Rate Lock-In for Continual Learning: Information-Theoretic Limits of Post-Deployment Revision

An action rule chosen before future tasks are known can cost more to encode after task arrival than a rule chosen with those tasks in hand. We call this excess output rate lock-in. In a three-state example, every minimum-rate deterministic rule incurs a penalty of 2/3 bit per input for some arriving task, although each future permits zero penalty when known before installation. Installing a conditional action distribution gives a smaller, positive penalty. The penalty can arise while every old action remains unchanged, leaving old-task accuracy unchanged. Lock-in can grow without bound as the state space grows. We characterize when an optimal extension can preserve an installed rule and derive deterministic and randomized rate-revision curves. Under their respective coding criteria and a fixed revision budget, insufficient rate forces invalid actions; action-gap and state-visit assumptions convert this obstruction into decision-loss bounds. We also bound sensitivity to estimated state probabilities and valid-action sets. Finite grid and routing audits demonstrate positive lock-in and quantify the revisions needed to remove it.