Uncertainty Aware Quality-Diversity Optimization For Offline Biological Sequence Design

Alona Rimon; Hannah Janmohamed; Maxime Allard; Antoine Cully

cs.LGOct 31, 2026

Uncertainty Aware Quality-Diversity Optimization For Offline Biological Sequence Design

Authors: Alona Rimon, Hannah Janmohamed, Maxime Allard, Antoine Cully

Organizations: Imperial College London · Helical

Abstract

Designing sequences such as nucleic acids and proteins with desired properties is a fundamental challenge in biology. Due to the vast, discrete nature of sequence spaces and the high cost of experimental evaluation, offline computational sequence design plays a crucial role in proposing novel sequences before costly wet-lab validation. In practice, it is also essential that proposed designs are diverse to increase the likelihood of downstream experimental success. This motivates methods that balance performance, novelty, and diversity, whilst mitigating against uncertainty inherent to offline optimization. Quality-Diversity optimization (QD) can discover diverse, high-performing solutions, making it well suited to this problem, but its elitist nature makes reliable exploration under uncertainty challenging. To address this, we introduce Prior-guided Offline MAP-Elites (POME), an uncertainty-aware QD framework explicitly adapted to the offline regime. Our method leverages foundation models as priors to guide search toward biologically plausible regions and enable robust exploration under uncertainty. Across three sequence design tasks, POME consistently improves both performance and diversity over prior offline QD methods, and achieves the most reliable balance compared to offline MBO baselines, obtaining the best performance on two tasks and the second-best on the third, while maintaining high diversity and novelty.

Figures & tables

Panel of Figure 1 — Figure 1: Overview of POME, our offline QD optimization framework. (a) An ensemble of surrogate models is trained on the offline dataset, while a foundation model is pre-trained on large unlabeled biological corpora. (b) Sequences are sampled from the archive, mutated using the foundation model, evaluated via an uncertainty-aware combination of surrogate predictions and the foundation model prior, and reinserted if they improve the corresponding cell elite.

Figure 2: An example of a 2D Pareto front illustrating the trade-off between predicted fitness and certainty across solutions.

Figure 3: Quality-Diversity trade-offs across tasks (max and mean score vs. diversity). Starred points denote Pareto-optimal methods and lines connect the Pareto front.

Figure 4: Relationship between surrogate-predicted score and true oracle performance across tasks (mean top-128 scores). Baseline QD methods show misalignment, whereas POME yields closer and more consistent alignment throughout optimization. Note that surrogate scores are on different scales across methods, hence plots are shown separately. Oracle evaluations are performed post hoc for analysis only and are not used at any stage of training, model development, or optimization.

Name	Max	Mean	Diversity	Novelty
CbAS	0.95 $\pm$ 0.01	0.71 $\pm$ 0.03	26.74 $\pm$ 0.60	19.70 $\pm$ 0.13
BO-qEI	0.88 $\pm$ 0.07	0.77 $\pm$ 0.05	27.61 $\pm$ 0.69	20.64 $\pm$ 0.40
CMA-ES	0.99 $\pm$ 0.01	0.58 $\pm$ 0.04	25.01 $\pm$ 1.20	21.24 $\pm$ 0.21
GRAD	0.91 $\pm$ 0.03	0.60 $\pm$ 0.01	26.26 $\pm$ 0.25	19.05 $\pm$ 0.19
REINFORCE	0.94 $\pm$ 0.02	0.67 $\pm$ 0.02	28.44 $\pm$ 0.11	19.60 $\pm$ 0.06
COMs	0.96 $\pm$ 0.02	0.75 $\pm$ 0.03	27.51 $\pm$ 0.90	19.67 $\pm$ 0.20

Table 1: Performance, diversity, and novelty on the 5’UTR task. Results are averaged over 10 runs.

