The interaction between the agent and the environment forms the core of the Reinforcement Learning process. This interaction isn't a one-off event; it's a continuous cycle, often visualized as a loop, where the agent perceives, acts, and learns from the consequences. Understanding this workflow is fundamental to grasping how RL algorithms operate.

Let's break down this interaction loop step-by-step. We typically model time in discrete steps: $t=0, 1, 2, 3, \dots$ . At each time step $t$ , the following sequence occurs:

Observation: The agent observes the current state of the environment. We denote this state as $S_t \in \mathcal{S}$ , where $\mathcal{S}$ is the set of all possible states. The state representation $S_t$ should contain all relevant information the agent needs to make a decision.
Action Selection: Based on the observed state $S_t$ , the agent selects an action $A_t \in \mathcal{A}(S_t)$ , where $\mathcal{A}(S_t)$ is the set of actions available in state $S_t$ . This selection is governed by the agent's current policy, $\pi$ . The policy $\pi(a|s)$ defines the probability of taking action $a$ when in state $s$ . For deterministic policies, it directly maps a state to an action.
Environment Transition & Reward: The environment receives the agent's action $A_t$ . Based on $S_t$ and $A_t$ , two things happen:
- The environment transitions to a new state, $S_{t+1}$ . This transition is determined by the environment's dynamics, often modeled as a probability distribution $p(s'|s, a) = P(S_{t+1}=s' | S_t=s, A_t=a)$ . In many practical scenarios, the agent doesn't know this transition function explicitly; it learns through interaction.
- The environment provides a scalar reward signal, $R_{t+1} \in \mathbb{R}$ , to the agent. This reward reflects the immediate consequence of taking action $A_t$ in state $S_t$ . It's important to remember the agent's goal is typically not just to maximize this immediate reward, but the cumulative reward over time (the return).
Next Step: The agent finds itself in state $S_{t+1}$ , having received reward $R_{t+1}$ . The cycle repeats for time step $t+1$ : observe $S_{t+1}$ , select $A_{t+1}$ , and so on.

This ongoing cycle generates a sequence of states, actions, and rewards, often called a trajectory or experience:

$S_0, A_0, R_1, S_1, A_1, R_2, S_2, A_2, R_3, \dots$

This sequence represents the agent's interaction history. It's precisely this experience data that most RL algorithms use to learn and improve the agent's policy $\pi$ , aiming to select actions that maximize the expected cumulative future reward.

We can visualize this interaction loop:

The Reinforcement Learning interaction loop. The agent observes the state ( $S_t$ ), selects an action ( $A_t$ ) based on its policy ( $\pi$ ), the environment responds with a reward ( $R_{t+1}$ ) and transitions to a new state ( $S_{t+1}$ ), and the cycle continues.

This loop forms the basis for both episodic tasks, which you learned about previously, where the interaction naturally breaks down into sequences (episodes) that end in a terminal state (like winning or losing a game), and continuing tasks, where the interaction potentially goes on forever (like managing an energy grid). In episodic tasks, the loop terminates upon reaching a terminal state, and a new episode often begins from some initial state distribution. In continuing tasks, the loop runs indefinitely. For these tasks, the concept of discounting future rewards using a factor $\gamma \in [0, 1)$ becomes particularly significant, ensuring that the sum of future rewards (the return) typically remains finite and giving preference to more immediate rewards.

The data generated by this interaction loop, specifically the transitions experienced as tuples like $(S_t, A_t, R_{t+1}, S_{t+1})$ , is the raw material for learning. Algorithms like Q-learning, SARSA, or Policy Gradient methods (which we will cover in later chapters) process this stream of experience to update the agent's policy or internal estimates of value, gradually guiding the agent towards better decision-making and achieving its objective of maximizing long-term cumulative reward.