Certified Behavioral Retention for Continual Adaptation with Held-Out Anchors

Continual adaptation requires deciding not only how to update a model, but whether to commit the update without exceeding a declared budget for changes to protected behavior. We introduce Certified Anchor-Based Adaptation (CABA), a candidate-agnostic post-update gate that reserves historical observations from candidate optimization, compares old and candidate policies on frozen representations, and selects the largest tested interpolation coefficient whose worst-anchor forward KL divergence does not exceed the budget. The finite retention check requires neither action labels nor complete trajectories. We develop a theory-led certification framework that separates measured anchor retention from conditional off-anchor guarantees. Under explicit representation-coverage and Lipschitz assumptions, an accepted update satisfies a uniform behavioral-divergence bound on protected support. The analysis provides explicit regularity bounds for affine softmax heads, high-probability coverage and compression guarantees, monotonicity conditions for interpolation paths, grid-resolution bounds, and trajectory-level and sequential-composition guarantees. These results specify the assumptions needed to interpret a finite acceptance check, rather than asserting global safety or preserved task accuracy. In the reported controlled UCI Human Activity Recognition study, used as a non-stationary sensor-policy proxy, CABA reduces mean forgetting from $1.01\%$ for unconstrained adaptation to $0.00\%$ at budget $\epsilon=0.05$, while reducing final average accuracy from $93.04\%$ to $88.48\%$. This proof of concept illustrates a retention–plasticity trade-off; it does not establish foundation-model or robotic performance. CABA supplies an auditable retention check for compatible candidate generators exposing comparable policy distributions and a declared update path, while deployment additionally requires separate evidence of current-task utility.