REIGN: Robust Expected Information Gain for Navigating Adaptive Perturbation Screens

High-throughput perturbation screens span related experimental contexts, but each query costs reagents, instrument time, and analyst attention. Adaptive experiment selection can speed up hit discovery, yet standard Bayesian optimization treats each context in isolation, ignoring shared structure. We propose REIGN, which combines a conjugate hierarchical Gaussian surrogate with a cross-context information-gain acquisition function. The surrogate propagates posteriors from completed contexts to new ones via exponential moving average updates; the acquisition inflates within-context posterior variance by the estimated between-context variability, directing exploration toward actions whose effects are least stable across prior contexts. We evaluate on three cached-oracle benchmarks: SciPlex3 (99 compounds, 3 cell lines), Shifrut2018 (120 CRISPR targets, 4 donor$\times$stimulation conditions), and Buchwald-Hartwig (264 reaction conditions, 15 substrate contexts). On Buchwald-Hartwig, REIGN reaches $\mathrm{Hit@1} = 0.351$ (95\% CI $[0.325, 0.375]$), tied with BO-UCB (0.352) and well above greedy transfer (0.252, $p < 0.001$, $n{=}50$ seeds), Thompson sampling (0.303), and max-value entropy search (0.304). Turning off cross-context transfer drops every method to random-level performance ($\mathrm{Hit@1} = 0.197$, Cohen's $d{=}1.0$), confirming that the hierarchical surrogate, not the acquisition rule, drives the gains. On SciPlex3 and Shifrut2018 (3-4 contexts), all adaptive methods cluster together and greedy remains competitive, consistent with insufficient contexts for the hierarchical prior to mature. A controlled context-count sweep on Buchwald-Hartwig pins down this transition: exploration-based methods pull ahead of greedy only once roughly 15 contexts have been observed.