Summary of Nearly-tight Approximation Guarantees For the Improving Multi-armed Bandits Problem, by Avrim Blum and Kavya Ravichandran
Nearly-tight Approximation Guarantees for the Improving Multi-Armed Bandits Problem
by Avrim Blum, Kavya Ravichandran
First submitted to arxiv on: 1 Apr 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Data Structures and Algorithms (cs.DS); 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 The proposed paper provides near-tight upper and lower bounds for the improving multi-armed bandits problem. This problem involves a setting with K arms, each having a reward function that increases concavely as the arm is pulled more times. The authors demonstrate that any randomized online algorithm will suffer at least an O(sqrt(K)) approximation factor relative to the optimal reward for some instance. To counter this, they offer a randomized online algorithm that guarantees an O(sqrt(K)) approximation factor if it knows the maximum achievable reward by the optimal arm in advance. By removing this assumption at a cost of an extra O(log K) approximation factor, the authors achieve an overall O(sqrt(K) * log K) approximation relative to optimal. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary The paper studies how to make good decisions when you don’t know what will happen next. It’s like playing a game with many different options, and you need to choose which one to pick. The problem is that the best option changes as you play more rounds. The authors show that any way of making decisions will make mistakes, but they also give an algorithm that makes mistakes at most a certain amount. This is important because it helps us understand how to make good choices when we’re not sure what will happen. |
