Learning in an Echo Chamber: Online Learning with Replay Adversary

As machine learning systems increasingly train on self-annotated data, they risk reinforcing errors and becoming echo chambers of their own beliefs. We model this phenomenon by introducing a learning-theoretic framework: Online Learning in the Replay Setting. In round \(t\), the learner outputs a hypothesis \(\hat{h}_t\); the adversary then reveals either the true label \(f^{*}(x_t)\) or a replayed label \(\hat{h}_i(x_t)\) from an earlier round \(i \lt t\). A mistake is counted only when the true label is shown, yet classical algorithms such as the SOA or the halving algorithm are easily misled by the replayed errors.