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.

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.

Drawbacks of ignoring the causal mechanisms when performing imitation learning have recently been acknowledged. Several approaches both to assess the feasibility of imitation and to circumvent causal confounding and causal misspecifications have been proposed in the literature.However, the potential benefits of the incorporation of additional information about the underlying causal structure are left unexplored.An example of such overlooked information is context-specific independence (CSI), i.e., independence that holds only in certain contexts.We consider the problem of causal imitation learning when CSI relations are known.We prove that the decision problem pertaining to the feasibility of imitation in this setting is NP-hard.Further, we provide a necessary graphical criterion for imitation learning under CSI and show that under a structural assumption, this criterion is also sufficient.Finally, we propose a sound algorithmic approach for causal imitation learning which takes both CSI relations and data into account.