# TorchOpt: An Efficient Library for Differentiable Optimization

arXiv: https://arxiv.org/abs/2211.06934 · HTML: https://mlsanity.com/paper/2211.06934/

## Key facts

- Cited by 17 papers in the map (data through 14 Oct 2026).
- Builds on 21 of its 26 references that are in the map.
- First posted on arXiv 13 Nov 2022.

## Builds on (most cited first, 21 of 21)

- [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)
- [Categorical Reparameterization with Gumbel-Softmax](https://mlsanity.com/paper/1611.01144/) (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)
- [Evolution Strategies as a Scalable Alternative to Reinforcement Learning](https://mlsanity.com/paper/1703.03864/) (2017)
- [Meta-Learning with Implicit Gradients](https://mlsanity.com/paper/1909.04630/) (2019)
- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [Optimizing Millions of Hyperparameters by Implicit Differentiation](https://mlsanity.com/paper/1911.02590/) (2019)
- [Differentiation of Blackbox Combinatorial Solvers](https://mlsanity.com/paper/1912.02175/) (2019)
- [Efficient and Modular Implicit Differentiation](https://mlsanity.com/paper/2105.15183/) (2021)
- [Meta-Gradient Reinforcement Learning](https://mlsanity.com/paper/1805.09801/) (2018)
- [On the Iteration Complexity of Hypergradient Computation](https://mlsanity.com/paper/2006.16218/) (2020)
- [Generalized Inner Loop Meta-Learning](https://mlsanity.com/paper/1910.01727/) (2019)
- [Discovering Reinforcement Learning Algorithms](https://mlsanity.com/paper/2007.08794/) (2020)
- [learn2learn: A Library for Meta-Learning Research](https://mlsanity.com/paper/2008.12284/) (2020)
- [ES-MAML: Simple Hessian-Free Meta Learning](https://mlsanity.com/paper/1910.01215/) (2019)
- [Torchmeta: A Meta-Learning library for PyTorch](https://mlsanity.com/paper/1909.06576/) (2019)
- [Betty: An Automatic Differentiation Library for Multilevel Optimization](https://mlsanity.com/paper/2207.02849/) (2022)
- [CROSSBOW: Scaling Deep Learning with Small Batch Sizes on Multi-GPU Servers](https://mlsanity.com/paper/1901.02244/) (2019)
- [A Theoretical Understanding of Gradient Bias in Meta-Reinforcement Learning](https://mlsanity.com/paper/2112.15400/) (2021)

## Built on by (most cited first, 17 of 17)

- [A Survey of Contextual Optimization Methods for Decision Making under Uncertainty](https://mlsanity.com/paper/2306.10374/) (2023)
- [TorchDEQ: A Library for Deep Equilibrium Models](https://mlsanity.com/paper/2310.18605/) (2023)
- [Differentiation Through Black-Box Quadratic Programming Solvers](https://mlsanity.com/paper/2410.06324/) (2024)
- [Differentiable Model Predictive Control on the GPU](https://mlsanity.com/paper/2510.06179/) (2025)
- [GEAR: A GPU-Centric Experience Replay System for Large Reinforcement Learning Models](https://mlsanity.com/paper/2310.05205/) (2023)
- [FreeAugment: Data Augmentation Search Across All Degrees of Freedom](https://mlsanity.com/paper/2409.04820/) (2024)
- [A Fully First-Order Layer for Differentiable Optimization](https://mlsanity.com/paper/2512.02494/) (2025)
- [RAIFLE: Reconstruction Attacks on Interaction-based Federated Learning with Adversarial Data Manipulation](https://mlsanity.com/paper/2310.19163/) (2023)
- [Automatic Differentiation of Optimization Algorithms with Time-Varying Updates](https://mlsanity.com/paper/2410.15923/) (2024)
- [Exploring the Potential of Bilevel Optimization for Calibrating Neural Networks](https://mlsanity.com/paper/2503.13113/) (2025)
- [Adaptive Scaling of Policy Constraints for Offline Reinforcement Learning](https://mlsanity.com/paper/2508.19900/) (2025)
- [From Data to Rewards: a Bilevel Optimization Perspective on Maximum Likelihood Estimation](https://mlsanity.com/paper/2510.07624/) (2025)
- [Unified Control for Inference-Time Guidance of Denoising Diffusion Models](https://mlsanity.com/paper/2512.12339/) (2025)
- [Generalized Information Gathering Under Dynamics Uncertainty](https://mlsanity.com/paper/2601.21988/) (2026)
- [Bayesian Meta-Learning with Expert Feedback for Task-Shift Adaptation through Causal Embeddings](https://mlsanity.com/paper/2602.19788/) (2026)
- [Feed m Birds with One Scone: Accelerating Multi-task Gradient Balancing via Bi-level Optimization](https://mlsanity.com/paper/2603.07389/) (2026)
- [Scalable and Differentiable Point-Cloud Registration Using Maximum Mean Discrepancy](https://mlsanity.com/paper/2606.27818/) (2026)

## Abstract (arXiv)

Recent years have witnessed the booming of various differentiable optimization algorithms. These algorithms exhibit different execution patterns, and their execution needs massive computational resources that go beyond a single CPU and GPU. Existing differentiable optimization libraries, however, cannot support efficient algorithm development and multi-CPU/GPU execution, making the development of differentiable optimization algorithms often cumbersome and expensive. This paper introduces TorchOpt, a PyTorch-based efficient library for differentiable optimization. TorchOpt provides a unified and expressive differentiable optimization programming abstraction. This abstraction allows users to efficiently declare and analyze various differentiable optimization programs with explicit gradients, implicit gradients, and zero-order gradients. TorchOpt further provides a high-performance distributed execution runtime. This runtime can fully parallelize computation-intensive differentiation operations (e.g. tensor tree flattening) on CPUs / GPUs and automatically distribute computation to distributed devices. Experimental results show that TorchOpt achieves 5.2× training time speedup on an 8-GPU server. TorchOpt is available at: https://github.com/metaopt/torchopt/.