Protein optimization aims to discover high-fitness sequences under a limited experimental budget. Existing machine-learning methods use task-specific predictors, biological priors, or ranking-aware objectives to guide which variants are tested in the next experimental round. However, these methods cannot adapt to shifts in the reliability of predictive evidence as measurements accumulate and ensure the correct ranking of key high-fitness candidates. To address these challenges, we propose Batch-Aligned Tail Arbitration (BATA), which uses experimental feedback to adaptively combine prior-informed and task-specific rankings for next-batch selection, with calibration focused on the batch-aligned high-fitness region. Across measured GB1, PABP, and TrpB landscapes, BATA achieves the best mean task rank (1.67) in final best fitness after 480 measurements. Controlled comparisons further show task-dependent gains from high-fitness calibration and batch alignment. Our work introduces feedback-calibrated predictor arbitration, where experimental feedback dynamically determines how predictive evidence guides next-batch selection, opening a new direction for protein optimization.
Figures & tables
Figure 1: BATA overview. Measured fitness trains both predictors and calibrates their relative influence. Five-fold out-of-fold (OOF) predictions are converted to ranks to fit a mixture weight on the observed high-fitness region. After refitting on all measurements, the predictors rank unmeasured candidates. Their weighted ranks guide batch selection, and the new measurements start the next round.
Method
GB1
PABP
TrpB
Final rank
AUC rank
BATA
0.8512±0.1083
2.4169±0.4232
0.9209±0.0422
1.67
2.00
ALDE
0.9347±0.0904
1.8183±0.1814
0.8958±0.1099
3.00
2.67
EVOLVEpro-650M
0.7344±0.0966
2.3676±0.4745
0.8982±0.0839
3.00
3.00
REAP100-650M
0.8958±0.0944
1.9960±0.2371
0.8858±0.1177
3.33
3.67
RF
0.8294±0.1070
1.9849±0.2533
0.8934±0.1224
4.00
3.67
Table 1: Main optimization results. Final@480 is the best observed fitness after 480 measurements. Entries give means ± sample standard deviations over 35 matched initializations per task (Main-35). The last two columns average the task-wise ranks of Final@480 and Query-AUC, the area-under-curve metric for discovery speed. Lower mean ranks are better. Bold marks the best task mean or mean rank.
Figure 2: Optimization trajectories. Lines show mean best-observed fitness and bands show pointwise 95% bootstrap confidence intervals over 35 matched campaigns per method and task (Main-35). Points mark the initial measurements and each completed batch. Fitness values use each task’s native scale.
Figure 3: Initialization sensitivity. (a) Mean Final@480 ranks in Main-35 and the sensitivity setting, which uses 70 initializations for GB1 and TrpB and retains 35 for PABP. (b,c) Mean Final@480 and 95% bootstrap intervals for each cohort. Within each method, upper markers show Main-35 and lower markers show the separate 70-initialization cohort. Colors and marker shapes identify methods. Gray lines connect cohort means.
Figure 4: Feedback changes predictor weights. (a) Mean weights on the prior-informed predictor, with pointwise 95% bootstrap intervals over 35 Main-35 campaigns per task. (b) Light lines connect each campaign’s first and last weights; squares and open diamonds show the mean and median, respectively. A lower prior-informed weight gives the task-specific predictor more influence in the combined ranking.
Figure 5: Calibration objectives. (a) All nine paired Final@480 differences between T-DCG-96 (BATA) and the alternative objectives, with the study’s 95% bootstrap intervals over 24 matched groups per task. T-DCG-96 applies discounted cumulative gain (DCG) weights at a measured-fitness rank cutoff of 96. Ties use average ranks, so the number of weighted variants can differ from 96. Positive differences favor T-DCG-96; separate task axes retain the native fitness units. (b) Mean task ranks for Final@480 and Query-AUC from the same 288 optimization runs. Lower ranks are better.