Name	Max	Mean	Diversity	Novelty
CbAS	0.85 $\pm$ 0.05	0.58 $\pm$ 0.01	6.52 $\pm$ 0.02	2.36 $\pm$ 0.04
BO-qEI	0.67 $\pm$ 0.11	0.56 $\pm$ 0.00	6.52 $\pm$ 0.03	2.29 $\pm$ 0.04
CMA-ES	0.88 $\pm$ 0.04	0.60 $\pm$ 0.02	5.07 $\pm$ 0.33	2.39 $\pm$ 0.08
GRAD	0.82 $\pm$ 0.06	0.57 $\pm$ 0.01	6.45 $\pm$ 0.04	2.31 $\pm$ 0.06
REINFORCE	0.85 $\pm$ 0.03	0.57 $\pm$ 0.01	6.53 $\pm$ 0.04	2.30 $\pm$ 0.05
COMs	0.74 $\pm$ 0.02	0.51 $\pm$ 0.02	6.00 $\pm$ 0.08	2.23 $\pm$ 0.04

Table 2: Performance, diversity, and novelty on the TFBind task. Results are averaged over 10 runs.

Name	Max	Mean	Diversity	Novelty
CbAS	0.87 $\pm$ 0.07	0.45 $\pm$ 0.02	22.99 $\pm$ 1.78	10.49 $\pm$ 0.93
BO-qEI	0.99 $\pm$ 0.01	0.98 $\pm$ 0.00	3.32 $\pm$ 0.11	1.33 $\pm$ 0.04
CMA-ES	0.50 $\pm$ 0.03	0.29 $\pm$ 0.01	194.03 $\pm$ 1.3	183.1 $\pm$ 2.12
GRAD	0.27 $\pm$ 0.14	0.16 $\pm$ 0.19	4.95 $\pm$ 1.50	78.86 $\pm$ 27.58
REINFORCE	0.99 $\pm$ 0.00	0.98 $\pm$ 0.00	1.98 $\pm$ 0.18	0.66 $\pm$ 0.09
COMs	0.76 $\pm$ 0.30	0.76 $\pm$ 0.30	0.11 $\pm$ 0.16	6.72 $\pm$ 9.51

Table 3: Performance, diversity, and novelty on the GFP task. Results are averaged over 10 runs.

Appendix figures & tables10 assets

Supplementary material from the paper’s appendix.

Appendix

Figure 5: Overview of the offline model-based optimization evaluation protocol. A hidden dataset is used to train an oracle, which may be used to relabel the visible offline dataset provided to the optimization algorithm. The offline MBO method then generates a batch of candidate designs, which are evaluated by the oracle for benchmarking.

Task	Sequence Space	Objective	Oracle	Offline Dataset
5’UTR	50-nt RNA (A, C, G, U)	Maximize ribosome load	ResNet-Based	140,000 samples (bottom 50%) Range: – 0.1679-0.5924 (data) – 0.1632-0.7179 (oracle)
TFBind-10	10-nt DNA (A, C, G, T)	Maximize binding affinity (pho4)	Exact lookup	100,000 samples (sampled uniformly from bottom 50%) Range: – 0.0-0.556 (data) – 0.0-1.0 (oracle)
GFP	237-AA Protein	Maximize fluorescence values	ResNet-Based	18,695 samples (sampled $\propto\exp(-f(x))$ ) Range: – 0.7351-0.9614 (data) – 0.7351-0.9784 (oracle)

Appendix

Table 4: Overview of the sequence design tasks used in our experiments.

Dataset	Method	$\tau=0.7$	$\tau=0.8$	$\tau=0.9$	$\tau=0.95$
5’UTR	MAP-Elites	$\mathbf{97.88\pm 0.84}$	$19.06\pm 1.77$	$0.01\pm 0.01$	$0.01\pm 0.01$
	One-Shot QD	$95.41\pm 1.11$	$19.46\pm 4.13$	$0.10\pm 0.11$	$0.02\pm 0.04$
	POME	$95.81\pm 0.52$	$\mathbf{85.15\pm 1.50}$	$\mathbf{70.36\pm 5.24}$	$\mathbf{39.04\pm 4.92}$
	POME-MO	$89.52\pm 2.09$	$36.41\pm 3.65$	$5.80\pm 2.48$	$1.15\pm 0.66$
TFBind	MAP-Elites	$6.90\pm 0.46$	$0.39\pm 0.07$	$0.00\pm 0.01$	$0.00\pm 0.00$
	One-Shot QD	$5.99\pm 0.49$	$0.35\pm 0.08$	$0.01\pm 0.01$	$0.00\pm 0.00$

