What RL Is

action and action space

An action is a single choice the agent makes—move left, bid five dollars, apply this much motor torque. The action space is the set of all choices available, the agent's entire repertoire. Defining it well shapes everything downstream: too few options and the agent can't express good behavior; too many and learning becomes a needle-in-a-haystack search.

Action spaces come in flavors. Discrete spaces are a finite menu—up, down, left, right—as in most board and video games. Continuous spaces are real-valued dials, like a steering angle or a joint's torque, common in robotics and control. Some problems mix both, or have actions that are only legal in certain states. Which kind you have strongly influences which RL methods fit.

A_t \in \mathcal{A}(s)

the action chosen at time t comes from the set of actions allowed in the current state.