cs.LGSep 29, 2026
SaveFeedback-Calibrated Protein Optimization with Batch-Aligned Tail Arbitration
Organizations: School of Computer Science and Technology, University of Science and Technology of China, Hefei, Anhui, China
Abstract
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 | 1.67 | 2.00 | |||
| ALDE | 3.00 | 2.67 | |||
| EVOLVEpro-650M | 3.00 | 3.00 | |||
| REAP100-650M | 3.33 | 3.67 | |||
| RF | 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 , HIS7 and GRB2 use , and the separate TrpB sensitivity cohort uses . 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 |
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 | 2.00 | |||
| ALDE | 2.67 | |||
| EVOLVEpro-650M | 3.00 | |||
| REAP100-650M | 3.67 | |||
| RF | 3.67 |
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 |
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 |
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.