BRIDGE-MO: Risk-Aware Witness-Guided Optimization for Multi-Objective Joint Target Attainment

Pareto-based multi-objective optimization is widely used in scientific design to balance competing objectives. However, Pareto optimality is often poorly matched to joint target attainment, where success requires all properties to cross fixed thresholds simultaneously. Pareto methods may continue improving already-satisfied objectives or expanding the trade-off frontier while a bottleneck property remains below target. To address this issue, we introduce Bayesian Risk-Aware Intervention-Driven Guided Exploration for Multi-Objective Optimization (BRIDGE), an optimizer that represents alternative routes to joint attainment through a compact frontier of witness points. An LLM proposes structured intervention cards conditioned on these witnesses, while posterior bottleneck screening and constrained reweighting guide candidate selection with independent exploration and real-evaluation feedback. We derive a conditional, one-step Gaussian-process certificate for risk-gated candidates under an idealized posterior model. Across six finite-pool scientific optimization tasks spanning two to eleven objectives, BRIDGE achieves strong joint-margin trajectories and competitive target-attainment and Pareto performance, supported by module ablations and model-sensitivity analyses. Our results suggest that BRIDGE provides a practical and theoretically grounded framework for scientific optimization focused on simultaneous target satisfaction instead of trade-off expansion.