Summary of Sequential Probability Assignment with Contexts: Minimax Regret, Contextual Shtarkov Sums, and Contextual Normalized Maximum Likelihood, by Ziyi Liu et al.
Sequential Probability Assignment with Contexts: Minimax Regret, Contextual Shtarkov Sums, and Contextual Normalized Maximum Likelihood
by Ziyi Liu, Idan Attias, Daniel M. Roy
First submitted to arxiv on: 4 Oct 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Machine Learning (stat.ML)
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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 tackle the fundamental problem of online learning with logarithmic loss, focusing on an arbitrary hypothesis class that may not be parametric. The goal is to develop a complexity measure that captures minimax regret and determine a general optimal algorithm. Building upon seminal work by Shtarkov and Rakhlin et al., the authors introduce the contextual Shtarkov sum as a novel complexity measure, which equals the minimax regret in the worst case. This leads to the derivation of the minimax optimal strategy, cNML (contextual Normalized Maximum Likelihood). The findings apply to sequential experts with non-binary labels, extending previous work. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary This paper explores how computers can make predictions when they don’t have all the information. It’s like trying to guess what someone will do next based on a few hints. The researchers want to find the best way for computers to learn and adapt over time. They develop a new method, cNML (contextual Normalized Maximum Likelihood), that works well even when we don’t know everything about the situation. This is important because it can help computers make better decisions in situations where they have incomplete information. |
Keywords
» Artificial intelligence » Likelihood » Online learning
