A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear a...A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear and logistic regression.We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs,using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters.We describe three general classes of convex optimization models,maximum a posteriori(MAP)models,utility maximization models,and agent models,and present a numerical experiment for each.展开更多
We consider the problem of minimizing a block separable convex function(possibly nondifferentiable, and including constraints) plus Laplacian regularization, a problem that arises in applications including model fitti...We consider the problem of minimizing a block separable convex function(possibly nondifferentiable, and including constraints) plus Laplacian regularization, a problem that arises in applications including model fitting, regularizing stratified models, and multi-period portfolio optimization. We develop a distributed majorization-minimization method for this general problem, and derive a complete, self-contained, general,and simple proof of convergence. Our method is able to scale to very large problems, and we illustrate our approach on two applications, demonstrating its scalability and accuracy.展开更多
We describe a modular rewriting system for translating optimization problems written in a domain-specific language(DSL)to forms compatible with low-level solver interfaces.Translation is facilitated by reductions,whic...We describe a modular rewriting system for translating optimization problems written in a domain-specific language(DSL)to forms compatible with low-level solver interfaces.Translation is facilitated by reductions,which accept a category of problems and transform instances of that category to equivalent instances of another category.Our system proceeds in two key phases:analysis,in which we attempt to find a suitable solver for a supplied problem,and canonicalization,in which we rewrite the problem in the selected solver’s standard form.We implement the described system in version 1.0 of CVXPY,a DSL for mathematical and especially convex optimization.By treating reductions as first-class objects,our method makes it easy to match problems to solvers well-suited for them and to support solvers with a wide variety of standard forms.展开更多
文摘A convex optimization model predicts an output from an input by solving a convex optimization problem.The class of convex optimization models is large,and includes as special cases many well-known models like linear and logistic regression.We propose a heuristic for learning the parameters in a convex optimization model given a dataset of input-output pairs,using recently developed methods for differentiating the solution of a convex optimization problem with respect to its parameters.We describe three general classes of convex optimization models,maximum a posteriori(MAP)models,utility maximization models,and agent models,and present a numerical experiment for each.
文摘We consider the problem of minimizing a block separable convex function(possibly nondifferentiable, and including constraints) plus Laplacian regularization, a problem that arises in applications including model fitting, regularizing stratified models, and multi-period portfolio optimization. We develop a distributed majorization-minimization method for this general problem, and derive a complete, self-contained, general,and simple proof of convergence. Our method is able to scale to very large problems, and we illustrate our approach on two applications, demonstrating its scalability and accuracy.
文摘We describe a modular rewriting system for translating optimization problems written in a domain-specific language(DSL)to forms compatible with low-level solver interfaces.Translation is facilitated by reductions,which accept a category of problems and transform instances of that category to equivalent instances of another category.Our system proceeds in two key phases:analysis,in which we attempt to find a suitable solver for a supplied problem,and canonicalization,in which we rewrite the problem in the selected solver’s standard form.We implement the described system in version 1.0 of CVXPY,a DSL for mathematical and especially convex optimization.By treating reductions as first-class objects,our method makes it easy to match problems to solvers well-suited for them and to support solvers with a wide variety of standard forms.
