# Meta-Learning with Differentiable Convex Optimization

## TL;DR

MetaOptNet introduces a meta-learning approach utilizing differentiable convex optimization for linear classifiers, achieving state-of-the-art results in few-shot learning benchmarks by learning generalizable feature embeddings.

## Contribution

The paper proposes a novel meta-learning method that leverages differentiable convex optimization for linear classifiers, improving few-shot learning performance and generalization.

## Key findings

- Achieves state-of-the-art results on multiple few-shot benchmarks.
- Utilizes implicit differentiation and dual formulation for efficient optimization.
- Supports high-dimensional embeddings with modest computational overhead.

## Abstract

Many meta-learning approaches for few-shot learning rely on simple base learners such as nearest-neighbor classifiers. However, even in the few-shot regime, discriminatively trained linear predictors can offer better generalization. We propose to use these predictors as base learners to learn representations for few-shot learning and show they offer better tradeoffs between feature size and performance across a range of few-shot recognition benchmarks. Our objective is to learn feature embeddings that generalize well under a linear classification rule for novel categories. To efficiently solve the objective, we exploit two properties of linear classifiers: implicit differentiation of the optimality conditions of the convex problem and the dual formulation of the optimization problem. This allows us to use high-dimensional embeddings with improved generalization at a modest increase in computational overhead. Our approach, named MetaOptNet, achieves state-of-the-art performance on miniImageNet, tieredImageNet, CIFAR-FS, and FC100 few-shot learning benchmarks. Our code is available at https://github.com/kjunelee/MetaOptNet.