Learning When to Trust in Contextual Social Bandits

Robust reinforcement learning typically assumes that feedback sources are either globally trustworthy or corrupted within a fixed global budget. We identify a more subtle failure mode that escapes this dichotomy, which we call \emph{Contextual Sycophancy}. In this failure, evaluators are truthful in benign contexts but systematically biased in critical ones, so that no single evaluator is reliable everywhere and the corrupt evaluators may form a \emph{majority} in the contexts that matter. Our first result is an information-theoretic lower bound. We exhibit two problem instances that induce \emph{identical} social-feedback distributions yet have disjoint optimal actions, proving that \emph{any} algorithm relying on social feedback alone (including any robust aggregator, regardless of breakdown point) incurs $Ω(T)$ latent regret. This shows that breaking contextual sycophancy is impossible without having some information. We then show that a sparse stream of ground-truth audits, available with probability $p_{\mathrm{aud}}$, is sufficient. We propose \ESA, which learns a per-evaluator contextual \emph{trust boundary} from audits and re-weights feedback accordingly, and we prove a high-probability latent-regret bound of $\tilde{\mathcal{O}}\!\big(\sqrt{T\,d_{VC}/p_{\mathrm{aud}}} + d\sqrt{T} + ε_{\mathrm{tol}}T\big)$, where $d_{VC}$ is the complexity of the adversary's bias strategy. The audit-dependence $1/\sqrt{p_{\mathrm{aud}}}$ matches the information-theoretic necessity of audits. Empirically, \ESA\ recovers the ground truth when $80\%$ of the social layer is adversarial, a regime in which median- and mean-based robust baselines fail.