Research map / Probabilistic and scientific modeling / Bayesian optimization
Procrastinated Tree Search: Black-Box Optimization with Delayed, Noisy, and Multi-Fidelity Feedback
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use PCTS with delayed-UCB1-σ or delayed-UCB-V instead of the competing optimizers | Black-box optimization with delayed, noisy, and multi-fidelity feedback · Synthetic functions and hyperparameter tuning tasks | convergence speed | Helped |
| Use PCTS with delayed-UCB1-σ or delayed-UCB-V instead of competing methods | Synthetic-function optimization · Hartmann3, Branin, CurrinExp | simple regret: approximately 1 to 3 order lower simple regret | Helped |
| Use PCTS with delayed-UCB1-σ or delayed-UCB-V instead of competing methods | Hyperparameter tuning · SVM on NewsGroup; XGB and NN on MNIST | cross-validation accuracy | Helped |
| Allow expected delay to grow as $O(\log T)$ rather than using non-delayed feedback | PCTS with delayed-UCB1 · Black-box optimization | expected simple regret | No clear effect |
| Allow expected delay to grow as $O(T^{1-\alpha})$ | PCTS with delayed-UCB1 · Black-box optimization | expected simple regret: $T^{\frac{1-\alpha}{d+2}}$ | Hurt |
| Add known-variance noise to feedback | HOO · Black-box optimization | expected simple regret: $\sigma^{2/(d+2)}$ | Hurt |
| Estimate variance with delayed-UCB-V when noise variance is unknown, rather than using known-variance UCB-σ | PCTS · Black-box optimization with noisy feedback | expected simple regret: $(((\sigma/\nu_1)^2+2b/\nu_1)\ln T)^{1/(d+2)}$; known-variance cost: $((\sigma/\nu_1)^2 \ln T)^{1/(d+2)}$ | Hurt |
| Use feedback with multi-fidelity bias and cost | PCTS with delayed-UCB-V · Black-box optimization under a total cost budget | expected simple regret: $\bigO\left((H(\Lambda))^{-\frac{1}{d'+2}} \left(\ln H(\Lambda)+ \frac{\tau}{(\sigma/\nu_1)^2+2b/\nu_1}\right)^{\frac{1} | Mixed |
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