Understanding Q Learning and Deep Q Networks: Advancements and Challenges

Hello again,

Today’s topic is a continuation of our exploration into the fascinating world of Q Learning and Deep Q Networks (DQN). In our previous discussion, we delved into the fundamentals of Q Learning, utilizing the Bellman equation to derive Q-values and ultimately determine the optimal policy for an agent. We also introduced Deep Q Networks, which leverage deep neural networks to approximate Q-values instead of maintaining a traditional Q-table. This article will build upon that foundation, addressing some of the challenges that arise in DQN and the innovative solutions that have been developed to overcome them.

Recap of Deep Q Networks

Deep Q Networks take the current state of the environment as input and output a Q-value for each possible action. The action with the highest Q-value is selected for execution by the agent. The training process relies on the Temporal Difference (TD) Error, which is the difference between the predicted Q-value and the target Q-value derived from the Bellman equation. This approach allows us to approximate Q-values using a neural network, but it also introduces several challenges that we need to address.

Moving Q-Targets

One of the primary challenges in training DQNs is the issue of moving Q-targets. The TD Error is calculated using the Q-target, which is derived from the immediate reward and the discounted maximum Q-value of the next state. However, since the same weights are updated for both the target and the predicted value, we end up in a situation where we are constantly chasing a moving target. This can lead to oscillations in the training process, making it difficult for the agent to converge.

To mitigate this issue, DeepMind introduced a clever solution: the use of two neural networks. The first network is the main DQN, while the second, known as the Target Network, is updated less frequently. This approach, termed Fixed Q-Targets, allows the target weights to remain stable for longer periods, reducing the oscillation in training.

class DQNAgent:
    def __init__(self, state_size, action_size):
        self.model = self._build_model()
        self.target_model = self._build_model()
        self.update_target_model()

    def update_target_model(self):
        self.target_model.set_weights(self.model.get_weights())

Maximization Bias

Another significant challenge is maximization bias, which occurs when DQNs tend to overestimate the value of actions. If the network overestimates a Q-value, that action is more likely to be selected in the future, perpetuating the overestimation. This can lead to suboptimal policies.

To address this, we can employ a technique called the Double Deep Q Network (DDQN). In this approach, one network is responsible for selecting the action with the maximum Q-value, while the other network evaluates that action. By decoupling action selection from target Q-value generation, we can significantly reduce overestimation and improve training stability.

def train_model(self):
    if len(self.memory) < self.train_start:
        return
    batch_size = min(self.batch_size, len(self.memory))
    mini_batch = random.sample(self.memory, batch_size)
    update_input = np.zeros((batch_size, self.state_size))
    update_target = np.zeros((batch_size, self.state_size))
    action, reward, done = [], [], []

    for i in range(batch_size):
        update_input[i] = mini_batch[i][0]
        action.append(mini_batch[i][1])
        reward.append(mini_batch[i][2])
        update_target[i] = mini_batch[i][3]
        done.append(mini_batch[i][4])

    target = self.model.predict(update_input)
    target_next = self.model.predict(update_target)
    target_val = self.target_model.predict(update_target)

    for i in range(self.batch_size):
        if done[i]:
            target[i][action[i]] = reward[i]
        else:
            a = np.argmax(target_next[i])
            target[i][action[i]] = reward[i] + self.discount_factor * (target_val[i][a])

    self.model.fit(update_input, target, batch_size=self.batch_size, epochs=1, verbose=0)

Dueling Deep Q Networks

As we continue to refine our approach, we encounter the concept of Dueling Deep Q Networks. In traditional Q Learning, Q-values represent the expected return of an action from a given state. However, we can decompose Q-values into two components: the State Value function (V(s)) and the Advantage function (A(s, a)).

The advantage function captures how much better an action is compared to others in a given state, while the value function indicates how good it is to be in that state. By representing the Q function as a sum of these two components, we can enhance the agent’s ability to evaluate states without being overly influenced by the specific actions available.

def build_model(self):
    input = Input(shape=self.state_size)
    shared = Conv2D(32, (8, 8), strides=(4, 4), activation='relu')(input)
    shared = Conv2D(64, (4, 4), strides=(2, 2), activation='relu')(shared)
    shared = Conv2D(64, (3, 3), strides=(1, 1), activation='relu')(shared)
    flatten = Flatten()(shared)

    advantage_fc = Dense(512, activation='relu')(flatten)
    advantage = Dense(self.action_size)(advantage_fc)
    advantage = Lambda(lambda a: a[:, :] - K.mean(a[:, :], keepdims=True), output_shape=(self.action_size,))(advantage)

    value_fc = Dense(512, activation='relu')(flatten)
    value = Dense(1)(value_fc)
    value = Lambda(lambda s: K.expand_dims(s[:, 0], -1), output_shape=(self.action_size,))(value)

    q_value = merge([value, advantage], mode='sum')
    model = Model(inputs=input, outputs=q_value)
    model.summary()

    return model

Prioritized Experience Replay

Finally, we address the optimization of experience replay. In traditional experience replay, the agent randomly samples past experiences to learn from them. However, not all experiences are equally valuable. To enhance learning efficiency, we can implement Prioritized Experience Replay, where experiences are sampled based on their significance, determined by the magnitude of the TD Error.

The central idea is that experiences with higher TD Errors are more urgent to learn from. By prioritizing these experiences, we can improve the learning process and ensure that the agent focuses on the most informative experiences.

class PER:
    e = 0.01
    a = 0.6

    def __init__(self, capacity):
        self.tree = SumTree(capacity)

    def _getPriority(self, error):
        return (error + self.e) ** self.a

    def add(self, error, sample):
        p = self._getPriority(error)
        self.tree.add(p, sample)

    def sample(self, n):
        batch = []
        segment = self.tree.total() / n
        for i in range(n):
            a = segment * i
            b = segment * (i + 1)
            s = random.uniform(a, b)
            (idx, p, data) = self.tree.get(s)
            batch.append((idx, data))
        return batch

    def update(self, idx, error):
        p = self._getPriority(error)
        self.tree.update(idx, p)

Conclusion

In summary, we have explored several advancements in the realm of Deep Q Learning, including Fixed Q-Targets, Double Deep Q Networks, Dueling Deep Q Networks, and Prioritized Experience Replay. Each of these innovations addresses specific challenges faced in training DQNs, enhancing their stability and efficiency.

As we continue to push the boundaries of reinforcement learning, it is essential to stay informed about these developments. The potential applications of these techniques are vast, and their importance in the field of artificial intelligence cannot be overstated.

If you’re eager to dive deeper into this subject, I highly recommend checking out the Advanced AI: Deep Reinforcement Learning Course in Python on Udemy.

Next time, we will introduce Policy Gradients and the REINFORCE algorithm. Until then, let’s keep learning!