OptNet: Differentiable Optimization as a Layer in Neural Networks

Code

• github.com/locuslab/optnet
  OfficialIn paperpytorch★ 0
• github.com/Kyubyong/sudoku
  OfficialIn papertf★ 0
• github.com/mitmath/matrixcalc
  jax★ 579
• github.com/locuslab/e2e-model-learning
  pytorch★ 0
• github.com/quentinll/diffqcqp
  torch★ 0
• github.com/kevin-tracy/qpax
  jax★ 0
• github.com/msakai/chainer-optnet
  none★ 0
• github.com/pfnet-research/chainer-differentiable-mpc
  pytorch★ 0

Abstract

This paper presents OptNet, a network architecture that integrates optimization problems (here, specifically in the form of quadratic programs) as individual layers in larger end-to-end trainable deep networks. These layers encode constraints and complex dependencies between the hidden states that traditional convolutional and fully-connected layers often cannot capture. We explore the foundations for such an architecture: we show how techniques from sensitivity analysis, bilevel optimization, and implicit differentiation can be used to exactly differentiate through these layers and with respect to layer parameters; we develop a highly efficient solver for these layers that exploits fast GPU-based batch solves within a primal-dual interior point method, and which provides backpropagation gradients with virtually no additional cost on top of the solve; and we highlight the application of these approaches in several problems. In one notable example, the method is learns to play mini-Sudoku (4x4) given just input and output games, with no a-priori information about the rules of the game; this highlights the ability of OptNet to learn hard constraints better than other neural architectures.

Tasks

Reproductions