Let's illustrate the difference with an example. In the preceding grid world environment, the goal of the agent is to reach state I starting from state A without visiting the shaded states. In each of the states, the agent can perform any of the four actions: up, down, left, and right to achieve the goal.
A Deterministic Policy tells the agent to perform one particular action in a state. Thus, the deterministic policy maps the state to one particular action and is often denoted by 𝜇. Formally, given a state s at a time t, a deterministic policy tells the agent to perform one particular action a. It can be expressed as:
