Abstract
Choosing a recovery process for scale-up requires connecting laboratory results with product requirements, process costs, and scale effects. We analyze records from Pacific Northwest National Laboratory's Computer Intelligence for Critical Element Recovery and Optimization (CICERO) workflow for autonomous selective precipitation. Active learning uses prior results to choose experiments. In a conditional retrospective benchmark with fitted models and recycled neodymium-iron-boron (NdFeB) magnet records, active learning finds the best recorded result with fewer experiments than nonadaptive space filling. Enrichment is the selected rare-earth-to-iron ratio relative to that in the feed. Adaptive policies reach the recorded enrichment maximum by 16 to 24 wells (individual experiments), versus 48. Our two-stage reconstruction ties two adaptive alternatives at 16 wells. Conditional analyses of recycled samarium-cobalt (SmCo) magnets show a Round 2 tradeoff between purity and nominal yield, the recovery fraction calculated from an assumed starting amount - NdFeB Round 1 routes differ in enrichment. Rankings for produced water from oil and gas extraction depend on phase and dilution assumptions requiring confirmation. We propose choosing batches by their expected reduction in downstream Bayes risk: the minimum expected loss among available process decisions under current beliefs. In exploratory simulations, a hybrid that filters candidates has lower estimated loss than the implemented joint search across routes and conditions. Differences involving the synthetic two-stage policy are small relative to estimation uncertainty. We outline a pre-registered prospective test under a shared loss and logging standard, requiring clarified measurements and records, a defined process decision and relevant outputs, credible economic inputs, and validation at the intended scale.
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Autonomous laboratories automate experimental execution, but a campaign must also decide which recovery pathway merits optimization. We formulate this as a sequential decision problem with a discrete pathway-identification stage and a continuous within-pathway optimization stage under heterogeneous experimental costs. Our implementation, Coactive learning, combines a cost-sensitive Bayesian hypothesis-discrimination policy motivated by EC2 (Golovin et al., 2010) with Gaussian-process Bayesian optimization (Srinivas et al., 2010). Under explicitly stated assumptions, the expected spend of one fixed-budget campaign attempt is bounded by the expected pathway-identification cost plus the capped within-pathway optimization budget. We evaluate the method on synthetic benchmarks constrained by selected results reported for PNNL's CICERO selective-precipitation study (Ritchhart et al., 2026). The method performs comparably to an oracle-pathway Bayesian-optimization reference and to a strong split-plate baseline that discriminates pathways with its first plate, without receiving an oracle label for the correct pathway. It is given a candidate hypothesis space and a diagnostic likelihood model. On an NdFeB-inspired instance, it avoids the simulated penalty of a commit-first baseline that initially selects a plausible but inferior hydroxide pathway. This hypothetical wrong-first-commitment scenario is motivated by the hydroxide-oxalate performance contrast reported by CICERO. We characterize the sensitivity of these conclusions to the assumed cost model. The code and benchmark are open source.
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Active learning studies the fundamental question: what data should we choose to observe? The greedy algorithm in optimal experiment design is a common heuristic and also equivalent to myopic Bayesian active learning for linear regression, the common framework where long-term planning is replaced with the one-step optimal choice. In this work, we prove a first-of-its-kind approximation ratio for the greedy algorithm's risk that is tight up to an absolute constant. The approximation ratio is linear in the maximum initial leverage score (MILS), a newly identified quantity fundamental to the greedy algorithm's performance. Finally, we illustrate the results with simple numerical simulations.
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Learning effective policies for adaptive data acquisition remains challenging: posterior-based methods rely on surrogate models and posterior approximations that can be misspecified or biased, while direct policy-learning methods map from historical observations and fail to exploit available model representations, making learning harder. We introduce policy learning with belief representations (POLAR), based on the insight that optimal data acquisition depends on the observation history only through a sufficient belief state. Specifically, POLAR decouples representation learning from policy learning by leveraging pretrained predictive foundation models as belief-state encoders, training a policy head on top of their representations. This yields a simple, unified amortised policy learning framework for Bayesian experimental design, Bayesian optimisation, and active learning, differing only in the task-specific utility used to train the policy. Empirically, we find that POLAR outperforms state-of-the-art amortised methods across diverse tasks while requiring far fewer training samples, demonstrating a significant step in the scalability and efficiency of amortised data acquisition.
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