When Deep Learning Meets Polyhedral Theory: A Survey

no code implementations • 29 Apr 2023 • Joey Huchette, Gonzalo Muñoz, Thiago Serra, Calvin Tsay

In the past decade, deep learning became the prevalent methodology for predictive modeling thanks to the remarkable accuracy of deep neural networks in tasks such as computer vision and natural language processing.

Neural Network Verification as Piecewise Linear Optimization: Formulations for the Composition of Staircase Functions

no code implementations • 27 Nov 2022 • Tu Anh-Nguyen, Joey Huchette

We derive a \emph{strong formulation} for each neuron in a network using piecewise linear activation functions.

Contextual Reserve Price Optimization in Auctions via Mixed Integer Programming

1 code implementation • NeurIPS 2020 • Joey Huchette, Haihao Lu, Hossein Esfandiari, Vahab Mirrokni

Moreover, we show that this MIP formulation is ideal (i. e. the strongest possible formulation) for the revenue function of a single impression.

The Convex Relaxation Barrier, Revisited: Tightened Single-Neuron Relaxations for Neural Network Verification

no code implementations • NeurIPS 2020 • Christian Tjandraatmadja, Ross Anderson, Joey Huchette, Will Ma, Krunal Patel, Juan Pablo Vielma

We improve the effectiveness of propagation- and linear-optimization-based neural network verification algorithms with a new tightened convex relaxation for ReLU neurons.

Contextual Reserve Price Optimization in Auctions via Mixed-Integer Programming

1 code implementation • 20 Feb 2020 • Joey Huchette, Haihao Lu, Hossein Esfandiari, Vahab Mirrokni

Moreover, we show that this MIP formulation is ideal (i. e. the strongest possible formulation) for the revenue function of a single impression.

Strong mixed-integer programming formulations for trained neural networks

no code implementations • 20 Nov 2018 • Ross Anderson, Joey Huchette, Christian Tjandraatmadja, Juan Pablo Vielma

We present an ideal mixed-integer programming (MIP) formulation for a rectified linear unit (ReLU) appearing in a trained neural network.

Strong convex relaxations and mixed-integer programming formulations for trained neural networks

1 code implementation • 5 Nov 2018 • Ross Anderson, Joey Huchette, Christian Tjandraatmadja, Juan Pablo Vielma

We present strong convex relaxations for high-dimensional piecewise linear functions that correspond to trained neural networks.

Optimization and Control 90C11

JuMP: A Modeling Language for Mathematical Optimization

1 code implementation • 9 Aug 2015 • Iain Dunning, Joey Huchette, Miles Lubin

JuMP is an open-source modeling language that allows users to express a wide range of optimization problems (linear, mixed-integer, quadratic, conic-quadratic, semidefinite, and nonlinear) in a high-level, algebraic syntax.

Optimization and Control Mathematical Software