Brandon Amos, J. Zico Kolter
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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 archite ...
cture: 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.
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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.
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Evidence graph: 2 refs, 1 links.
Utility signals: depth 60/100, grounding 58/100, status medium.
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138
Citations
23
References
Tasks
Computer science, Solver, Differentiable function, Exploit, Layer (electronics), Backpropagation, Convolutional neural network, Artificial neural network
Methods
Optimization problem
Domains
Artificial intelligence, Mathematics
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