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What update does Q-learning perform?

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Answer

  • Q(s, a) <- Q(s, a) + alpha · (r  +  γ    maxa  Q(s,  a)    Q(s,  a))(r\; + \;\gamma\; \cdot \;\operatorname{max}_{a}\;Q(s, \;a)\; - \;Q(s, \;a)).
  • This bootstraps toward the maximum future value at s', which is why it's off-policy: the target uses the greedy next action regardless of what the agent actually did.
  • With function approximation (DQN), you use a replay buffer and a target network to stabilize learning.
Check yourself — multiple choice
  • The Q-learning target uses r only
  • The target is r + gamma · Q(s', a) where a is the next action taken
  • The target is r + gamma · maxa\operatorname{max}_{a}' Q(s', a')
  • Q-learning does not use gamma

Q-learning bootstraps with max over next actions — that's what makes it off-policy.

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