38 research outputs found
Online Learning with Low Rank Experts
We consider the problem of prediction with expert advice when the losses of
the experts have low-dimensional structure: they are restricted to an unknown
-dimensional subspace. We devise algorithms with regret bounds that are
independent of the number of experts and depend only on the rank . For the
stochastic model we show a tight bound of , and extend it to
a setting of an approximate subspace. For the adversarial model we show an
upper bound of and a lower bound of
Oracle-Based Robust Optimization via Online Learning
Robust optimization is a common framework in optimization under uncertainty
when the problem parameters are not known, but it is rather known that the
parameters belong to some given uncertainty set. In the robust optimization
framework the problem solved is a min-max problem where a solution is judged
according to its performance on the worst possible realization of the
parameters. In many cases, a straightforward solution of the robust
optimization problem of a certain type requires solving an optimization problem
of a more complicated type, and in some cases even NP-hard. For example,
solving a robust conic quadratic program, such as those arising in robust SVM,
ellipsoidal uncertainty leads in general to a semidefinite program. In this
paper we develop a method for approximately solving a robust optimization
problem using tools from online convex optimization, where in every stage a
standard (non-robust) optimization program is solved. Our algorithms find an
approximate robust solution using a number of calls to an oracle that solves
the original (non-robust) problem that is inversely proportional to the square
of the target accuracy
Deep Optimal Transport: A Practical Algorithm for Photo-realistic Image Restoration
We propose an image restoration algorithm that can control the perceptual
quality and/or the mean square error (MSE) of any pre-trained model, trading
one over the other at test time. Our algorithm is few-shot: Given about a dozen
images restored by the model, it can significantly improve the perceptual
quality and/or the MSE of the model for newly restored images without further
training. Our approach is motivated by a recent theoretical result that links
between the minimum MSE (MMSE) predictor and the predictor that minimizes the
MSE under a perfect perceptual quality constraint. Specifically, it has been
shown that the latter can be obtained by optimally transporting the output of
the former, such that its distribution matches the source data. Thus, to
improve the perceptual quality of a predictor that was originally trained to
minimize MSE, we approximate the optimal transport by a linear transformation
in the latent space of a variational auto-encoder, which we compute in
closed-form using empirical means and covariances. Going beyond the theory, we
find that applying the same procedure on models that were initially trained to
achieve high perceptual quality, typically improves their perceptual quality
even further. And by interpolating the results with the original output of the
model, we can improve their MSE on the expense of perceptual quality. We
illustrate our method on a variety of degradations applied to general content
images of arbitrary dimensions
Nested Diffusion Processes for Anytime Image Generation
Diffusion models are the current state-of-the-art in image generation,
synthesizing high-quality images by breaking down the generation process into
many fine-grained denoising steps. Despite their good performance, diffusion
models are computationally expensive, requiring many neural function
evaluations (NFEs). In this work, we propose an anytime diffusion-based method
that can generate viable images when stopped at arbitrary times before
completion. Using existing pretrained diffusion models, we show that the
generation scheme can be recomposed as two nested diffusion processes, enabling
fast iterative refinement of a generated image. We use this Nested Diffusion
approach to peek into the generation process and enable flexible scheduling
based on the instantaneous preference of the user. In experiments on ImageNet
and Stable Diffusion-based text-to-image generation, we show, both
qualitatively and quantitatively, that our method's intermediate generation
quality greatly exceeds that of the original diffusion model, while the final
slow generation result remains comparable