DebtMerge: Long-Horizon Expert Evolution for Continual Model Merging

Continual model merging (CMM) sequentially integrates task-specific experts without joint retraining. Existing methods mainly make local merge decisions based on the incoming task and current expert state, without accounting for the cumulative effects of past merges. Over long task streams, this can lead to persistent historical perturbation, insufficient integration of incoming knowledge, and growing expert-capacity pressure. Jointly optimizing expert selection and update parameters is also constrained by costly candidate evaluations. To address these, we introduce DebtMerge, a long-horizon optimization framework for expert-managed CMM that jointly addresses long-horizon control and finite-budget merge optimization. DebtMerge formulates CMM as an online problem with time-average targets and uses Lyapunov virtual queues to represent accumulated stability, plasticity, and resource debts. These debts induce a per-arrival objective, while stability and plasticity debts guide geometry initialization without future task information. To optimize this objective under a fixed evaluation budget, DebtMerge uses evolutionary transfer optimization over merge recipes specifying expert structure, knowledge composition, and integration geometry. Compatible historical recipe blocks are adapted to the current expert bank and debt state, with objective feedback guiding their reuse toward promising combinations. We characterize debt-guided directional control, incorporate finite-budget solver error into the long-horizon control bound, and derive sufficient conditions for preserving historical predictions under stated assumptions. Experiments across vision and language models show improved average performance over the compared merging baselines.