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Quality-Weighted Vendi Scores And Their Application To Diverse Experimental Design
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Extends the Vendi score to a quality-weighted variant (qVS) and uses it as the objective for diverse active search and Bayesian optimization, with a greedy batch selection procedure.
Problem
Experimental design methods such as active search and Bayesian optimization over-exploit and collapse onto local optima, yielding low diversity among high-quality discoveries.
Approach
Multiply the Vendi score (exponential of the entropy of normalized kernel eigenvalues) by the average item quality score, giving a quality-weighted, order-q controllable diversity objective that replaces local-penalization distance constraints; optimized greedily for batch selection.
Key results
- qVS-AS achieves the highest Vendi score in most settings across photoswitch, metal glass, and FashionMNIST tasks, with the best method usually matching the evaluation order q.
- Abstract reports a 70%-170% increase in the number of effective discoveries compared to baselines.
- In the MOF task, qVS-BayesOpt with q=0.1 gives the best objective value, while some q values perform worse than regular BayesOpt (q=0).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use qVS-AS instead of diversity-blind active search | Active search · Bulk metal glass discovery | Vendi Score | Helped |
| Use qVS-BayesOpt instead of regular BayesOpt | Bayesian optimization · Lunar lander | best objective value | Helped |
| Use qVS-BayesOpt instead of regular BayesOpt | Bayesian optimization · MOF storage capacity optimization | best objective value | Helped |
| Use qVS-BayesOpt instead of regular BayesOpt | Bayesian optimization · Rover path finding | best objective value | Mixed |
| Set q=0.1 rather than q=0 (ablation) | qVS-BayesOpt · MOF storage capacity optimization | best objective value | Helped |
| Vary the order q across settings (ablation) | qVS-AS · Photoswitch, bulk metal glass, and FashionMNIST discovery | Vendi Score | Mixed |
| Set q=0 instead of using a diversity-sensitive order (ablation) | qVS-BayesOpt · MOF storage capacity optimization | best objective value | Hurt |
Surprising findings
- Encouraging diversity did not slow optimization progress and improved performance in lunar lander and MOF search, where regular BayesOpt could be trapped in local optima.
- Regular BayesOpt yielded lower effective discovery count than even random search in the MOF task.
Limitations
- No theoretical optimality guarantee for the greedy qVS optimization.
- Quality-diversity trade-off controlled by order q requires tuning; q=1 used as default.
- Cannot be applied to ROBOT/TuRBO-style methods for discrete structured spaces; MOF task uses UCB baseline instead of TuRBO.
Experimental setup
Datasets: photoswitch molecules bulk metal glass alloys FashionMNIST rover path-finding lunar lander MOF storage database
Benchmarks: photoswitch molecular discovery bulk metal glass materials discovery FashionMNIST product recommendation rover path-finding lunar lander MOF ammonia storage
Metrics: Vendi score max pairwise distance kernel matrix determinant best objective value effective discovery count
Baselines: random search ECI SELECT TuRBO ROBOT UCB
Builds on: Vendi score TuRBO ROBOT determinantal point processes
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