Whilepreviousworkprovide worst-case bounds for arbitrary convex functions, it is often the case that the function at hand belongs to a smaller class that enjoys faster rates.

We develop algorithms for private stochastic convex optimization that adapt to the hardness of the specific function we wish to optimize. While previous work provide worst-case bounds for arbitrary convex functions, it is often the case that the function at hand belongs to a smaller class that enjoys faster rates. Concretely, we show that for functions exhibiting κ-growth around the optimum, i.e., f ( x) f (x

Variational inference was employed in prior work to inferz (and w implicitly), and to obtain a point estimate ofθ, as a by-product of optimising the variational lower bound. Critically, in this representation weights are only implicitly parametrized through the use of these latent variables, which transforms inference onweights into inference ofthemuch smaller collection oflatent unit variables.

Each module could be either parallel module or fusion module, which is determined by optimizing the architecture parametersαp and αf. Specifically,the learned twoarchitectures both contain eight fusion modules and four parallel modules, and the only one difference between them is the position ofthefusion andtheparallel modules. From theobservations, wecould conclude that: 1) themulti-scale information isremarkably important toimage restoration. Image restoration using very deep convolutional encoder-decoder networks with symmetric skip connections. From the top to the bottom for each image, the noise levels areσ = 30,50,70. From the left to the right are Input, BM3D[1],RED[9],WNNM[3],NLRN[6],DuRN-P [7],N3Net[10],CLEARER, andGround truth.