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A non-starving policy is a (behavior) policy that is theoretically guaranteed to visit each state and take all possible actions from each state an infinite number of times, so that to always update $$Q(s,a), \forall s,\forall a$$, an infinite number of times. In the context of off-policy prediction, this criterion implies that any trajectory will have no zero probability under a behavior policy. As a consequence, the experience from the behavior policy sufficiently covers the possibilities of any target policy.
An example of a non-starving policy is the $$\epsilon$$-greedy policy, which, with $$0<\epsilon\le 1$$ (which is usually a small number between 0 and 1) probability, takes a random action from a given state, and, with $$1-\epsilon$$ probability, takes the current best action, that is, the action with the highest value from a given state, according to the current value function.
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