Figure 6: Stronger task-specific predictor. Paired mean Final@480 differences (Fine-only M20 minus BATA) with 95% confidence intervals. Positive values favor Fine-only M20. GB1 and PABP use n=35 , HIS7 and GRB2 use n=24 , and the separate TrpB sensitivity cohort uses n=70 . Fine-only M20 uses a 20-member task-specific ensemble, removes the prior-informed predictor, and changes the selection rule on some tasks.
Appendix figures & tables11 assets
Supplementary material from the paper’s appendix.
Appendix
Task
Representation
Task-specific predictor
Selection
GB1
One-hot
Five-member Ridge ensemble
Thompson-style
PABP
ESM2-650M
One random forest, 100 trees
Greedy mean
TrpB
ESM2-650M
Five bootstrap forests, 100 trees each
Thompson-style
Appendix
Table A1: Task-specific predictors and selection rules in the main BATA comparison. Every task uses five DCA-based Ridge models for the prior-informed predictor.
Method
GB1
PABP
TrpB
Mean rank
BATA
0.6638±0.0727
1.9530±0.2650
0.7783±0.0553
2.00
ALDE
0.7111±0.0736
1.6602±0.1351
0.7689±0.0888
2.67
EVOLVEpro-650M
0.5877±0.0945
2.0122±0.3526
0.7579±0.0808
3.00
REAP100-650M
0.6723±0.0847
1.7809±0.1391
0.7426±0.1056
3.67
RF
0.6600±0.0920
1.8190±0.1699
0.7449±0.1035
3.67
Appendix
Table A2: Main-35 discovery speed. Query-AUC means ± sample standard deviation (SD) over 35 matched initializations per task. Higher Query-AUC and lower mean rank are better.
Figure A1: Campaign outcome distributions. Empirical cumulative distributions of Main-35 Final@480 and Query-AUC. Each curve contains 35 outcomes for one method and task, measured on that task’s native fitness scale.
Table A3: Sensitivity results. Means ± standard deviation (SD) and mean task ranks for GB1 and TrpB with 70 initializations and PABP with 35. The two sections report Final@480 and Query-AUC, respectively.
Objective
GB1
PABP
TrpB
Final rank
AUC rank
G-Rank
0.8297
2.3605
0.9045
3.33
3.67
T-Uniform-96
0.8445
2.2353
0.9191
3.00
3.00
T-DCG-96
0.8496
2.4072
0.9301
1.33
1.33
T-DCG-192
0.8503
2.3401
0.9186
2.33
2.00
Appendix
Table A4: Calibration-objective results. Mean Final@480 over 24 matched groups per task. Final and Query-AUC ranks are computed from task means and then averaged; lower ranks are better.
Figure A2: Matched groups across calibration objectives. Each light line connects one group’s outcomes under the four objectives; squares show objective means. Each task contains 24 matched groups.
Figure A3: Mixture weights across all campaigns. Each task contains 35 campaigns and four decision rounds. Zero assigns all weight to the task-specific predictor; one assigns all weight to the prior-informed predictor. All heatmaps use this shared scale.
Figure A4: Runtime and ensemble size. (a) Complete-campaign wall times and medians from three engineering timings per configuration. (b) Elapsed times of three M100 attempts stopped after two rounds at their time limits. These times cover incomplete campaigns.
Figure A5: Controls with matched task-specific predictor capacity. Paired mean Final@480 differences and 95% bootstrap intervals for BATA minus task-specific-only prediction and equal-rank combination, using 24 matched initializations per main task. Each task has a separate axis in its native fitness units. Positive values favor BATA.
Task
BATA
G20
Fine-only M20
GB1
0.8802
0.8519
0.8549
PABP
2.3132
2.2571
2.0830
TrpB
0.9399
0.9554
0.9665
HIS7
1.4138
1.4138
1.3227
GRB2
0.6276
0.6276
0.5964
Mean rank
1.40
2.20
2.40
Appendix
Table A5: Independent confirmation of the switching rule. Mean Final@480 over ten matched initializations per task. Bold marks the best task mean. Ranks use the released deterministic tie rule: decreasing mean, then increasing arm identifier.
