Static regret to a single expert is often the wrong target for strictly online prediction under non-stationarity, where the best expert may switch repeatedly over time. We study Policy-Controlled Generalized Share (PCGS), a general strictly online framework in which the generalized-share recursion is fixed while the post-loss update controls are allowed to vary adaptively. Its principal instantiation in this paper is PCGS-TF, which uses a causal Transformer as an update controller: after round t
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