Explain the horizon-dependent behavior of WDBO-BOBA(N) under different exploration rates

Explain why the relationship between the performance of WDBO-BOBA(N) and its exploration parameter β differs between fixed-observation and fixed-time horizons, particularly in light of the substantial changes that the WDBO observation-removal procedure induces in the Gaussian-process surrogate model and, consequently, in BOBA performance.

Background

The paper evaluates standard and normalized variants of BOBA, including WDBO-BOBA(N), using the exploration parameter β under two evaluation protocols: a fixed number of observations and a fixed wall-clock time. For the Powell benchmark, the authors report that the relationship between performance and β changes across these two horizons for WDBO-BOBA(N).

The authors attribute this unresolved behavior tentatively to the way WDBO performs under different fixed-horizon settings: its observation-removal policy substantially adjusts the Gaussian-process surrogate, which may in turn alter BOBA’s performance. The paper does not establish why this dependence occurs or characterize the mechanism connecting the horizon, WDBO’s surrogate updates, and the optimal exploration rate.

References

It is unclear why, but the authors assume this is due to how WDBO performs in different fixed horizon settings adjusts drastically the GP which in turn would affect BOBA’s performance.

— BOBA: Dynamic Bayesian Optimization through Bayesian Active Inference  (2609.26021 - Kelly et al., 22 Sep 2026) in Appendix A.1, subsection “Powell”