Constant-exploration guarantees for general temporal kernels

Extend constant-exploration guarantees for time-varying Gaussian process bandits to more general temporal kernels, and characterize which forms of nonstationarity are sufficient to prevent posterior overconfidence.

Background

The paper establishes constant-exploration regret guarantees for the time-varying Gaussian process model whose temporal dependence is geometric and arises from a Markov drift recursion. The authors identify the restriction to this geometric temporal kernel as the principal limitation of the analysis.

The unresolved extension concerns temporal kernels beyond the geometric Markov structure. The goal is both to preserve constant-exploration guarantees and to determine the nonstationarity conditions that prevent the posterior from becoming permanently overconfident. This would clarify the scope of the local-confidence-event technique developed in the paper.

References

Several extensions remain open. Most importantly, the present analysis relies on the geometric temporal kernel induced by the Markov drift model. Extending constant-exploration guarantees to more general temporal kernels would clarify which forms of nonstationarity are sufficient to prevent posterior overconfidence.

— Sharper Regret Bounds for Time-Varying Gaussian Process Bandits with Constant Exploration  (2608.18863 - Mandl et al., 19 Aug 2026) in Section 6, Conclusion

Another important direction is to remove the assumption that the drift parameter is known and fixed, allowing β to be adapted online when the rate of temporal variation is unknown or changes over time.

— Sharper Regret Bounds for Time-Varying Gaussian Process Bandits with Constant Exploration  (2608.18863 - Mandl et al., 19 Aug 2026) in Section 6, Conclusion

Finally, sharper concentration tools for the realized regret of TV-GP-UCB could improve the current high-probability bounds and better reflect the empirical stability observed in the simulations.

— Sharper Regret Bounds for Time-Varying Gaussian Process Bandits with Constant Exploration  (2608.18863 - Mandl et al., 19 Aug 2026) in Section 6, Conclusion