Appendix

Table 5: Archive profile: percentage of cells exceeding oracle thresholds

\tau

Method	Runtime (min)	Peak GPU Power (W)
MAP-Elites	20.89	192.51
POME	41.40	218.68

Appendix

Table 6: Computational cost on the UTR task (averaged over 10 runs).

Task	Method	Max	Mean	Diversity	Novelty
UTR	POME	1.03 $\pm$ 0.02	0.86 $\pm$ 0.01	25.55 $\pm$ 1.38	20.24 $\pm$ 0.21
UTR	POME (random mut.)	1.01 $\pm$ 0.02	0.83 $\pm$ 0.02	27.45 $\pm$ 1.28	20.13 $\pm$ 0.29
UTR	POME-MO	0.99 $\pm$ 0.00	0.77 $\pm$ 0.00	26.63 $\pm$ 1.09	19.66 $\pm$ 0.15
UTR	POME-MO (random mut.)	0.96 $\pm$ 0.03	0.77 $\pm$ 0.01	26.85 $\pm$ 0.83	19.68 $\pm$ 0.12
TFBind	POME	0.89 $\pm$ 0.02	0.61 $\pm$ 0.01	6.51 $\pm$ 0.19	2.51 $\pm$ 0.10
TFBind	POME (random mut.)	0.86 $\pm$ 0.02	0.60 $\pm$ 0.01	6.63 $\pm$ 0.21	2.51 $\pm$ 0.03

Appendix

Table 7: Ablation of foundation-model guided mutations across tasks.

Task	Method	Max	Mean	Diversity	Novelty
UTR	POME	1.03 $\pm$ 0.02	0.86 $\pm$ 0.01	25.55 $\pm$ 1.38	20.24 $\pm$ 0.21
UTR	Prior-only	1.00 $\pm$ 0.01	0.82 $\pm$ 0.02	25.20 $\pm$ 0.35	20.62 $\pm$ 0.07
TFBind	POME	0.89 $\pm$ 0.02	0.61 $\pm$ 0.01	6.51 $\pm$ 0.19	2.51 $\pm$ 0.10
TFBind	Prior-only	0.86 $\pm$ 0.01	0.58 $\pm$ 0.01	6.74 $\pm$ 0.07	2.43 $\pm$ 0.07
GFP	POME (full)	0.96 $\pm$ 0.02	0.48 $\pm$ 0.03	12.29 $\pm$ 0.61	7.77 $\pm$ 0.25
GFP	Prior-only	0.91 $\pm$ 0.02	0.47 $\pm$ 0.02	15.27 $\pm$ 0.73	7.97 $\pm$ 0.19

Appendix

Table 8: Effect of removing surrogate-based scoring across tasks.

Task	Method	Max	Mean	Diversity	Novelty
UTR	POME (full)	1.03 $\pm$ 0.02	0.86 $\pm$ 0.01	25.55 $\pm$ 1.38	20.24 $\pm$ 0.21
UTR	Fixed uncertainty	1.03 $\pm$ 0.01	0.82 $\pm$ 0.01	28.14 $\pm$ 1.00	20.46 $\pm$ 0.17
TFBind	POME (full)	0.89 $\pm$ 0.02	0.61 $\pm$ 0.01	6.51 $\pm$ 0.19	2.51 $\pm$ 0.10
TFBind	Fixed uncertainty	0.86 $\pm$ 0.03	0.62 $\pm$ 0.00	6.20 $\pm$ 0.37	2.54 $\pm$ 0.07
GFP	POME (full)	0.96 $\pm$ 0.02	0.48 $\pm$ 0.03	12.29 $\pm$ 0.61	7.77 $\pm$ 0.25
GFP	Fixed uncertainty	0.79 $\pm$ 0.20	0.44 $\pm$ 0.01	12.23 $\pm$ 0.45	7.80 $\pm$ 0.08

Appendix

Table 9: Effect of adaptive vs. fixed uncertainty estimation.

