Introduction to Deep Reinforcement Learning: Theory, Algorithms, and Applications

This article provides a comprehensive introduction to deep reinforcement learning (DRL), categorizing algorithms into three main families: value‑based, policy‑based, and actor‑critic (AC) methods.

It begins with the mathematical foundations of reinforcement learning, describing the Markov Decision Process (MDP) as a tuple \{S, A, P, R\} where S is the set of states, A the set of actions, P the state‑transition probability, and R the reward function. The Bellman equations for the state‑value function V(s) and the action‑value function Q(s,a) are presented, establishing the goal of maximizing the expected cumulative reward.

Value‑based algorithms are illustrated by the Deep Q‑Network (DQN). DQN uses a convolutional neural network (CNN) to approximate Q‑values and consists of an evaluation network, a target network, an experience replay buffer, and an ε‑greedy exploration strategy. Training proceeds in three stages: (1) initial random data collection, (2) exploration with ε‑greedy updates, and (3) exploitation where actions are chosen greedily.

Policy‑based algorithms directly optimize a stochastic policy \(\pi_\theta(a|s)\) by maximizing the expected return \(J(\theta)\). The policy‑gradient theorem yields the update \(\Delta\theta \propto \nabla_\theta \log \pi_\theta(a|s)\, G\), where \(G\) is the return. Representative methods include PG, DPG, and DDPG.

Actor‑Critic (AC) algorithms combine both approaches. The actor updates the policy using gradients supplied by a critic that estimates the value function, enabling single‑step updates and reducing variance compared with pure policy gradients. The AC framework underlies popular algorithms such as A3C, PPO, and DDPG.

Figures in the original text illustrate the DRL pipeline, the DQN network diagram, and the AC architecture. The article concludes with a list of references and a brief team introduction.