# Meta-Learning Parameterized First-Order Optimizers using Differentiable Convex Optimization

arXiv: https://arxiv.org/abs/2303.16952 · HTML: https://mlsanity.com/paper/2303.16952/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 25 of its 37 references that are in the map.
- First posted on arXiv 29 Mar 2023.

## Builds on (most cited first, 25 of 25)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Very Deep Convolutional Networks for Large-Scale Image Recognition](https://mlsanity.com/paper/1409.1556/) (2014)
- [Model-Agnostic Meta-Learning for Fast Adaptation of Deep Networks](https://mlsanity.com/paper/1703.03400/) (2017)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [Prototypical Networks for Few-shot Learning](https://mlsanity.com/paper/1703.05175/) (2017)
- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [Matching Networks for One Shot Learning](https://mlsanity.com/paper/1606.04080/) (2016)
- [Meta-Learning in Neural Networks: A Survey](https://mlsanity.com/paper/2004.05439/) (2020)
- [Mastering Chess and Shogi by Self-Play with a General Reinforcement Learning Algorithm](https://mlsanity.com/paper/1712.01815/) (2017)
- [Learning to learn by gradient descent by gradient descent](https://mlsanity.com/paper/1606.04474/) (2016)
- [Deep Equilibrium Models](https://mlsanity.com/paper/1909.01377/) (2019)
- [OptNet: Differentiable Optimization as a Layer in Neural Networks](https://mlsanity.com/paper/1703.00443/) (2017)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Input Convex Neural Networks](https://mlsanity.com/paper/1609.07152/) (2016)
- [Meta-SGD: Learning to Learn Quickly for Few-Shot Learning](https://mlsanity.com/paper/1707.09835/) (2017)
- [How to train your MAML](https://mlsanity.com/paper/1810.09502/) (2018)
- [Learning to Optimize](https://mlsanity.com/paper/1606.01885/) (2016)
- [Differentiable MPC for End-to-end Planning and Control](https://mlsanity.com/paper/1810.13400/) (2018)
- [SATNet: Bridging deep learning and logical reasoning using a differentiable satisfiability solver](https://mlsanity.com/paper/1905.12149/) (2019)
- [Handbook of Convergence Theorems for (Stochastic) Gradient Methods](https://mlsanity.com/paper/2301.11235/) (2023)
- [Implicit Deep Learning](https://mlsanity.com/paper/1908.06315/) (2019)
- [Few-Shot Image Recognition by Predicting Parameters from Activations](https://mlsanity.com/paper/1706.03466/) (2017)
- [The Limits and Potentials of Deep Learning for Robotics](https://mlsanity.com/paper/1804.06557/) (2018)
- [Generalized Inner Loop Meta-Learning](https://mlsanity.com/paper/1910.01727/) (2019)

## Built on by (most cited first, 1 of 1)

- [Shadow Program Inversion with Differentiable Planning: A Framework for Unified Robot Program Parameter and Trajectory Optimization](https://mlsanity.com/paper/2409.08678/) (2024)

## Abstract (arXiv)

Conventional optimization methods in machine learning and controls rely heavily on first-order update rules. Selecting the right method and hyperparameters for a particular task often involves trial-and-error or practitioner intuition, motivating the field of meta-learning. We generalize a broad family of preexisting update rules by proposing a meta-learning framework in which the inner loop optimization step involves solving a differentiable convex optimization (DCO). We illustrate the theoretical appeal of this approach by showing that it enables one-step optimization of a family of linear least squares problems, given that the meta-learner has sufficient exposure to similar tasks. Various instantiations of the DCO update rule are compared to conventional optimizers on a range of illustrative experimental settings.