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The Bellman Equation
1
1
1 1 1
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The Bellman Equation
1
1
1 A
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The Bellman Equation
s = a particular state (room)
a = action
s′ = state to which the robot goes from s
𝜸 = discount factor
R(s, a) = a reward function which takes a state s and action a and outputs a reward value
V(s) = value of being in a particular state
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The Bellman Equation
1
*
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The Bellman Equation
Discount Factor = 0.9
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The Bellman Equation
1
0.9
START 0.729 0.81
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The Bellman Equation
0.9 1
0.81 0.9 1
0.729 0.81 0.9
0.66 0.729 0.81
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Markov Decision Processes
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The Bellman Equation
o
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The Bellman Equation
↑
← o →
↓
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The Bellman Equation
The probability of moving from room s to room s′ with action a
expectation of the situation that the robot incurs randomness
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The Bellman Equation
↑ 0.8
0.03 ← o → 0.03
↓ 0.1
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The Bellman Equation
↑ 0.8
0.03 ← o → 0.03
↓ 0.1
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Transitioning to Q-Learning
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Q-Learning
↑ 0.8 (V(s1))
0.03 (V(s4))← o → 0.03 (V(s2))
↓ 0.1 (V(s3))
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Q-Learning
Q (s1,a1)
Q (s4,a4) o Q (s2,a2)
Q (s3,a3)
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Q-Learning
Q (s1,a1)
Q (s4,a4) o Q (s2,a2)
Q (s3,a3)
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Q-Learning
Q (s1,a1)
Q (s4,a4) o Q (s2,a2)
Q (s3,a3)
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Q-Learning
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Q-Learning
___
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Q-Learning
___
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Implementing Q-Learning
In Python (NumPy)
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PROBLEM STATEMENT
L1 L2 L3
L4 L5 L6
L7 L8 L9
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What is Q Learning? Edureka