Input Convex Neural Networks

By Brandon Amos, Lei Xu, J. Kolter. 2016

872 citations recorded by the source corpus.

This paper presents the input convex neural network architecture. These are scalar-valued (potentially deep) neural networks with constraints on the network parameters such that the output of the network is a convex function of (some of) the inputs. The networks allow for efficient inference via optimization over some inputs to the network given others, and can be applied to settings including structured prediction, data imputation, reinforcement learning, and others. In this paper we lay the basic groundwork for these models, proposing methods for inference, optimization and learning, and analyze their representational power. We show that many existing neural network architectures can be made input-convex with a minor modification, and develop specialized optimization algorithms tailored to this setting. Finally, we highlight the performance of the methods on multi-label prediction, image completion, and reinforcement learning problems, where we show improvement over the existing state of the art in many cases.

Subfields: Artificial Intelligence, Computer Vision and Pattern Recognition, Model Architectures

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Citations in the corpus

Q-Prop: Sample-Efficient Policy Gradient with An Off-Policy Critic (2016, neutral): “1”, it outperforms other methods as well as the DDPG results reported in prior work (Duan et al., 2016; Amos et al., 2016).”
OptNet: Differentiable Optimization as a Layer in Neural Networks (2017, methodology): “Among many other applications, these architectures are well-studied for generic classification and structured prediction tasks (Goodfellow et al., 2013; Stoyanov et al., 2011; Brakel et al., 2013; LeCun et al., 2006; Belanger & McCallum, 2016; Belanger et al., 2017; Amos et al., 2017); in vision for”
QT-Opt: Scalable Deep Reinforcement Learning for Vision-Based Robotic Manipulation (2018, methodology): “Prior work has sought to address this by using a second network that amortizes the maximization [15, 16], or constraining the Q-function to be convex in a, making it easy to maximize analytically [29, 35].”
Leave no Trace: Learning to Reset for Safe and Autonomous Reinforcement Learning (2017, methodology): “Our methods can also be used directly with any other Q-learning methods ((Watkins & Dayan, 1992; Mnih et al., 2013; Gu et al., 2017; Amos et al., 2016; Metz et al., 2017)).”
EMaQ: Expected-Max Q-Learning Operator for Simple Yet Effective Offline and Online RL (2020, background): “NAF (Gu et al., 2016b) and ICNN (Amos et al., 2017) directly constrain the function family of Q-functions such that the optimization can be closed-form or tractable.”
Discrete Sequential Prediction of Continuous Actions for Deep RL (2017, methodology): “[1] Brandon Amos, Lei Xu, and J Zico Kolter.”
Deep Value Networks Learn to Evaluate and Iteratively Refine Structured Outputs (2017, background): “Alternatively, one can make use of input convex neural networks (Amos et al., 2016) to guarantee convergence to optimal (cid:98) y .”
Learning single-cell perturbation responses using neural optimal transport (2021, background): “In order to learn the resulting optimal transport, i.e., the solution of the minimization problem in (6), Makkuva et al. (2020) parametrize both dual variables f and g using input convex neural networks (§ 2.3) (Amos et al., 2017).”
Task-based End-to-end Model Learning in Stochastic Optimization (2017, background): “Recent approaches have looked into similar argmin differentiations [28, 29], though the methodology we present here is more general and handles the stochasticity of the objective.”
Deep Multi-Agent Reinforcement Learning for Decentralized Continuous Cooperative Control (2020, methodology): “We rely on CEM instead of other continuous Q - learning approaches (Gu et al., 2016; Amos et al., 2017) because of its empirical success (see Section 5).”
Deep Structured Energy-Based Image Inpainting (2018, methodology): “Amos et al. [21] proposed input convex neural networks (ICNNs) which share similar architectural properties compared to SPENs.”
Continuous Control with Action Quantization from Demonstrations (2021, background): “Typical strategies to solve the Q-value maximization include enforcing the Q-value to be concave (Gu et al., 2016; Amos et al., 2017) making it easy to optimize through e.”
Learning Approximate Inference Networks for Structured Prediction (2018, methodology): “ below provide more evidence for making this transition. An alternative to what we pursue here would be to obtain an easier convex optimization problem for inference via input convex neural networks (Amos et al., 2017). 5 Published as a conference paper at ICLR 2018 Table 1: Test F1 when comparing m”
Differentiation of Blackbox Combinatorial Solvers (2019, methodology): “However, the function f ( y(w) ) is a result of a minimization process and it is known that for smooth spaces Y there are techniques for such “differentiation through argmin” [2, 3, 11, 13, 38, 40].”
Piecewise Linear Neural Network verification: A comparative study (2017, background): “Aside from some specific class of NN (Amos et al., 2017), this remains a hard problem.”
End-to-End Learning for Structured Prediction Energy Networks (2017, methodology): “(5) can be naturally extended to certain alternative optimization methods, such as gradient descent with momentum, or L-BFGS (Liu & Nocedal, 1989; Domke, 2012).”
Strong mixed-integer programming formulations for trained neural networks (2018, background): “Throughout this stream of the literature, there is discussion of the performance for specific subclasses of neural network models, including binarized [44] or input convex [3] neural networks.”
Lifted Relational Neural Networks: Efficient Learning of Latent Relational Structures (2018, methodology): “A number of eﬃcient methods have recently been proposed for structured output prediction, such as the work on so-called input convex neural networks (Amos, Xu, & Kolter, 2017).”
CAQL: Continuous Action Q-Learning (2019, methodology): “Parameterizing the Q-function with an input-convex neural network (Amos et al., 2017) ensures it is concave.”