On Perturbed Proximal Gradient Algorithms

By Yves F. Atchadé, Gersende Fort, Eric Moulines. 2014

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In Optimization & Training

Citations in the corpus

An Analysis of the Adaptation Speed of Causal Models (2020, methodology): “When we set h(x) = 1/2‖x‖(2), we recover something called the proximal stochastic gradient method (Duchi & Singer, 2009), also known as Perturbed proximal gradient algorithm (Atchadé et al., 2017).”
Distributed Fixed Point Methods with Compressed Iterates (2019, background): “er semicontinuous and proper function Rd!(1 ;+1], and prox H is the proximity operator of Hdened as prox H (x) := argmin y2Rd ˆ 1 2 kx yk2 + H(y) ˙ : The map T prox-SGD also satises the Assumptions [2,3]. A xed point of T prox-SGD is a minimizer of F+ H. 5 Davis-Yin splitting Davis-Yin splitting [12”
Analysis of nonsmooth stochastic approximation: the differential inclusion approach (2018, result): “[3] have extended these results in the Markovian noise case.”
Dualize, Split, Randomize: Fast Nonsmooth Optimization Algorithms (2020, methodology): “Moreover, the value of r boils down to r = max Consider the applications of SGD covered by Assumption 1, and mentioned in Sect.”
On Acceleration with Noise-Corrupted Gradients (2018, methodology): “…the setting of stochastic methods, in which the gradient is only estimated from a subset of its components (Lan, 2012; Ghadimi & Lan, 2012; 2013; Atchade et al., 2014; Krichene & Bartlett, 2017; Jain et al., 2018), the setting of differentially private empirical risk minimization, in which…”
A Stochastic Semismooth Newton Method for Nonsmooth Nonconvex Optimization (2018, methodology): “, the perturbed proximal gradient method [6] studied by Atchadé et al.”
Unified Analysis of Stochastic Gradient Methods for Composite Convex and Smooth Optimization (2020, methodology): “The only diﬀerence is that in [5] the authors assume that f is convex.”