Summary of Regret Minimization and Statistical Inference in Online Decision Making with High-dimensional Covariates, by Congyuan Duan et al.
Regret Minimization and Statistical Inference in Online Decision Making with High-dimensional Covariates
by Congyuan Duan, Wanteng Ma, Jiashuo Jiang, Dong Xia
First submitted to arxiv on: 10 Nov 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 This paper investigates regret minimization, statistical inference, and their interplay in high-dimensional online decision-making based on the sparse linear context bandit model. The researchers integrate the -greedy bandit algorithm for decision-making with a hard thresholding algorithm for estimating sparse bandit parameters and introduce an inference framework based on a debiasing method using inverse propensity weighting. They demonstrate that under certain conditions, their method achieves either O(T^{1/2}) regret or classical O(T^{1/2})-consistent inference, indicating an unavoidable trade-off between exploration and exploitation. Additionally, they show that a pure-greedy bandit algorithm, combined with a debiased estimator based on average weighting, can simultaneously achieve optimal O(T) regret and O(T^{1/2})-consistent inference. The paper also explores the use of a simple sample mean estimator to provide valid inference for the optimal policy’s value. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In this study, researchers explore how to make good decisions when there is limited information available. They create a new algorithm that combines two other techniques: one for making decisions and another for figuring out what’s happening behind the scenes. The results show that sometimes you have to balance trying new things with sticking to what works. The paper also talks about using simple math to understand how well a decision is doing. |
Keywords
* Artificial intelligence * Inference
