Thompson Sampling for Non-Monotone Convex Ridge Bandits: Monotonicity Is Not Needed for Polynomial Regret

Bakhtiari, Lattimore and Szepesvári (COLT 2025) proved that Thompson sampling (TS) has Bayesian regret $\tilde O(d^{5/2}\sqrt n)$ for bandit convex optimisation with convex \emph{monotone} ridge losses $f(x)=\ell(\ip{x}θ)$, and asked whether monotonicity of the link is necessary. We give a qualitati