Time-Varying Bayesian Optimization Without a Metronome
Anthony Bardou, Patrick Thiran
TL;DR
This paper extends Time-Varying Bayesian Optimization by deriving regret bounds that account for non-uniform sampling frequencies, leading to improved algorithms like BOLT that outperform existing methods on synthetic and real-world tasks.
Contribution
It introduces the first regret analysis for TVBO with variable sampling frequencies and proposes practical guidelines and an improved algorithm based on this analysis.
Findings
BOLT outperforms state-of-the-art TVBO algorithms in experiments.
The analysis provides insights into dataset size and stale data policies.
The regret bound explicitly accounts for changing observation sampling frequencies.
Abstract
Time-Varying Bayesian Optimization (TVBO) is the go-to framework for optimizing a time-varying, expensive, noisy black-box function . However, most of the asymptotic guarantees offered by TVBO algorithms rely on the assumption that observations are acquired at a constant frequency. As the GP inference complexity scales with the cube of its dataset size, this assumption is unrealistic in the long run. In this paper, we relax this assumption and derive the first upper regret bound that explicitly accounts for changes in the observations sampling frequency. Based on this analysis, we formulate practical recommendations about dataset sizes and stale data policies of TVBO algorithms. We illustrate how an algorithm (BOLT) that follows these recommendations performs better than the state-of-the-art of TVBO through experiments on synthetic and real-world problems.
Peer Reviews
Decision·Submitted to ICLR 2026
- The proposed algorithm comes with regret guarantees and convincing empirical evaluations. - I found the results on optimal dataset sizes especially intriguing.
- Unfortunately, the biggest weakness of the paper is that the problem formulation is nonsensical in the sense that a trivial algorithm can achieve constant regret. The problem lies in the definition of regret that sums only the regret at the observed locations $R_T = \sum r_i$ and letting the algorithm decide on the sample times $t_i$. A trivial algorithm that will always achieve $\Theta(1)$ regret samples once and never again achieves $R_T = r_1$. Clearly, this solution is non-sensical in th
Overall, this paper is well written, and I can understand that the GP model's computational time may be slow, since it is $O(n^3)$.
Regarding the problem setup and motivation: - If we adopt the rank-one update of the GP model, the computational time in each step is $O(t^2)$. Bayesian optimization generally considers the case where the objective function evaluation is more dominant compared with the computational time $O(t^2)$. Are there any specific examples where $O(t^2)$ can be a severe bottleneck? - If the computation of the GP model can be a bottleneck, we can consider other surrogate models or other optimization approac
The problem setting seems interesting and the theoretical analysis for general R(n) is shown first by the paper according to the authors.
The problem setting should have been explained in more detail, while the authors mention that it has not been widely studied. For me, it is currently unclear how theoretical analysis justifies the proposed model. The rate itself of the regret bound is not largely different from existing studies, and the novelty is claimed for revealing the relation between the bound and response time R(n). However, since the bound is quite loose, I do not think the derived bound reveals some essential relation
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Taxonomy
TopicsMachine Learning and Algorithms · Reservoir Engineering and Simulation Methods · Fault Detection and Control Systems