However, such interleaving methods struggle to produce final results that look like natural objects of interest (i.e., manifold feasibility)

We further discuss the sample complexity for a desired approximation accuracy.

Neural Information Processing Systems http://nips.cc/

We identify three key challenges when using learned dual variables in a primal-dual algorithm.

When n = 2, the constraint matrixA has E = I2 1>2 and G = 1>2 I2. Now we simplify the matrixAby removing a specific set of redundantrows. Furthermore, the rows of A are categorized into a single set so that the criterion in Proposition 3.2 holds true (thedashed lineintheformulation of Aservesasapartition ofthissingle setintotwosets). We use the proof by contradiction. In particular, assume that problem(10) is a MCF problem whenm 3andn 3,Proposition 3.3 implies that the constraint matrixAisTU.

Bandits, Reinforcement Learning

Pretrained diffusion models (DMs) have recently been popularly used in solving inverse problems (IPs). The existing methods mostly interleave iterative steps in the reverse diffusion process and iterative steps to bring the iterates closer to satisfying the measurement constraint. However, such interleaving methods struggle to produce final results that look like natural objects of interest (i.e., manifold feasibility) and fit the measurement (i.e., measurement feasibility), especially for nonlinear IPs. Moreover, their capabilities to deal with noisy IPs with unknown types and levels of measurement noise are unknown. In this paper, we advocate viewing the reverse process in DMs as a function and propose a novel plug-in method for solving IPs using pretrained DMs, dubbed DMPlug. DMPlug addresses the issues of manifold feasibility and measurement feasibility in a principled manner, and also shows great potential for being robust to unknown types and levels of noise. Through extensive experiments across various IP tasks, including two linear and three nonlinear IPs, we demonstrate that DMPlug consistently outperforms state-of-the-art methods, often by large margins especially for nonlinear IPs.