Why Did Bayesian Optimization Recommend This Recipe? Action-Level Decomposition of Value and Uncertainty

Bayesian optimization (BO) efficiently searches for material recipes that match a target property, but a recommendation does not reveal which constituent changes drive its acquisition score. We define the deterministic acquisition component as the value remaining when predictive uncertainty vanishes and the residual as the uncertainty-induced component. Shapley linearity attributes both components to constraint-preserving composition and process changes from the current best observed recipe to a recommendation. This common baseline compares heterogeneous myopic acquisitions without relying on acquisition-specific algebraic splits. Across eight datasets and 480 BO episodes, expected utility (EXP), optimistic utility (OPT), and Thompson sampling (TS) shared deterministic-value attributions exactly, whereas their uncertainty-induced attributions showed weak rank agreement and frequent sign disagreement. Family-blocked analysis confirmed that the uncertainty channel remained substantial across all seven experimental families. Reversing which positive or negative uncertainty-induced contributions were down-weighted changed optimization outcomes for all four acquisitions, although it did not significantly outperform the best tuned scalar weighting. Code and experiment artifacts are available at https://anonymous.4open.science/r/TRACE-anon-7D64.