Example. Lifecycle compute allocation and a finite rollout observation bound [ftip-0067]
Example. Lifecycle compute allocation and a finite rollout observation bound [ftip-0067]
A componentwise lifecycle allocation separates resource accounting from the finite number of rollouts available for observation.
In the coordinate order of Definition [ftip-005H], declare a lifecycle budget vector \(\mathbf B\). Its rollout coordinate permits \(N\) attempts. If each attempt has declared success probability \(p\), then \[ \Pr (\text {at least one success})=1-(1-p)^N\leq Np. \] Only the rollout coordinate enters this calculation; no sum or conversion among heterogeneous coordinates is defined.
The finite bound is the union bound applied to Bernoulli rollouts; finite-horizon success probabilities are standard policy-evaluation objects in [sutton2018reinforcement, Section 3.5]. Independence is needed only for the displayed exact expression. The budget vector is illustrative: neither empirical optimality nor interchangeability of heterogeneous units is inferred from it.