faster learning algorithm than
66:Learn how and when to remove this message
2369:Journal of the Royal Statistical Society
1793:{\displaystyle G_{}^{}(l)=(1-(1-p)^{l})}
1718:{\displaystyle g_{}^{}(l)=(1-p)^{l-1}p}
529:is computed by the following equation.
2378:
2193: := p.Φ (current state)
1835:{\displaystyle p_{}^{}={\frac {1}{k}}}
1604:: The number of basis functions q has.
2330:Konidaris, George; Scott Kuindersma;
423:. The prior for each weight follows
18:
2231:p.tr2 p.tr2 := đŸp.tr2 + r
1640:on the diagonal and zeros elsewhere
13:
2306:Jeevanandam, Nivash (2021-09-13).
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845:{\displaystyle P_{j}^{\text{MAP}}}
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2282:Stateâactionârewardâstateâaction
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2195:// Update sufficient statistics
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287:{\displaystyle P(j,t,q)_{}^{}}
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2094:// Determine the Viterbi path
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2085:the number of particles â„ N
1921:is the number of particles,
1633:{\displaystyle \delta ^{-1}}
1270:{\displaystyle \Phi (x_{i})}
108:
7:
2386:Machine learning algorithms
2270:
10:
2402:
2210:p.z := đŸp.z + Φ
813:{\displaystyle P_{t}(j,q)}
16:Machine learning algorithm
1925:is the time of computing
247:with the fit probability
206:{\displaystyle p(q\in Q)}
2312:Analytics India Magazine
2197:p.A := p.A + Φ
2037:{\displaystyle P(j,t,q)}
1999:a mixture of gaussians.
1959:{\displaystyle P(j,t,q)}
1610:: an m by m matrix with
522:{\displaystyle P(j,t,q)}
328:{\displaystyle P(j,t,q)}
81:(CST) is a hierarchical
79:Constructing skill trees
2258:
2139:// Update all particles
1849:: Expected skill length
2080:// Filter if necessary
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167:{\displaystyle t\in T}
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83:reinforcement learning
2107:max_particle :=
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1910:{\displaystyle O(Nc)}
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1878:{\displaystyle O(NL)}
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1592:{\displaystyle n=t-j}
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134:{\displaystyle R_{t}}
2071:p ∈ particles
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1988:{\displaystyle O(c)}
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1885:and storage size is
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488:The fit probability
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87:maximum a posteriori
36:confusing or unclear
2349:Konidaris, George;
2214:p.b := p.b + r
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232:{\displaystyle j+1}
44:clarify the article
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1565:đŸ: Gamma function
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2173:// Initialization
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1646:The skill length
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854:Viterbi algorithm
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91:George Konidaris
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2365:Fearnhead, Paul
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1995:change points.
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2052:The following
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48:the talk page
45:
39:
37:
32:This article
30:
21:
20:
2368:
2354:
2351:Andrew Barto
2339:
2332:Andrew Barto
2315:. Retrieved
2311:
2301:
2262:
2250:
2242:
2227:p.tr1 + 2đŸr
2194:
2186:
2183:
2179:
2175:
2172:
2168:
2164:
2158:
2155:
2152:
2149:
2145:
2144:p ∈ P
2141:
2138:
2135:
2131:
2130:q ∈ Q
2127:
2124:
2121:
2104:
2100:
2096:
2093:
2090:
2086:
2082:
2079:
2076:
2072:
2068:
2064:
2060:
2051:
2001:
1997:
1852:
1645:
1143:
769:
487:
243:using model
147:
112:
99:Andrew Barto
78:
77:
62:
53:
42:Please help
33:
2239:Assumptions
774:with model
178:with prior
174:and models
2317:2021-12-05
2293:References
2247:Advantages
2054:pseudocode
2048:Pseudocode
38:to readers
2161:max_path
1772:−
1763:−
1705:−
1691:−
1623:−
1619:δ
1584:−
1536:−
1529:γ
1508:∑
1457:Φ
1427:∑
1391:−
1361:−
1323:∑
1249:Φ
1201:Φ
1182:Φ
1162:∑
1120:∀
1105:−
1099:−
1087:−
1073:−
919:−
913:−
901:−
736:Γ
707:Γ
624:−
590:δ
574:−
570:π
470:δ
461:σ
195:∈
159:∈
109:Algorithm
105:in 2010.
56:July 2023
2380:Category
2271:See also
2165:function
2063:t = 1:T
1917:, where
852:using a
2265:PinBall
34:may be
2201:Φ
2189:Φ
2184:end if
2178:t = 0
2159:return
2099:t = 1
2259:Uses
2180:then
2105:else
2087:then
1126:<
820:and
101:and
2153:end
2150:end
2142:for
2136:end
2128:for
2122:end
2111:max
2097:for
2091:end
2077:end
2069:for
2061:for
1021:max
1012:MAP
977:MAP
838:MAP
239:to
2382::
2334:;
2310:.
2176:if
2169:is
2146:do
2132:do
2101:do
2083:if
2073:do
2065:do
856:.
778:,
485:.
97:,
93:,
2371:.
2357:.
2342:.
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2029:q
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2020:,
2017:j
2014:(
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1980:c
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63:(
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54:(
50:.
40:.
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