I write this as part of what I do in explaining ML (and goodness forbid, AI) concepts to non-technical friends.

Reinforcement learning (RL) is a machine learning approach where an agent learns to make decisions by interacting with an environment to achieve a specific goal. The agent improves over time by receiving rewards for good actions and penalties for bad actions, and it uses these signals to adjust its behavior.

1. Core Components:
Agent: The decision-maker (e.g., a robot, software, or AI program).
Environment: Everything the agent interacts with (e.g., a virtual world, stock market simulation, or a game).
State (S): A snapshot of the environment at a given time (e.g., the position of pieces in a chess game).
Action (A): The decision or move the agent can make (e.g., moving a pawn in chess).
Reward (R): A feedback signal the agent receives after performing an action (positive for good actions, negative for bad ones).

2. The Learning Process:
The agent observes the current state of the environment.
It chooses an action based on its current knowledge (using a policy, which is its strategy for decision-making).
The environment transitions to a new state, and the agent receives a reward.
The agent updates its policy to increase the likelihood of choosing actions that lead to better rewards in the future.

3. Key Goal:
The agent aims to maximize the cumulative reward over time (not just immediate rewards). This involves balancing:
Exploration: Trying new actions to discover their potential rewards.
Exploitation: Using known actions that have yielded high rewards in the past.

4. Underlying Algorithm: Many RL algorithms, like Q-Learning or Deep Q-Networks (DQN), use mathematical frameworks like:
Value Functions: Estimating the expected reward of a state or state-action pair.
Policy Functions: Directly mapping states to actions.

5. Example in Practice:
Imagine teaching a robot to walk:
States: The robot’s current position and angles of its joints.
Actions: Moving its legs in different directions.
Reward: +1 for moving forward, -1 for falling. Over time, the robot learns which sequences of movements keep it balanced and moving forward, optimizing its walking ability.

Using a dog analogy, the policy is the dog’s strategy for deciding what to do in a given situation. It tells the dog how to behave (or what action to take) based on what it observes in its environment.

Example with the Dog Analogy:

1. State: The current situation, such as:
The ball is on the ground.
The ball is far away.
The ball has been thrown.

2. Action: The dog’s possible responses, such as:
Run toward the ball.
Lie down.
Bark.
Ignore the ball.

3. Policy: The strategy the dog uses to decide:
“If the ball is thrown, run after it.”
“If the ball is on the ground, pick it up and bring it back.”
“If the owner praises me, keep doing the same thing.”

Formal Definition:
The policy is a function or rule that maps a state (e.g., “the ball is far away”) to an action (e.g., “run toward the ball”). In reinforcement learning, the policy can be:
Deterministic: Always choosing the same action for a given state.
Stochastic: Assigning probabilities to actions (e.g., 80% chance to run toward the ball, 20% chance to bark).

For the dog, as it learns through trial and error (getting rewards like treats), it refines its policy to make better decisions over time. In RL terms, the policy gets optimized to maximize the total reward (e.g., praise or treats). The policy is not the range of actions the dog has access to; it’s the strategy that determines which action the dog chooses in a given situation (state).

Clarification:
Range of Actions: This is the set of all possible things the dog can do. For example, actions like running, barking, sitting, lying down, or fetching the ball.
Policy: This is a rule or mapping that tells the dog which action to take based on the current situation (state).

Scenario: The ball is thrown.

The dog has these possible actions:
1. Run toward the ball.
2. Sit and wait.
3. Bark.
4. Ignore the ball.

Policy:
The policy is the dog’s strategy, such as:
If the ball is thrown, then run toward it.
If the ball is close, then pick it up and bring it back.
The policy chooses the best action (e.g., fetch the ball) out of all possible actions based on what the dog has learned will lead to the greatest reward.

Key Point: The range of actions is static and defines what the dog can do, while the policy evolves and adapts to decide what the dog should do in any given state to maximize rewards. The policy directly relates the state to the action. In reinforcement learning, a policy is a function or mapping that tells the agent (or in the analogy, the dog) what action to take in a given state.

Formal Definition: The policy is denoted as , where:
 (state): Represents the current situation or condition of the environment.
 (policy): Specifies the action that the agent should take in that state.
Thus, the policy answers the question:
“Given this state, what action should I take?”

To reemphasize using the dog analogy:
Components:
State: The current situation in the environment.
Example: “The ball is 10 feet away,” or “The ball is in my mouth.”
Action: What the dog can do.
Example: Run, pick up the ball, drop the ball, or bark.
Policy: The strategy that links the state to the action.
Example:
If the ball is 10 feet away, the policy might say, “Run toward the ball.”
If the ball is in your mouth, the policy might say, “Bring it back to the owner.”
The policy evolves as the dog learns through trial and error, improving its decisions to maximize rewards (like treats or praise).

Key Idea: The policy is the decision-making function that determines what action to take based on the current state of the environment. It’s the agent’s “brain” for mapping states to actions.