Training deep neural networks effectively typically relies on the assumption that the input data points are independent and identically distributed (i.i.d.). However, when an RL agent interacts with an environment sequentially, the generated experiences $(s_t, a_t, r_t, s_{t+1})$ are anything but i.i.d. Consecutive states are highly correlated, and the distribution of experiences changes as the agent's policy evolves. Training a deep Q-network directly on these sequential, correlated experiences often leads to instability and poor convergence. The network can easily overfit to recent, correlated trajectories, forgetting past, potentially valuable experiences.

Experience replay is a biologically inspired mechanism introduced with DQN to address these challenges. Instead of performing an update using only the most recent transition, the agent stores its experiences in a large data structure called a replay buffer (or replay memory), often denoted as $D$ . This buffer typically has a fixed capacity and operates like a FIFO (First-In, First-Out) queue: when the buffer is full and a new experience arrives, the oldest one is removed.

The core process works as follows:

Store: At each time step $t$ , after the agent interacts with the environment and observes the transition $(s_t, a_t, r_t, s_{t+1})$ , this transition tuple is stored in the replay buffer $D$ .
Sample: Instead of updating the Q-network based on the current transition $(s_t, a_t, r_t, s_{t+1})$ , we sample a mini-batch of transitions $(s_j, a_j, r_j, s_{j+1})$ uniformly at random from the entire buffer $D$ .
Update: The Q-network's parameters $\theta$ are updated using gradient descent on the loss calculated over this mini-batch.

The Experience Replay process: Transitions are stored in a buffer, and mini-batches are randomly sampled from this buffer to perform Q-network updates.

This random sampling has two primary benefits:

Breaking Correlations: By sampling randomly from a large history of transitions, the updates are based on a diverse set of experiences. This breaks the strong temporal correlations present in sequential interactions, making the training data closer to the i.i.d. assumption required for stable stochastic gradient descent updates. This significantly stabilizes the learning process.
Increased Data Efficiency: Each experience transition can potentially be sampled and used for network updates multiple times. This allows the agent to learn more from each interaction, which is particularly beneficial in scenarios where data collection is expensive or time-consuming.

For each sampled transition $(s_j, a_j, r_j, s_{j+1})$ in a mini-batch $B$ , the target value $y_j$ is computed, often using a separate target network (discussed next) with parameters $\theta^-$ to further stabilize training:

y_j = r_j + \gamma \max_{a'} Q(s_{j+1}, a'; \theta^-)

If $s_{j+1}$ is a terminal state, then $y_j = r_j$ . The loss, typically Mean Squared Error (MSE), is then computed over the mini-batch:

L(\theta) = \frac{1}{|B|} \sum_{j \in B} \left( y_j - Q(s_j, a_j; \theta) \right)^2

The parameters $\theta$ of the main Q-network are then updated using gradient descent on this loss $L(\theta)$ .

The size of the replay buffer is an important hyperparameter. A larger buffer stores a more diverse set of experiences, reducing correlations but potentially including outdated information from older policies. A smaller buffer adapts faster to recent policy changes but might suffer from stronger correlations. Typical buffer sizes range from tens of thousands to millions of transitions, depending on the complexity of the task and memory constraints.

Experience replay was a significant component that enabled the success of DQN, transforming Q-learning with non-linear function approximators from an often unstable technique into a powerful and widely applicable deep reinforcement learning algorithm. While simple uniform sampling is standard, subsequent enhancements like Prioritized Experience Replay (PER), which we will discuss later in this chapter, further refine the sampling strategy for improved efficiency.