Accelerated Mirror Descent in Continuous and Discrete Time

By Walid Krichene, Alexandre M. Bayen, Peter L. Bartlett. 2015

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Citations in the corpus

Learning explanations that are hard to vary (2020, methodology): “This implies we can approximate C (θ∗) by solving a sequence of maximization problems with simple convex8 constrains, solvable with accelerated mirror descent [Krichene et al., 2015].”
Stochastic Modified Equations and Adaptive Stochastic Gradient Algorithms (2015, methodology): “Other deterministic continuous time approximation methods include Su et al. (2014); Krichene et al. (2015); Wibisono et al. (2016).”
On Acceleration with Noise-Corrupted Gradients (2018, unknown): “Recently, some of the mystery of acceleration has faded, as different works have provided natural interpretations and alternative proofs for accelerated methods (Allen-Zhu & Orecchia, 2017; Krichene et al., 2015; Wibisono et al., 2016; Bubeck et al., 2015; Lessard et al., 2016; Hu & Lessard, 2017; D”
A Lyapunov Analysis of Momentum Methods in Optimization (2016, background): “O C ] 3 1 D”
Stochastic Mirror Descent in Variationally Coherent Optimization Problems (2017, background): “However, this would make (2)For related approaches based on the theory of dynamical systems, see [21] and [12].”
Underdamped Langevin MCMC: A non-asymptotic analysis (2017, background): “Also related is the recent work on understanding acceleration of first-order optimization methods as discretizations of second-order differential equations [23, 24, 25].”
A variational perspective on accelerated methods in optimization (2016, methodology): “For p = 2, Su et al. [32] and Krichene et al. [17] treat the case when we start at t = 0 with initial condition ( X 0 , W 0 ) = ( x 0 , ∇ h ( x 0 )), so that ˙ X 0 = 0.”