Q-function

See also: Machine learning terms

Q-function in Machine Learning

The Q-function, also known as the state-action value function or simply Q-value, is a fundamental concept in the field of Reinforcement Learning (RL). It represents the expected cumulative reward an agent will receive from a specific state by taking a certain action and then following a given policy. Mathematically, the Q-function is denoted as Q(s, a), where 's' represents the state and 'a' represents the action.

Definition

Formally, the Q-function is defined as follows:

Q(s, a) = E[∑(t=0)^∞ γ^t * R(s_t, a_t) | s_0 = s, a_0 = a, π]

Here, 'E' denotes the expectation, 'γ' is the discount factor (0 ≤ γ < 1), 'R' is the reward function, and 'π' is the policy followed by the agent. The sum runs from 't=0' to '∞', indicating that the Q-function considers the entire future trajectory of the agent. The discount factor 'γ' is used to give more importance to immediate rewards rather than distant rewards.

Q-Learning Algorithm

Q-Learning is a popular model-free, off-policy reinforcement learning algorithm that makes use of the Q-function to learn the optimal policy for a given environment. The algorithm iteratively updates the Q-values in a Q-table or Q-network until convergence, using the following update rule:

Q(s, a) ← Q(s, a) + α * (R(s, a) + γ * max_a' Q(s', a') - Q(s, a))

In this equation, 'α' represents the learning rate (0 < α ≤ 1), 's' and 'a' are the current state and action, 's and 'a are the next state and the action that yields the maximum Q-value in that state, and 'R(s, a)' is the immediate reward received after taking action 'a' in state 's'.

Deep Q-Networks

Deep Q-Network (DQN) is a notable advancement in Q-Learning that combines the Q-function with Deep Learning. DQN uses a deep neural network, known as the Q-network, to approximate the Q-function, eliminating the need for a Q-table. This allows the algorithm to tackle problems with large or continuous state and action spaces more efficiently.

Explain Like I'm 5 (ELI5)

Imagine you're playing a game, and you're trying to figure out the best move to make in each situation to win. The Q-function is like a helpful friend who tells you how many points you can expect to get if you make a certain move and then continue playing the game well. The more points you can get by following the advice, the better the move.

In the game, you might not know the best moves right away. So, you use a technique called Q-Learning to learn from your experiences. As you play the game more and more, your helpful friend (the Q-function) becomes smarter and gives you better advice.

Sometimes, the game can be very complicated, with many different situations and moves. In this case, you can use a powerful computer brain called a Deep Q-Network to help your friend give you the best advice, even when the game is really hard.