首次证明了先验不匹配下插件式梯度下降的收敛性，突破了以往理论限制。
A New Convergence Analysis of Plug-and-Play Proximal Gradient Descent Under Prior Mismatch
- 提出新理论框架，无需依赖难以验证的假设
- 证明等变插件方法能降低误差方差并收紧收敛界
- 为实际应用中训练与推理分布不一致提供理论支持
本文针对先验不匹配场景下插件式近端梯度下降（PnP-PGD）提出了新的收敛性理论，其中去噪器在与推理任务不同的数据分布上训练。据我们所知，这是首个在先验不匹配条件下对PnP-PGD的收敛性证明。相比现有PnP算法理论，新结果去除了多个严格且不可验证的假设。此外，我们还推导了等变插件方法（EPnP）在相同设定下的收敛性理论，证明其可减少误差方差并显式收紧收敛边界。
原文摘要 · Abstract (English)
In this work, we provide a new convergence theory for plug-and-play proximal gradient descent (PnP-PGD) under prior mismatch where the denoiser is trained on a different data distribution to the inference task at hand. To the best of our knowledge, this is the first convergence proof of PnP-PGD under prior mismatch. Compared with the existing theoretical results for PnP algorithms, our new results removed the need for several restrictive and unverifiable assumptions. Moreover, we derive the convergence theory for equivariant PnP (EPnP) under the prior mismatch setting, proving that EPnP reduces error variance and explicitly tightens the convergence bound.
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