Feedback Control for Multi-Objective Graph Self-Supervision

Abstract

Can multi-task self-supervised learning on graphs be coordinated without the usual tug-of-war between objectives? Graph self-supervised learning (SSL) offers a growing toolbox of pretext objectives like mutual information, reconstruction, and contrastive learning, yet combining them reliably remains challenging due to objective interference and training instability. Most multi-pretext pipelines use per-update mixing, forcing every parameter update to be a compromise and leading to three failure modes: Disagreement (conflict-induced negative transfer), Drift (nonstationary objective utility), and Drought (hidden starvation of underserved objectives). We argue that coordination is fundamentally a temporal allocation problem: deciding when each objective receives optimization budget, not merely how to weigh them. We introduce ControlG, a control-theoretic framework that recasts multi-objective graph SSL as feedback-controlled temporal allocation by estimating per-objective difficulty and pairwise antagonism, planning target budgets via a Pareto-aware log-hypervolume planner, and scheduling with a Proportional-Integral-Derivative (PID) controller. Across 9 datasets, ControlG consistently outperforms state-of-the-art baselines while producing an auditable schedule that reveals which objectives drove learning.