# This Too Shall Pass: Removing Stale Observations in Dynamic Bayesian Optimization

arXiv: https://arxiv.org/abs/2405.14540 · HTML: https://mlsanity.com/paper/2405.14540/

## Key facts

- Cited by 6 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 35 references that are in the map.
- First posted on arXiv 23 May 2024.

## Builds on (most cited first, 14 of 14)

- [Scalable Global Optimization via Local Bayesian Optimization](https://mlsanity.com/paper/1910.01739/) (2019)
- [Batch Bayesian Optimization via Local Penalization](https://mlsanity.com/paper/1505.08052/) (2015)
- [Multi-Objective Bayesian Optimization over High-Dimensional Search Spaces](https://mlsanity.com/paper/2109.10964/) (2021)
- [Online Deep Learning: Learning Deep Neural Networks on the Fly](https://mlsanity.com/paper/1711.03705/) (2017)
- [Adaptive and Safe Bayesian Optimization in High Dimensions via One-Dimensional Subspaces](https://mlsanity.com/paper/1902.03229/) (2019)
- [Time-Varying Gaussian Process Bandit Optimization](https://mlsanity.com/paper/1601.06650/) (2016)
- [Inducing Point Allocation for Sparse Gaussian Processes in High-Throughput Bayesian Optimisation](https://mlsanity.com/paper/2301.10123/) (2023)
- [Weighted Gaussian Process Bandits for Non-stationary Environments](https://mlsanity.com/paper/2107.02371/) (2021)
- [Bayesian Optimization for Synthetic Gene Design](https://mlsanity.com/paper/1505.01627/) (2015)
- [No-Regret Algorithms for Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2102.06296/) (2021)
- [Bayesian Optimization for Dynamic Problems](https://mlsanity.com/paper/1803.03432/) (2018)
- [Relaxing the Additivity Constraints in Decentralized No-Regret High-Dimensional Bayesian Optimization](https://mlsanity.com/paper/2305.19838/) (2023)
- [Event-Triggered Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2208.10790/) (2022)
- [INSPIRE: Distributed Bayesian Optimization for ImproviNg SPatIal REuse in Dense WLANs](https://mlsanity.com/paper/2204.10184/) (2022)

## Built on by (most cited first, 6 of 6)

- [Time-Varying Bayesian Optimization Without a Metronome](https://mlsanity.com/paper/2501.18963/) (2025)
- [Time-Aware Latent Space Bayesian Optimization](https://mlsanity.com/paper/2603.00935/) (2026)
- [Asymptotic Performance of Time-Varying Bayesian Optimization](https://mlsanity.com/paper/2505.13012/) (2025)
- [Symmetry-Aware Bayesian Optimization via Max Kernels](https://mlsanity.com/paper/2509.25051/) (2025)
- [Sharper Regret Bounds for Time-Varying Gaussian Process Bandits with Constant Exploration](https://mlsanity.com/paper/2608.18863/) (2026)
- [BOBA: Dynamic Bayesian Optimization through Bayesian Active Inference](https://mlsanity.com/paper/2609.26021/) (2026)

## Abstract (arXiv)

Bayesian Optimization (BO) has proven to be very successful at optimizing a static, noisy, costly-to-evaluate black-box function f : S → ℝ. However, optimizing a black-box which is also a function of time (i.e., a dynamic function) f : S × T → ℝ remains a challenge, since a dynamic Bayesian Optimization (DBO) algorithm has to keep track of the optimum over time. This changes the nature of the optimization problem in at least three aspects: (i) querying an arbitrary point in S × T is impossible, (ii) past observations become less and less relevant for keeping track of the optimum as time goes by and (iii) the DBO algorithm must have a high sampling frequency so it can collect enough relevant observations to keep track of the optimum through time. In this paper, we design a Wasserstein distance-based criterion able to quantify the relevancy of an observation with respect to future predictions. Then, we leverage this criterion to build W-DBO, a DBO algorithm able to remove irrelevant observations from its dataset on the fly, thus maintaining simultaneously a good predictive performance and a high sampling frequency, even in continuous-time optimization tasks with unknown horizon. Numerical experiments establish the superiority of W-DBO, which outperforms state-of-the-art methods by a comfortable margin.