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This work introduces \emph{ECHO-OFTRL}: optimistic follow-the-regularized-leader (OFTRL) equipped with an EMA cascade for high-order optimism (ECHO), where EMA denotes exponential moving average, and leverages a new form of optimism inspired by modern filter design.
The proposed update incorporates the objective gradient inside the denoising step, yielding an inference-time method that uses only a pretrained denoiser and gradient evaluations and is analyzed as an inexact projected-gradient method for constrained optimization over learned feasible geometries.
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