TETHER: Task-Evolving Teacher for History-Efficient Regularization in Continual Robot Learning

In continual robot manipulation, sequential fine-tuning can cause a language-conditioned flow-matching policy to generate similar actions under distinct past task conditions. We introduce TETHER (Task-Evolving Teacher for History-Efficient Regularization), which preserves past condition–action correspondences in a shared policy without storing individual demonstrations. The preceding policy serves as a frozen, task-evolving teacher. Task Statistics Memory (TSM) retains compact state-cluster statistics and local state-to-visual-feature maps to reconstruct paired proprioceptive and visual conditions. The teacher estimates an action coordinate for each reconstructed condition, defining action queries at which the student matches its velocity while learning new tasks through flow matching. Magnitude-Aware Regularization (MAR) gives small teacher pose motions greater relative weight, strengthening directional guidance that popular squared-error matching can underemphasize. We evaluate TETHER on simulated benchmarks and real-robot tasks. TETHER achieves strong performance compared to the state-of-the-art methods, notably with the best Area Under the Curve (AUC) and lowest Negative Backward Transfer (NBT) across various tasks, showing that its regularization effectively mitigates forgetting of previously learned condition–action correspondences.