Derives an explicit volume-dependent lower bound on regret for GP bandits on Riemannian manifolds that matches the exponent of known upper bounds and includes a new geometric constant.
A domain-shrinking based Bayesian optimization algorithm with order-optimal regret performance,
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Manifold-Aware Information Gain and Lower Bounds for Gaussian-Process Bandits on Riemannian Quotient Spaces
Derives an explicit volume-dependent lower bound on regret for GP bandits on Riemannian manifolds that matches the exponent of known upper bounds and includes a new geometric constant.