Nonlinear Programming

By Dimitri P. Bertsekas. 1995

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Citations in the corpus

A Tight and Unified Analysis of Extragradient for a Whole Spectrum of Differentiable Games (2019, background): “. Seeing optimization algorithms as the repeated applicationof someoperatorallows us to deducetheirconvergencepropertiesfromspectrumofthis operator. This point of view was presented in Polyak (1987); Bertsekas (1999) and recently used in Arjevani et al. (2016); Mescheder et al. (2017); Gidel et al. ”
Barrier Frank-Wolfe for Marginal Inference (2015, background): “The following descent lemma is proved in Bertsekas (1999) (Prop.”
Optimization Methods for Large-Scale Machine Learning (2016, neutral): “For example, Bertsekas and co-authors [11] have proposed incremental gradient methods, the randomized versions of which can be viewed as instances of a basic SG method for minimizing a finite sum.”
Fast Convergence of Stochastic Gradient Descent under a Strong Growth Condition (2013, methodology): “In the context of non-linear least squares problems this condition is equivalent to requiring that all residuals be zero at the solution, and can be used to show local superlinear convergence of Gauss-Newton algorithms [Bertsekas, 1999, §1.5.1]. Under condition (5), Solodov [1998] and Tseng [1998] h”
Learning World Graphs to Accelerate Hierarchical Reinforcement Learning (2019, positive): “angian Relaxation. The overall optimization objective consists of action sequence reconstruction, KL-divergence, L 0 and L T (Equation 3). We tune the objective weights iusing Lagrangian relaxation [43, 8, 10], treating i’s as learnable parameters and performing alternative optimization between i”
Reinforcement learning in robotics: A survey (2013, background): “In the limit when γ approaches 1, the metric approaches what is known as the average-reward criterion (Bertsekas, 1995), J = lim H→∞ E { 1 H H∑ h=0 Rh } .”
OptNet: Differentiable Optimization as a Layer in Neural Networks (2017, neutral): “These techniques also come up in bilevel optimization (Gould et al., 2016; Kunisch & Pock, 2013) and sensitivity analysis (Bertsekas, 1999; Fiacco & Ishizuka, 1990; Bonnans & Shapiro, 2013).”
AlgaeDICE: Policy Gradient from Arbitrary Experience (2019, positive): “where we have used Danskin’s theorem (Bertsekas, 1999) to ignore gradients of π through ν∗ π.”
Smoothed Dual Embedding Control (2017, background): “bjective function L (V;ˇ;ˆ) as L (w V;w ˇ;w ˆ). First, we note that the inner (dual) problem is standard least-squares regression with parameter w ˆ, so can be solved using a variety of algorithms (Bertsekas, 2016); in the presence of special structures like convexity, global optima can be found eci”
Speeding Up Distributed Machine Learning Using Codes (2015, background): “ved between the coded and uncoded schemes. B.Data Shufﬂing and Communication Overheads Distributed learning algorithms on large-scale networked systems have been extensively studied in the literature [51]–[61]. Many of the distributed algorithms that are implemented in practice share a similar algor”
A Survey of Motion Planning and Control Techniques for Self-Driving Urban Vehicles (2016, methodology): “2) [68]b No Cyl. algebr. decomp. [76] No diff. constraints Yes No Exp. in dimension. [65] No Variational Methods Variational methods (Sec IV-C) Lipschitz-continuous Jacobian No Locally optimal O(1=) [77]k;l Yes Graph-search Methods Road lane graph + Dijkstra (Sec IV-D1) Arbitrary Noc Nod O(n+ mlog )”