Removing the valuable-decomposition assumption

Remove Assumption 8, which requires that almost every request admit a decomposition whose expected reward sufficiently exceeds its normalized success-conditioned resource demand, while retaining finite-time guarantees for proxy-based contextual constrained kernel bandits.

Background

The concrete GP-based performance bounds rely on Assumption 8, an additional condition ensuring the existence of a sufficiently valuable decomposition for almost every request. This assumption is used to control the proxy constraint-surrogate error and the optimality gap introduced by conservative proxying. The paper does not establish its guarantees without this condition and explicitly leaves its removal unresolved.