We just published a paper (arxiv.org/abs/2607.23896). It's about robotic chemistry labs, but it starts from something anyone who has renovated a house knows: the expensive mistake usually isn't doing the work badly. It's doing the wrong work beautifully.
In our benchmark, an agent that spends $185 on a few cheap tests before picking its chemistry hits the recovery target for about $5,000. An agent that skips the tests, picks the obvious-looking chemistry, and optimizes it flawlessly spends $24,090. Same robot, same skill, five times the bill. All it did wrong was answer the wrong question well.
The method is called Coactive learning, short for cost-aware active learning. The paper, the code, and every number below are public.
Robots got fast. Decisions didn't.
Autonomous labs are here. Robots dispense the liquids, instruments read the results, and software plans the next batch of experiments overnight. A recent standout is PNNL's CICERO platform, which pulls valuable metals out of messy real-world feedstocks: oilfield wastewater and shredded magnets from end-of-life hard drives.
The planning software in these labs is good at one job: fine-tuning a recipe. Given a chemistry, it will find the best temperature, concentration, and mixing ratios with impressive efficiency. What it doesn't ask is whether you handed it the right recipe. Which metal should this campaign go after? Which reagent chemistry can actually get it? And is it worth running a $100 assay before committing to a $4,800 plate of 96 experiments?
Hospitals settled this long ago. Nobody gets wheeled into surgery before the blood work. The cheap test earns its keep by steering the expensive decision that follows. Today's lab agents mostly skip the blood work, and nothing in their math even lets them ask about it, because standard experiment-picking rules have no notion of price.
The idea: keep score in dollars
Our fix is simple to state. Put every possible action, the $100 assay and the $4,800 plate alike, on one scoreboard, and score each by how much progress it buys per dollar.
The campaign runs in two stages. First it treats the candidate chemistries as rival hypotheses and buys the cheapest evidence that tells them apart, committing only once it's genuinely confident (and admitting it if the evidence runs out, rather than guessing). Then it switches to classic Bayesian optimization and tunes the winning chemistry plate by plate. Cheap tests naturally run first, not because we hard-coded that, but because they cost a hundredth as much per unit of certainty. The prices decide the order.
Under the hood, the two stages descend from two results we each published over a decade ago: EC², from Deb's work with Daniel Golovin and Andreas Krause on learning from noisy, costly tests, and GP-UCB, from Niranjan's work with Andreas Krause, Sham Kakade, and Matthias Seeger, which won ICML's Test of Time award. This paper brings them together in one campaign.
What happened when we raced them
We built a simulated benchmark anchored to published results from the CICERO study (synthetic surfaces, real cost structure: $50 per well, $4,800 per plate). Every method gets the same underlying machinery, so the only thing being compared is judgment: how each policy decides what to run. Average cost to hit the recovery target, over 20 runs:
| Feedstock (achievable optimum) | Coactive | Oracle-pathway BO | Split-plate BO | Commit-first BO |
|---|---|---|---|---|
| Produced water, Mg (99.2%) | $4,980 | $5,370 | $5,370 | $5,370 |
| SmCo leachate, Sm (92.0%) | $7,600 | $9,450 | $9,450 | $9,450 |
| NdFeB leachate, Fe/REE (sep. 216) | $4,985 | $4,890 | $4,890 | $24,090 |
Three things stand out.
It keeps up with a method that's given the answer key. The oracle baseline is told the correct chemistry before it starts. Ours has to figure that out from scratch, and it still lands within 2% on the hardest feedstock while coming in cheapest on the other two.
One wrong guess costs more than optimization can win back. On the magnet feedstock, the obvious default reagent looks right and fails; a less obvious one succeeds. That mirrors a contrast reported in the CICERO study itself. Our commit-first baseline makes exactly that wrong commitment and burns roughly $19,000 of plates before recovering. The two-stage method avoids it for $185. Decades of work have gone into making optimizers a few percent better. This gain comes from a different lever entirely, and on this benchmark it is the largest one.
The information is what matters, not our particular way of buying it. The strongest baseline we tested splits its first plate across all the candidate chemistries and picks the best performer. On this benchmark it avoids the wrong commitment too, at essentially our cost. We report that plainly because it sharpens the real question: not whether to buy pathway information before committing (always), but which way of buying it is cheapest in your situation. A split plate works when all your candidates fit on one plate. Cheap targeted diagnostics should pull ahead when there are dozens of candidates, when assays cost far less than wells, or when the target is easy to miss. Testing that regime is where we're headed next.
(For the careful reader who notices random search performing well on the easiest feedstock: modest targets on small surfaces are easy to reach, and a single 96-well plate samples 96 conditions at once. Against tighter targets the optimizers separate cleanly from random. The appendix has the numbers.)
A budget you can write down in advance
The theory in the paper does something practical: it lets you price a campaign before running it. Under stated assumptions, expected spend is at most the identification cost plus a capped optimization budget, with an explicit success probability. And the cost of skipping identification isn't folklore, it's a proposition: at least the wasted-plate bill times the chance of guessing wrong, minus what the diagnostics cost you. Cheap tests plus plausible wrong guesses make that number large, which is exactly what the benchmark shows.
We're careful in the paper about what the math does and doesn't cover (the optimization bound applies to an idealized version of the procedure, and the discovery stage is motivated by EC² rather than inheriting its guarantee). Every assumption is written down where a reader can check it.
If you run a lab, your old logs are a benchmark
Two things we want to do next. Replay: take the logged experiments from any real campaign and score our policy against what actually happened, counterfactually, on real chemistry, without running anything new. And live validation: our method against a platform's incumbent optimizer on a real campaign, in separations or in neighboring problems like battery electrolyte formulation, anywhere discrete choices come before continuous tuning and cheap screens come before expensive runs.
The code is plain NumPy and runs in seconds on a laptop. If wrong early commitments cost your lab real money, get in touch.
View the code on GitHub → Read the paper →
Questions: dray@coactive.science, niranjan@coactive.science