Unified high-probability regret bounds for online convex optimisation with ℓq-Lipschitz losses via ℓp-regularised FTRL and cone-measure sampling from ℓr-spheres, for all p,q,r in [1,∞].
IfΘ ⊂Rd is convex set, andf is a convex function thenfh is convex onΘandf h(x)≥f(x)for allx∈Θ
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High-probability zeroth-order online convex optimisation beyond Euclidean geometry
Unified high-probability regret bounds for online convex optimisation with ℓq-Lipschitz losses via ℓp-regularised FTRL and cone-measure sampling from ℓr-spheres, for all p,q,r in [1,∞].