Summary of On the Performance Of Empirical Risk Minimization with Smoothed Data, by Adam Block et al.
On the Performance of Empirical Risk Minimization with Smoothed Data
by Adam Block, Alexander Rakhlin, Abhishek Shetty
First submitted to arxiv on: 22 Feb 2024
Categories
- Main: Machine Learning (stat.ML)
- Secondary: Machine Learning (cs.LG)
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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 In this paper, researchers explore the concept of smooth online learning in sequential decision-making, where the distribution of data at each time step is assumed to have bounded likelihood ratio with respect to a base measure conditioned on the history. They investigate the general setting where the base measure is unknown to the learner and focus on the performance of Empirical Risk Minimization (ERM) with square loss when the data are well-specified and smooth. The authors show that ERM can achieve sublinear error whenever a class is learnable with iid data, scaling as O(sqrt(comp(F)*T)), where comp(F) is the statistical complexity of learning F with iid data. They also establish a novel norm comparison bound for smoothed data and provide a lower bound indicating that their analysis of ERM is essentially tight. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In this study, scientists try to make it easier for machines to learn from data by smoothing out the process. This helps them avoid problems caused by statistical and computational hardness. They look at a specific method called Empirical Risk Minimization (ERM) and show that it can work well even when the base measure is unknown. The results are important because they help us understand how ERM works in different situations. |
Keywords
* Artificial intelligence * Likelihood * Online learning
