Summary of Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates, by Riccardo Grazzi et al.
Nonsmooth Implicit Differentiation: Deterministic and Stochastic Convergence Rates
by Riccardo Grazzi, Massimiliano Pontil, Saverio Salzo
First submitted to arxiv on: 18 Mar 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG); Optimization and Control (math.OC)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary Medium Difficulty summary: This paper tackles the problem of computing the derivative of the fixed-point of a parametric nondifferentiable contraction map, which has applications in machine learning for hyperparameter optimization, meta-learning, and data poisoning attacks. The authors analyze two approaches, iterative differentiation (ITD) and approximate implicit differentiation (AID), and improve upon previous work by Bolte et al. (2022) to establish linear rates for ITD and AID in the deterministic case. Additionally, they introduce NSID, a new stochastic method, and provide convergence rates that match those in the smooth setting. The authors also present illustrative experiments confirming their analysis. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary Low Difficulty summary: This paper is about finding a way to calculate something called the “derivative” of a complicated mathematical function. This calculation is important for many areas of machine learning, including optimizing settings and testing data quality. The researchers looked at two different methods for doing this calculation and improved upon previous work to make it more efficient. They also came up with a new method that works well in certain situations and tested it out. |
Keywords
* Artificial intelligence * Hyperparameter * Machine learning * Meta learning * Optimization
