deterministic policy

A deterministic policy is the simplest kind of rule: in any given state it always picks the same single action, with no element of chance. Show it the same situation twice and you will see the same move twice. It is like a strict recipe — at this step, do exactly this — and it is how we usually imagine an expert who has fully made up their mind.

It is written as a plain function a equals pi of s, mapping each state directly to an action rather than to a distribution over actions. Deterministic policies are appealing because an optimal one is guaranteed to exist for finite MDPs, and they are easy to act on. Their weakness is exploration: an agent that always does the same thing can never discover whether an untried action was better, so during learning we usually inject randomness from outside.