mlsanityData to 7 Oct 2026

Truncated Variance Reduction: A Unified Approach to Bayesian Optimization and Level-Set Estimation

arXiv 1610.07379 ↗First posted 24 Oct 2016stat.ML cs.IT cs.LGcited by 40

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Abstract (arXiv)

We present a new algorithm, truncated variance reduction (TruVaR), that treats Bayesian optimization (BO) and level-set estimation (LSE) with Gaussian processes in a unified fashion. The algorithm greedily shrinks a sum of truncated variances within a set of potential maximizers (BO) or unclassified points (LSE), which is updated based on confidence bounds. TruVaR is effective in several important settings that are typically non-trivial to incorporate into myopic algorithms, including pointwise costs and heteroscedastic noise. We provide a general theoretical guarantee for TruVaR covering these aspects, and use it to recover and strengthen existing results on BO and LSE. Moreover, we provide a new result for a setting where one can select from a number of noise levels having associated costs. We demonstrate the effectiveness of the algorithm on both synthetic and real-world data sets.

Key facts. Cited by 40 papers in the map (data through 7 Oct 2026). First posted on arXiv 24 Oct 2016.

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Citing papers per year: 2021: 7; 2022: 8; 2023: 6; 2024: 10; 2025: 4; 2026: 5.

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  1. 2021Optimal Order Simple Regret for Gaussian Process Banditscited by 52
  2. 2021Misspecified Gaussian Process Bandit Optimizationcited by 52
  3. 2021Value-at-Risk Optimization with Gaussian Processescited by 19
  4. 2021Nearly Optimal Algorithms for Level Set Estimationcited by 17
  5. 2021Risk-averse Heteroscedastic Bayesian Optimizationcited by 17
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  7. 2021Lenient Regret and Good-Action Identification in Gaussian Process Banditscited by 12
  8. 2021Entropy-based adaptive design for contour finding and estimating reliabilitycited by 10
  9. 2022Graph Neural Network Banditscited by 10
  10. 2023Learning Regions of Interest for Bayesian Optimization with Adaptive Level-Set Estimationcited by 8
  11. 2024Active Fine-Tuning of Multi-Task Policiescited by 8
  12. 2022Movement Penalized Bayesian Optimization with Application to Wind Energy Systemscited by 7
28 more
  1. 2024Transition Constrained Bayesian Optimization via Markov Decision Processescited by 7
  2. 2022Look-Ahead Acquisition Functions for Bernoulli Level Set Estimationcited by 6
  3. 2024Variational Search Distributionscited by 6
  4. 2024Accelerating Look-ahead in Bayesian Optimization: Multilevel Monte Carlo is All you Needcited by 4
  5. 2024Regret Analysis for Randomized Gaussian Process Upper Confidence Boundcited by 4
  6. 2024Sample-efficient Bayesian Optimisation Using Known Invariancescited by 4
  7. 2024Active Level Set Estimation for Continuous Search Space with Theoretical Guaranteecited by 3
  8. 2024Active Learning for Level Set Estimation Using Randomized Straddle Algorithmscited by 3
  9. 2025Distributionally Robust Active Learning for Gaussian Process Regressioncited by 3
  10. 2022Relaxed Gaussian process interpolation: a goal-oriented approach to Bayesian optimizationcited by 2
  11. 2023Provably Efficient Bayesian Optimization with Unknown Gaussian Process Hyperparameter Estimationcited by 2
  12. 2023Constrained Bayesian Optimization with Adaptive Active Learning of Unknown Constraintscited by 2
  13. 2023Practical Path-based Bayesian Optimizationcited by 2
  14. 2024Active Few-Shot Fine-Tuningcited by 2
  15. 2022Online Nonsubmodular Minimization with Delayed Costs: From Full Information to Bandit Feedbackcited by 1
  16. 2022Benefits of Monotonicity in Safe Exploration with Gaussian Processescited by 1
  17. 2023Efficient Determination of Safety Requirements for Perception Systemscited by 1
  18. 2024Robust Transfer Learning for Active Level Set Estimation with Locally Adaptive Gaussian Process Priorcited by 1
  19. 2025Multi-Metric Adaptive Experimental Design Under a Fixed Budget with Validationcited by 1
  20. 2025Bayes-Split-Edge: Bayesian Optimization for Constrained Collaborative Inference in Wireless Edge Systemscited by 1
  21. 2026CASHomon Sets: Efficient Rashomon Sets Across Multiple Model Classes and their Hyperparameterscited by 1
  22. 2022Online Subset Selection using α-Core with no Augmented Regretcited by 0
  23. 2023A Finite-Horizon Approach to Active Level Set Estimationcited by 0
  24. 2025An (ε,δ)-accurate level set estimation with a stopping criterioncited by 0
  25. 2026High-dimensional Level Set Estimation with Trust Regions and Double Acquisition Functionscited by 0
  26. 2026Multi-Objective Coverage via Constraint Active Searchcited by 0
  27. 2026Towards Regret Guarantees for One-Step Lookahead Bayesian Optimizationcited by 0
  28. 2026Online Adaptive Kernel Mixing for Gaussian Process Decision Makingcited by 0