Figure A6: Switching-rule results. (a) Task-wise Final ranks and released mean ranks in the independent ten-initialization cohort. (b) Fraction of campaigns using Fine-only M20 at each round. G20 uses the fixed threshold of 0.20. Decision rounds within a campaign are dependent.
Foundation models for protein structure prediction remain unreliable on certain targets. External oracles can flag and correct these failures, but biological oracles are expensive, making oracle budget a critical constraint. Existing guidance methods, such as FK-steering, DPO, and Best K-of-N sampling, differ in how they spend this budget, yet no systematic comparison exists to guide method selection. To bridge this gap, we benchmark these methods alongside the recently proposed Optimisation Over Outputs (O3), which applies off-the-shelf optimisers within a generative model's latent subspace. We extend the usage of O3 to protein structure prediction models. Overall, our work provides the first practical reference for oracle budget-aware guidance. Our evaluation on two protein targets, calmodulin (1CLL) and E. coli aspartate transcarbamoylase (9EEH), reveals that no single method consistently dominates across all budgets and oracles. Specifically, O3 proves most effective at low oracle budgets, while FK-steering and DPO demonstrate improved performance as the budget increases. We distil these findings into actionable recommendations for practitioners operating under real-world oracle-budget constraints.
Aleksandra Kalisz, Jack Simons, Krisztina Sinkovics +4
InstaDeep Ltd · University of Oxford · Lancaster University
AI for scientific discovery is entering an agentic era, where protein-engineering systems are expected to prioritize future wet-lab experiments rather than merely fit static measurements. We introduce TadA-Bench, a million-variant wet-lab replay benchmark from 31 TadA directed-evolution rounds for future-round discovery toward agentic protein engineering. TadA-Bench preserves the campaign chronology and defines a fixed-data replay task: given earlier experimental rounds, models rank variants that appear only in later rounds. It provides aligned DNA, RNA, and protein views, and uses Seq2Graph, a graph-based label-unification pipeline, to reconcile noisy enrichment measurements into consistent cross-round activity labels. Random-split controls show strong interpolation, but future-round ranking and finite-budget candidate selection are much weaker. Controlled analyses suggest that evolutionary coverage is more informative than local data density, positioning TadA-Bench as a reproducible wet-lab replay substrate for future-round discovery toward agentic protein engineering; the data and code are released on Hugging Face and GitHub.
Jin Gao, Juntu Zhao, Zirui Zeng +5
Shanghai Jiao Tong University · Shanghai Innovation Institute.
Designing proteins with desired functions or properties represents a core goal in synthetic biology and drug discovery. Recent advances in protein language models (PLMs) have enabled the generation of highly designable protein sequences, while preference alignment provides a promising way to steer designs toward desired functions and properties. Nevertheless, they often trigger catastrophic forgetting of pretrained knowledge, degrading basic designability and failing to balance multiple competing objectives. To address these issues, we draw inspiration from On-Policy Distillation (OPD), an advanced post-training method renowned for mitigating catastrophic forgetting through its mode-seeking nature. In this work, we propose ProteinOPD, a multi-objective preference alignment framework that can effectively balance multiple preference objectives while maintaining the inherent designability of PLMs. ProteinOPD adapts a pretrained PLM into preference-specific teachers and distills their knowledge into a shared student via token-level OPD on the student's own trajectories. During this process, the student is aligned to a unique normalized geometric consensus of weighted teachers while ensuring bounded optimization under conflicts. This bridges the gap for OPD in multi-objective/teacher alignment. Extensive experiments show that ProteinOPD achieves substantial gains on target preference objectives without compromising the designability, with an 8x training speedup over RL-based alignment competitors.
Yulin Zhang, He Cao, Zihao Jiang +6
Tsinghua University · International Digital Economy Academy · Hong Kong University of2026 Science and Technology (Guangzhou) +1