How do you implement a double deep Q network and why is it better than a regular deep Q network?
Reinforcement learning (RL) is a branch of machine learning that deals with learning from actions and rewards. In RL, an agent interacts with an environment and learns to optimize its behavior based on the feedback it receives. One of the challenges of RL is to balance exploration and exploitation, that is, to try new actions that might lead to better outcomes, or to stick with the actions that have proven to be successful so far.
A deep Q network (DQN) is a type of RL algorithm that uses a neural network to approximate the value function of the agent. The value function estimates the expected return (cumulative reward) of taking an action in a given state. A DQN learns to update the value function by using a technique called Q-learning, which involves comparing the actual and the predicted rewards of each action and minimizing the difference (the temporal difference error).
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Reinforcement learning involves estimating the values corresponding to different actions in a given state. This is achieved by storing these values in a table. However, this is infeasible for the case where state space is large or infinite. In this case, instead of storing these values in a table, a function is used to approximate the value function that takes a state as input and gives a value corresponding to every action as output. When the function used is a neural network, it is known as deep Q network.
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DQN is an off-policy RL algorithm that builds upon Q-learning but parameterizes the Q-function using a neural network θ ⇒ Q(s, a; θ) In addition to this DQN: Sample transitions (s, a, r', s') ∼ D from an experience replay buffer D to enhance training stability by breaking correlations in sequential data Copy the Q-network θf=copy(θ) and train on a target network Q(s,a; θf) that is frozen for C steps before its updated. Why? Due to the TD formulation the network is a part of the loss function. Thus if we fix the network for C rounds, then the training target is more stable and easier to learn. Update Steps: Δ(y, ŷ) = [r' γ max Q(s', a; θf) - Q(s, a; θ)] L(θ) = E[(s, a, r', s') ∼ Uniform(D)][1/2 Δ(y, ŷ)^2] θ←θ-α∇L(θ)
Q-learning is based on the Bellman equation, which states that the value of a state-action pair is equal to the immediate reward plus the discounted value of the best action in the next state. In other words, Q-learning tries to find the optimal policy that maximizes the value of each action in the long run. However, Q-learning has some drawbacks, such as overestimating the value of some actions, being sensitive to noise and correlations in the data, and requiring a large amount of memory and computation.
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As per the Bellman equation, we can estimate the value of a state-action pair if we know the immediate reward and the value corresponding to the best action in the next state. When an RL Agent takes an action A in state S, observes the reward R and lands in the next state S', we can estimate the value of all the actions in the S' using the same Deep Q-network and select the state-action pair with highest value. Now, target value can be calculated by adding reward to discounted value of best state-action (S', A') pair i.e., R gamma*Q(S', A'). We use this value as the target for state S as input to the Deep Q network. One thing to notice here is that we are using the same Deep Q-Network to estimate the value of Q(S', A'), which is noisy.
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Q-learning is an off-policy reinforcement learning algorithm that updates Q-values using a greedy strategy based on the maximum potential reward for the next state: Q(s, a) = Q(s, a) α[ r' γ max_a' Q(s', a') - Q(s, a) ], where α is the learning rate, γ is the discount factor, r' is the reward at time t 1, the max represents the maximum Q-value for the next state s'. The policy is derived from Q, such as ε-greedy action selection. Q-values are initialized arbitrarily and updated iteratively until convergence. Q-learning can overestimate Q-values, making it less stable in stochastic environments and prone to riskier exploratory decisions. This is due to the fact that we take the max to guess the future expected discounted rewards
A double deep Q network (DDQN) is an improvement over the DQN that addresses some of its limitations. The main idea of DDQN is to use two neural networks instead of one: a target network and an online network. The target network is a copy of the online network that is updated less frequently, and is used to generate the target values for the Q-learning update. The online network is used to select the best action in each state. This way, DDQN reduces the overestimation bias and the variance of the Q-learning update, and improves the stability and performance of the algorithm.
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Double Deep Q-Network DDQN (Not to be confused with Dueling DQN) is an improvement over the DQN algorithm, designed to reduce overestimation bias in action evaluation. It achieves this by separating the processes of action selection and evaluation. In DDQN, two networks are used: the policy network Q(s, a; θ) for selecting actions and a second target network for evaluating them. This separation helps address the overestimation issue of DQN.
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As mentioned in the previous paragraph, Deep Q-network uses the same network to estimate the value of Q(S', A'), which leads to several problems. Double Deep Q-Networks mitigates this problem by using a separate network to estimate the value of Q(S', A') and the weights of this network are not updated frequently.
To implement a DDQN, you must first initialize the online network and the target network with random weights, as well as a replay buffer which stores the agent's experiences. Interaction with the environment is done by choosing an action according to an epsilon-greedy policy. The experience is stored in the replay buffer and epsilon is updated according to a decay schedule. A batch of experiences are sampled from the replay buffer, preprocessed, and their target value is computed. The predicted value is computed as the output of the online network for the chosen action in the current state. The loss is then calculated as the mean squared error between the target and predicted values and used to update the online network's weights by using gradient descent. Finally, every N steps, copy the online network's weights to the target network.
DDQN has several advantages over DQN, such as reducing the overestimation bias and variance of the Q-learning update. This can lead to suboptimal policies and poor exploration, as well as instability and divergence. DDQN decouples the action selection and evaluation processes to avoid inflating the value of some actions, and by using a less frequently updated target network, it smooths out the fluctuations in the value function. Additionally, several empirical studies have shown that DDQN can achieve higher scores and faster learning rates than DQN on various RL tasks.
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