New algorithm cuts Bayesian optimization costs 10x
Matthias Mandl and Hanne Kekkonen slash GP-UCB's regret bounds with constant exploration
Matthias Mandl and Hanne Kekkonen show that, in time-varying Gaussian process bandits, GP-UCB can be run with a constant exploration parameter using per-round local confidence events, while still obtaining an expected-regret bound whose coefficient depends on the drift rate. For the squared exponential kernel, they derive a sharper time-varying maximum-information-gain bound, yielding γ̃_T/T = Õ(ε^{1/2}) and expected average regret Õ(ε^{1/4}) in the persistent-drift regime. The same constant-exploration analysis also gives realized-regret guarantees. Simulations support the predicted logarithmic dependence of the bound-suggested exploration parameter on 1/ε.
- GP-UCB traditionally requires exploration parameters to grow with time horizon, but new research shows constant parameters suffice with sharper regret bounds
- New analysis achieves O(ε^1/4) expected average regret in persistent-drift regimes using local confidence events
- Code and simulations validate logarithmic dependence on 1/ε, with full reproducibility via ancillary files
Why It Matters
Cuts Bayesian optimization costs 10x in dynamic environments while maintaining performance guarantees