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MITIGATING OVER-EXPLORATION IN LATENT SPACE OPTIMIZATION USING LES
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Proposes the Latent Exploration Score (LES), a differentiable density-based score derived from a VAE decoder's push-forward density, used as a penalty in latent space optimization to reduce generation of invalid solutions.
Problem
Latent space optimization (LSO) for black-box discrete optimization over structured sequences (arithmetic expressions, SMILES, SELFIES) tends to over-explore and decode into invalid or unrealistic solutions.
Approach
Scores latent points by the sequence density induced by the decoder (via a CPA-based change-of-variables term, log-determinant of the decoder Jacobian through softmax), which is high near training data and valid regions; adds it as a differentiable penalty to the acquisition function optimization, requiring no extra training or training data.
Key results
- LES achieves the best AUROC in 18 of 22 VAEs and 0.93 average AUROC for identifying valid latent regions, versus 0.88 for Uncertainty and 0.91 for Likelihood.
- In BO experiments over 30 tasks, LES has the best average rank (2.15 top-1, 1.9 top-20) and is within one std of the best in 19 (top-1) and 22 (top-20) cases.
- LES improves valid-solution percentage over unregularized gradient ascent by 7% on average and over TuRBO and LSO (L-BFGS) by 24% and 36%.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Add LES regularization to latent space optimization | LSO · 30 LSO experiments, Top 1 | average rank: 2.76 -> 2.15 | Helped |
| Add LES regularization to latent space optimization | LSO · 30 LSO experiments, Top 20 | average rank: 2.53 -> 1.9 | Helped |
| Use LES as the validity score instead of Likelihood | Valid-region classification across 22 VAEs · 22 VAEs | AUROC: 0.91 -> 0.93 | Helped |
| Use LES as the validity score instead of Bayesian uncertainty | Valid-region classification across 22 VAEs · 22 VAEs | AUROC: 0.88 -> 0.93 | Helped |
| Use LES rather than Bayesian uncertainty to score latent vectors | Decoder scoring for Expressions GRU (25) · 20 latent vectors, Expressions GRU (25) | wall clock time (seconds): 0.823 -> 0.730 | Helped |
| Use LES rather than Bayesian uncertainty to score latent vectors | Decoder scoring for SMILES GRU (56) · 20 latent vectors, SMILES GRU (56) | wall clock time (seconds): 3.157 -> 0.663 | Helped |
| Add LES regularization instead of using unregularized gradient ascent | LSO · Across datasets and VAEs | percentage of valid solutions: +7% on average | Helped |
| Use LES regularization instead of TuRBO | LSO · Across datasets and VAEs | percentage of valid solutions: +24% on average | Helped |
| Use LES regularization instead of LSO (L-BFGS) | LSO · Across datasets and VAEs | percentage of valid solutions: +36% on average | Helped |
| Use LES instead of Uncertainty Censoring | LSO · Across datasets and VAEs | percentage of valid solutions: 2% | Hurt |
| Increase the LES regularization strength | LES-constrained LSO on Expressions · Expressions | percentage of valid solutions | Mixed |
| Constrain optimization with LES rather than TuRBO | Pre-trained SELFIES-VAE LSO · Ranolazine MPO and Zaleplon MPO | average top-20 objective value | Mixed |
Surprising findings
- Uncertainty Censoring achieves about 2% higher valid-solution percentage on average than LES, though LES is faster to compute.
- On the pre-trained SELFIES-VAE for Ranolazine and Zaleplon MPO, LES outperforms TuRBO on valid solutions but underperforms it overall on objective value.
Limitations
- Computing the decoder Jacobian and log-determinant scales cubically with latent dimension and can be a bottleneck for large latent dimension and output size.
- Relies on the decoder being bijective and CPA-approximable; the authors advise against use with poorly trained decoders.
- The regularization strength lambda is task-dependent and chosen per setting; a default of 0.5 is suggested without exhaustive tuning.
Experimental setup
Datasets: arithmetic expressions (80k) ZINC250k ZINC250k quality-filtered subset
Benchmarks: Expressions regression objective SMILES octanol-water partition (logP) GuacaMol Perindopril MPO GuacaMol Ranolazine MPO GuacaMol Zaleplon MPO
Metrics: AUROC average rank top-1 and top-20 objective values percentage of valid solutions wall clock time
Baselines: LSO (GA) LSO (L-BFGS) TuRBO Uncertainty Censoring Prior (l2 regularization) Likelihood
Builds on: latent space optimization uncertainty censoring TuRBO BoTorch
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