In DQN, why not use target network to predict current state Q values, and not only next state q values? In doing a basic dq learning algorithm with nn from scratch, with replay memory, and minibatch gd, and I'm implementing target neural network to predict at every minibatch samples current and mext state q values, and in the end of minibatch, sync target network, bu I notice the weights diverge very easily, maybe because I used nn to predict current state q values? If yes, why not?

the agent code:

def start_episode_and_evaluate(self, discount_factor, learning_rate,
                                epsilon, epsilon_decay = 0.99, min_epsilon = 0.01):
        state = self.env.reset()
        done = False
        while not done:
            if np.random.uniform(0, 1) < epsilon: action = self.env.action_space.sample()
            else: action = np.argmax(self._nn.predict(state))
            next_state, reward, done, _ = self.env.step(action)
            self._replay_memory.put(state, action, reward, done, next_state)
            if len(self._replay_memory) >= self._batch_size:
                for state_exp, action_exp, reward_exp, done_exp, next_state_exp in self._replay_memory.get(batch_size=self._batch_size):
                    z, a = self._target_nn.forward_propagate(state_exp) #HERE I HAVE TO USE TARGET NETOWRK (_target_nn) OR THE MAIN NETWORK (_nn)?
                    q_values_target = np.copy(a[-1])
                    if done: q_values_target[action_exp] = reward_exp
                    else: q_values_target[action_exp] = reward_exp + discount_factor * np.max(self._target_nn.predict(next_state_exp))
                    self._nn.backpropagate(z, a, q_values_target, learning_rate)
                epsilon *= epsilon_decay
                if epsilon < min_epsilon:
                    epsilon = min_epsilon
            state = next_state

source: https://github.com/LorenzoTinfena/deep-q-learning-itt-final-project/blob/main/src/core/dqn_agent.py

  • $\begingroup$ Could you be clearer what you mean by "actual" here? There are no true values, everything is an estimate, and different estimates in DQN are used for different purposes. Nothing is labelled "actual". The target nn estimates are normally used to calculate the TD target for action value upate steps. The two other required prediction tasks - normally covered by the learning nn - are for selecting actions in the behaviour policy and for determining the error in predictions compared to the TD target. Is it one of those uses that you are considering using the target nn for? $\endgroup$ May 7, 2021 at 12:19
  • 1
    $\begingroup$ I believe Lorenzo meant current instead of actual. $\endgroup$
    – YuseqYaseq
    May 7, 2021 at 12:35
  • $\begingroup$ yes I meant current, sorry, bad very bad english $\endgroup$ May 7, 2021 at 12:53

1 Answer 1


Bellman equation for deterministic environments is given as follows $$ V(s) = max_aR(s, a) + \gamma V(s') $$ Where $V$ is a value function, $R$ is a reward function, $s$ is current state, $s'$ is next state, $a$ is an action. In DQN when optimizing $V$ it is assumed that $V(s')$ has on average lower error than $V(s)$. This is intuitively because $s'$ is closer to the end state for which $V$ is known and so there are fewer steps in which error can accumulate. This way we can progressively lower errors of $V$ for all states starting from the end states up to the starting state. I don't know how exactly you use current state to update weights but assuming it looks like this $$ \delta V(s) := \alpha(max_aR(s, a) + \gamma V(s) - V(s)) $$ instead of $$ \delta V(s) := \alpha(max_aR(s, a) + \gamma V(s') - V(s)) $$ i.e. you don't use $V(s')$ in the weights update what happens is the same error propagates over and over again because information about rewards in the later states is not propagated to earlier states.

As a concrete example imagine an environment with 3 states $s_1$, $s_2$ and $s_3$ where $s_1$ is starting state $s_3$ is the end state, the action space is only one move: go from state $s_i$ to state $s_{i+1}$ and reward function is 1 for moving to $s_3$ and 0 otherwise. What happens then is $$ \delta V(s_3) = 0 \\ \delta V(s_2) = \alpha (max_a(R(s_2, a) + \gamma V(s_2) - V(s_2)) = \alpha (1 + \gamma V(s_2) - V(s_2)) \\ \delta V(s_1) = \alpha (max_a(R(s_1, a) + \gamma V(s_1) - V(s_1)) = \alpha (0 + \gamma V(s_1) - V(s_1)) $$ Because starting value for $V(s_1)$ is 0 it's gradient will always be 0 and the network will never learn the value of this state. That's why it must take a loook at values of its next state.

  • $\begingroup$ Thank you for your answer, very complete, but I got it why compute next state q values, but my question was about target network, I mean, I have to use target network only for compute next state q values, or even current state q values, like in the code that I insert in the question $\endgroup$ May 7, 2021 at 13:12
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    $\begingroup$ You don't have to use two networks at all. You only need one network. Remove either _nn or _target_nn and perform all calculations on the remaining network. If I read your code correctly you don't even update weights right now because you perform forward prop on one network and backprop on the other network. $\endgroup$
    – YuseqYaseq
    May 7, 2021 at 14:26
  • $\begingroup$ Yes, but _sync_target_nn_weights method, copy _nn weights to _target_nn weights, actually the problem weights diverges and don't know why... $\endgroup$ May 7, 2021 at 16:04

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