Task	$q$	Max	Mean	Diversity	Novelty
5’UTR	0.5	$1.03\pm 0.01$	$0.83\pm 0.00$	$27.10\pm 1.60$	$20.17\pm 0.38$
	0.6	$1.02\pm 0.01$	$0.84\pm 0.03$	$26.10\pm 0.55$	$20.18\pm 0.10$
	0.7	$1.01\pm 0.00$	$0.86\pm 0.01$	$25.38\pm 0.67$	$20.12\pm 0.07$
	0.8	$1.03\pm 0.01$	$0.86\pm 0.02$	$25.64\pm 0.97$	$20.31\pm 0.14$
TFBind	0.5	$0.87\pm 0.03$	$0.56\pm 0.01$	$6.86\pm 0.06$	$1.58\pm 0.01$
	0.6	$0.88\pm 0.02$	$0.57\pm 0.02$	$6.84\pm 0.07$	$1.57\pm 0.05$

Appendix

Table 10: Sensitivity analysis of the quantile parameter

q

across tasks.

Task	Method	Max	Mean	Diversity	Novelty
5’UTR	POME (Ensemble)	$1.03\pm 0.02$	$0.86\pm 0.01$	$25.55\pm 1.38$	$20.24\pm 0.21$
	POME (GP)	$1.03\pm 0.01$	$0.86\pm 0.03$	$23.47\pm 4.06$	$20.28\pm 0.06$
TFBind-10	POME (Ensemble)	$0.89\pm 0.02$	$0.61\pm 0.01$	$6.51\pm 0.19$	$2.51\pm 0.10$
	POME (GP)	$0.91\pm 0.00$	$0.56\pm 0.01$	$6.26\pm 0.28$	$1.62\pm 0.05$
GFP	POME (Ensemble)	$0.96\pm 0.02$	$0.48\pm 0.03$	$12.29\pm 0.61$	$7.77\pm 0.25$
	POME (GP)	$0.97\pm 0.00$	$0.67\pm 0.06$	$13.46\pm 0.58$	$6.32\pm 0.35$

Appendix

Table 11: Comparison between Ensemble-based and GP-based uncertainty estimation in POME.

Task	Method	Max	Mean	Diversity	Novelty
UTR	POME-Pair	0.85 $\pm$ 0.03	0.75 $\pm$ 0.01	22.65 $\pm$ 1.56	19.74 $\pm$ 0.10
UTR	POME-Exp	0.90 $\pm$ 0.04	0.78 $\pm$ 0.02	20.94 $\pm$ 1.25	19.36 $\pm$ 0.18
TFBind	POME-Pair	0.78 $\pm$ 0.03	0.62 $\pm$ 0.00	5.14 $\pm$ 0.19	2.67 $\pm$ 0.06
TFBind	POME-Exp	0.83 $\pm$ 0.03	0.58 $\pm$ 0.01	6.16 $\pm$ 0.18	2.53 $\pm$ 0.05
GFP	POME-Pair	0.90 $\pm$ 0.03	0.43 $\pm$ 0.03	9.93 $\pm$ 0.47	7.96 $\pm$ 0.19
GFP	POME-Exp	0.67 $\pm$ 0.21	0.43 $\pm$ 0.01	10.12 $\pm$ 0.69	7.62 $\pm$ 0.29

Appendix

Table 12: Effect of alternative fitness formulations (POME-Pair and POME-Exp) across all tasks. Results are reported as mean

\pm

standard deviation over 5 runs.

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