Technology
Plug-in Estimation in High-Dimensional Linear Inverse Problems: A Rigorous Analysis
Alyson K. Fletcher, Parthe Pandit, Sundeep Rangan, Subrata Sarkar, Philip Schniter
Estimating a vector x from noisy linear measurements Ax + w often requires use of prior knowledge or structural constraints on x for accurate reconstruction. Several recent works have considered combining linear least-squares estimation with a generic or "plug-in" denoiser function that can be designed in a modular manner based on the prior knowledge about x.
Model
We further show that optimistic posterior sampling can control this Hellinger distance, when we measure model error via data likelihood. This technique allows us to design and analyze unified posterior sampling algorithms with state-of-the-art sample complexity guarantees for many model-based RL settings.