Questions
COGSCI 200 001 WN 2025 Homework #4: Reinforcement Learning
Multiple dropdown selections
Compare the first episode with the second episode, and consider what did and didn't change. Which of the following is true? Some of the Q values change. True The rewards change False The actions available from the Start state change False
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Step-by-Step Analysis
Question restatement: The task asks to compare the first episode with the second episode and determine which statements are true about changes between them. The three statements presented are:
1) Some of the Q values change. True
2) The rewards change False
3) The actions available from the Start state change False
Option 1 analysis: 'Some of the Q values change. True' In many reinforcement learning or decision-process contexts, moving from one episode to another can lead to updates in Q-values (the expected return for a state-action pair) due ......Login to view full explanationLog in for full answers
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Shown is the Q Actor-Critic (QAC) function, with line numbers. 1. Initialise 𝑠 , 𝜃 2. Sample 𝑎 ∼ 𝜋 𝜃 3. for each step do 4. Sample reward 𝑟 = 𝑅 𝑠 𝑎 ; sample transition 𝑠 ′ ∼ 𝑃 𝑠 , ⋅ 𝑎 5. Sample action 𝑎 ′ ∼ 𝜋 𝜃 ( 𝑠 ′ , 𝑎 ′ ) 6. 𝛿 = 𝑟 + 𝛾 𝑄 𝑤 ( 𝑠 ′ , 𝑎 ′ ) − 𝑄 𝑤 ( 𝑠 , 𝑎 ) 7. 𝜃 ← 𝜃 + 𝛼 ∇ 𝜃 𝑙 𝑜 𝑔 𝜋 𝜃 ( 𝑠 , 𝑎 ) 𝑄 𝑤 ( 𝑠 , 𝑎 ) 8. 𝑤 ← 𝑤 + 𝛽 𝛿 𝜙 ( 𝑠 , 𝑎 ) 9. 𝑎 ← 𝑎 ′ , 𝑠 ← 𝑠 ′ 10. end for Which of the following statements is true (can be more than one)?
The value of an action 𝑞 𝜋 ( 𝑠 , 𝑎 ) depends on the expected next reward and the expected value of the next state. We can think of this in terms of a small backup diagram, as follows: Let 𝑃 ( 𝑠 ′ | 𝑠 , 𝑎 ) be the transition probability and 𝑟 ¯ ( 𝑠 , 𝑎 , 𝑠 ′ ) = 𝐸 [ 𝑅 𝑡 + 1 | 𝑆 𝑡 = 𝑠 , 𝐴 𝑡 = 𝑎 , 𝑆 𝑡 + 1 = 𝑠 ′ ] the expected reward for the transion from state 𝑠 to state 𝑠 ′ via action 𝑎 . Rearrange the definition of 𝑞 𝜋 ( 𝑠 , 𝑎 ) in terms of these quantities, such that no expected-value notation appears in the equation. A. 𝑞 𝜋 ( 𝑠 , 𝑎 ) = ∑ 𝑠 ′ 𝑃 ( 𝑠 ′ ∣ 𝑠 , 𝑎 ) [ 𝑟 ¯ ( 𝑠 , 𝑎 , 𝑠 ′ ) + 𝛾 𝑞 𝜋 ( 𝑠 ′ , 𝑎 ) ] B. 𝑞 𝜋 ( 𝑠 , 𝑎 ) = ∑ 𝑠 ′ [ 𝑟 ¯ ( 𝑠 , 𝑎 , 𝑠 ′ ) + 𝛾 ] 𝑃 ( 𝑠 ′ ∣ 𝑠 , 𝑎 ) 𝑣 𝜋 ( 𝑠 ′ ) C. 𝑞 𝜋 ( 𝑠 , 𝑎 ) = ∑ 𝑠 ′ 𝑃 ( 𝑠 ′ | 𝑠 , 𝑎 ) [ 𝑟 ¯ ( 𝑠 , 𝑎 , 𝑠 ′ ) + 𝛾 𝑣 𝜋 ( 𝑠 ′ ) ] D. 𝑞 𝜋 ( 𝑠 , 𝑎 ) = 𝑃 [ 𝑠 ′ ∣ 𝑠 , 𝑎 ] [ 𝑟 ¯ ( 𝑠 , 𝑎 , 𝑠 ′ ) + 𝛾 𝑣 𝜋 ( 𝑠 ′ ) ]
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