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What is the idea behind double DQN?

The Bellman equation used to calculate the Q values to update the online network follows the equation:

value = reward + discount_factor * target_network.predict(next_state)[argmax(online_network.predict(next_state))]

The Bellman equation used to calculate the Q value updates in the original DQN is:

value = reward + discount_factor * max(target_network.predict(next_state))

But the target network for evaluating the action is updated using weights of the online_network and the value fed to the target value is basically the old q value of the action.

Any ideas on how or why adding another network based on weights from the first network helps? Any example?

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As the authors of this paper state it:

In $Q$-learning, the agent updates the value of executing an action in the current state, using the values of executing actions in a successive state. This procedure often results in an instability because the values change simultaneously on both sides of the update equation. A target network is a copy of the estimated value function that is held fixed to serve as a stable target for some number of steps.

If I remember it correctly, the main concern is that the network could end up in a positive feedback loop, making sufficient exploration of various action and state combinations less likely to occur, which could be detrimental to the learning task.

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