Double Q-learning is a machine learning algorithm that solves a problem with the traditional Q-learning algorithm. Q-learning tries to maximize the rewards an agent can get by taking different actions in different states. However, it has a problem with overestimating the value of certain actions, leading to a sub-optimal solution. Double Q-learning solves this problem by separating the selection of an action from its evaluation.
What is Q-learning?
Q-learning is a reinforcement learning algorithm that allows an agent to learn the optimal policy by maximizing the total reward in the environment. The agent tries different actions in different states and updates the Q-value table, which represents the expected future reward for taking an action in a certain state. The agent selects the action that has the maximum Q-value in a given state.
The update rule for the Q-value is:
$$Q(s_t, a_t) = Q(s_t, a_t) + \alpha \bigg(R_{t+1} + \gamma \max_a Q(s_{t+1}, a) - Q(s_t, a_t)\bigg)$$
Where $s_t$ is the current state, $a_t$ is the action taken in that state, $R_{t+1}$ is the reward for taking that action, $s_{t+1}$ is the resulting state, $\alpha$ is the learning rate, and $\gamma$ is the discount factor.
The algorithm tries to learn the optimal policy by maximizing the expected future reward. However, if the Q-values are overestimated, the algorithm can lead to sub-optimal solutions.
What is the problem with Q-learning?
The problem with Q-learning is that it overestimates the value of certain actions. This is due to the max operator, which uses the same values to select and evaluate an action. This can lead to overoptimistic value estimates, resulting in a sub-optimal policy.
For example, let's say we have two actions in a certain state, A and B. A has a Q-value of 10, and B has a Q-value of 9. According to Q-learning, A is the optimal action to take in that state. However, what if the true Q-values for A and B are 4 and 12, respectively? Q-learning would still select A as the optimal action, even though it is sub-optimal.
What is Double Q-learning?
Double Q-learning is an extension of Q-learning that tries to solve the overestimation problem. Double Q-learning separates the selection of an action from its evaluation by using two sets of Q-values.
Let's say we have two sets of Q-values, $Q_1$ and $Q_2$. In each step, we use $Q_1$ to select the best action and $Q_2$ to evaluate the value of that action:
$$Y^{DoubleQ}_t = R_{t+1} + \gamma Q_2\Big(s_{t+1}, \arg\max_a Q_1(s_{t+1}, a)\Big)$$
Here, $\arg\max_a Q_1(s_{t+1}, a)$ is the action with the highest Q-value according to $Q_1$. This action is the selected action. However, we evaluate the value of this action using $Q_2$. The intuition here is that $Q_1$ overestimates certain actions, but $Q_2$ should be less biased since it has learned a different set of values. This way, we can reduce the overestimation problem.
How does Double Q-learning work?
The general idea behind Double Q-learning is to reduce the overestimation problem in Q-learning by decoupling the selection of an action from its evaluation. The selection of an action is still based on the Q-values, but the evaluation is based on a different set of Q-values.
The update rule for Double Q-learning is:
$$Q_{1, t+1}(s_t, a_t) = Q_{1, t}(s_t, a_t) + \alpha \bigg(R_{t+1} + \gamma Q_{2,t}\Big(s_{t+1}, \arg\max_a Q_{1,t}(s_{t+1}, a)\Big) - Q_{1, t}(s_t, a_t)\bigg)$$ $$Q_{2, t+1}(s_t, a_t) = Q_{2, t}(s_t, a_t) + \alpha \bigg(R_{t+1} + \gamma Q_{1,t}\Big(s_{t+1}, \arg\max_a Q_{2,t}(s_{t+1}, a)\Big) - Q_{2, t}(s_t, a_t)\bigg)$$
Here, $Q_{1,t}(s_t, a_t)$ and $Q_{2,t}(s_t, a_t)$ are the Q-values of $Q_1$ and $Q_2$ in the current state and action. We update $Q_1$ using $Q_2$ to select the best action, and we update $Q_2$ using $Q_1$ to select the best action.
Both $Q_1$ and $Q_2$ converge to the optimal Q-values if we keep updating them. The algorithm works well with large state and action spaces, and it is more robust to overestimation than Q-learning.
Why is Double Q-learning important?
Double Q-learning is important because it solves the overestimation problem with Q-learning. It allows the agent to learn the optimal policy more efficiently and accurately than Q-learning. In other words, it helps to avoid sub-optimal solutions and leads to better performance.
Double Q-learning has been applied to different environments and problems, such as Atari games and robotics. It has shown to have better performance than Q-learning and DQN in many cases.
Double Q-learning is an extension of Q-learning that aims to solve the overestimation problem. It separates the selection of an action from its evaluation by using two sets of Q-values. This helps to avoid sub-optimal solutions and leads to better performance. Double Q-learning has been applied to many environments and problems, and it has shown to work well in practice.
If you are interested in learning more about reinforcement learning, consider taking an online course or reading some books on the topic. It is a fascinating field that has many applications in different domains, such as robotics, gaming, and transportation.
