Adapt Only When It Pays: Budgeted Decision-Loss Priority for Delayed Online Time-Series Adaptation

Abstract: Online time-series forecasters receive labels only after horizon-dependent delays, while every adaptation step spends limited compute. We study when an online learner should update, not how to adapt at every opportunity, and introduce ADOWIP: a residual-adapter framework with sealed delay queues, exact budget accounting, and auditable update telemetry. Its main scheduler is an observed decision-loss priority gate that updates only after feedback is revealed, when downstream loss, optionally penalized by prediction MSE, exceeds a calibrated empirical quantile and budget remains. We prove hard-budget feasibility, projected-OGD regret for a convex linear accepted-update subproblem, and stability plus conditional finite-sample gate-selection statements. On public ETT capacity-planning tasks, a frozen calibration/evaluation split selects a gate that lowers held-out decision loss against always, fixed-period, and drift-triggered exact-update baselines under matched compute. Secondary threshold/load-index ETT suites are mixed: 33 of 41 selected contrasts clear the stricter cross-artifact Holm family, and the 8 nonpassing rows are explicitly excluded from primary claims. The same protocol improves an external UCI Bike capacity proxy with 20/0 held-out wins, and a fixed gate passes three full-year Capital Bikeshare station-rebalancing contrasts. Probe-based and finance experiments remain negative, delimiting the current scope of decision-prioritized adaptation.