Q-Learning Algorithm in Reinforcement Learning

The Q-learning algorithm is one of the most classic model-free learning methods in reinforcement learning, which continuously updates the Q-value table to find the optimal policy. The core concept of Q-learning involves iteratively updating Q-values for state-action pairs, eventually converging to the optimal Q-function.

In optimal pathfinding applications, the Q-learning workflow consists of several key steps: First, define the environment's state space and action space. For path planning, states could represent current positions while actions correspond to movements like up, down, left, or right. Then initialize the Q-value table, typically as an all-zero matrix or with random values.

The algorithm learns through exploration-exploitation balance: The agent selects actions using ε-greedy policy (random exploration with probability ε, otherwise choosing the action with highest Q-value). After executing an action, the agent receives rewards and transitions to new states, then updates Q-values according to the Q-learning update rule: Q(s,a) ← Q(s,a) + α[r + γmaxₐ′Q(s′,a′) - Q(s,a)], where α is learning rate and γ is discount factor.

MATLAB's implementation advantage lies in its powerful matrix operations, efficiently handling Q-table updates. A typical implementation includes environment modeling, parameter configuration (learning rate, discount factor, etc.), main learning loop, and policy extraction modules. The main loop would involve nested iterations over states and actions while updating the Q-matrix.

Through multiple iterations, Q-values gradually converge. The optimal path policy is then derived by selecting actions with maximum Q-values for each state. While this tabular approach is simple, it effectively demonstrates reinforcement learning fundamentals and is particularly suitable for discrete state space problems like path planning. The algorithm can be implemented using matrix operations and logical indexing for efficient state transitions.