Consensus Accelerates Evolution: Black-Box Many-Task Optimization via Information-Geometric Consensus

Natural evolution strategies (NESs) provide a principled information-geometric framework for black-box optimization. However, scaling NESs to many concurrent tasks is hindered by hyperparameter sensitivity and high-variance natural-gradient estimates. With limited sampling per task, noisy distribution updates reduce useful progress and slow convergence. To address these limitations, we propose GemNES, an online meta-black-box optimizer using concurrent many-task optimization trajectories as supervision for data-efficient adaptation through dual-level information-geometric consensus (IGC). Specifically, global IGC pools normalized task-trajectory progress into a consensus signal for natural-gradient meta-policy updates and task-conditioned control. Meanwhile, local IGC aggregates aligned peer natural gradients in standardized tangent coordinates to improve each task update. Together, they encode cross-task agreement through natural-gradient updates on the meta-policy and task-distribution manifolds. Under alignment and regularity conditions, our analysis identifies a sufficient safe-transfer region, quantifies scale reduction relative to unsuppressed transfer, and derives tighter finite-horizon contraction for the evolving rank surrogate. Empirical results on synthetic many-task benchmarks and neural policy search demonstrate faster and more sustained convergence compared with representative baselines.