arXiv 26 Jun 2021 · Machine Learning · 3 citations (OpenAlex)
arXiv:2106.14077 · PDF · DOI · OpenAlex · Extracted main text
We study the best-arm identification problem with fixed confidence when contextual (covariate) information is available in stochastic bandits. Although we can use contextual information in each round, we are interested in the marginalized mean reward over the contextual distribution. Our goal is to identify the best arm with a minimal number of samplings under a given value of the error rate. We show the instance-specific sample complexity lower bounds for the problem. Then, we propose a context-aware version of the "Track-and-Stop" strategy, wherein the proportion of the arm draws tracks the set of optimal allocations and prove that the expected number of arm draws matches the lower bound asymptotically. We demonstrate that contextual information can be used to improve the efficiency of the identification of the best marginalized mean reward compared with the results of Garivier & Kaufmann (2016). We experimentally confirm that context information contributes to faster best-arm identification.
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The works this paper leans on most, across its whole bibliography — not restricted to papers in our corpus. Ranked by composite intensity, which combines how often a work is mentioned, how many sections mention it, and how much of that falls in the main text rather than the appendix.
| Reference | Intensity | Mentions | Sections | Main text | |
|---|---|---|---|---|---|
| 1 | Garivier, A. and Kaufmann, E (2016) Optimal Best Arm Identification with Fixed Confidence, in | 0.877 | 40 | 10 | 68% |
| 2 | Jedra, Y. and Proutiere, A (2020) Optimal Best-arm Identification in Linear Bandits | 0.843 | 5 | 3 | 60% |
| 3 | Kaufmann, E., Cappé, O., and Garivier, A (2016) On the Complexity of Best-Arm Identification in Multi-Armed Bandit Models | 0.838 | 17 | 6 | 59% |
| 4 | Kaufmann, E. and Koolen, W. M (2021) Mixture Martingales Revisited with Applications to Sequential Tests and Confidence Intervals | 0.693 | 6 | 1 | 100% |
| 5 | Juneja, S. and Krishnasamy, S (2019) Sample complexity of partition identification using multi-armed bandits, in | 0.644 | 2 | 2 | 100% |
| 6 | Russac, Y., Katsimerou, C., Bohle, D., Cappé, O., Garivier, A., and… (2021) A/B/n Testing with Control in the Presence of Subpopulations, in | 0.644 | 2 | 2 | 100% |
| 7 | Degenne, R., Koolen, W. M., and Ménard, P (2019) Non-Asymptotic Pure Exploration by Solving Games, in | 0.644 | 2 | 2 | 100% |
| 8 | Hahn, J., Hirano, K., and Karlan, D (2011) Adaptive experimental design using the propensity score | 0.585 | 3 | 1 | 100% |
| 9 | Cappé, O., Garivier, A., Maillard, O.-A., Munos, R., and Stoltz, G (2013) Kullback–Leibler upper confidence bounds for optimal sequential allocation | 0.511 | 2 | 1 | 100% |
| 10 | Karlan, D. and Wood, D. H (2014) The Effect of Effectiveness: Donor Response to Aid Effectiveness in a Direct Mail Fundraising Experiment, Working paper, Nationa… | 0.511 | 2 | 1 | 100% |
Showing the top 10 of 42 scored citations.
arXiv econ.EM papers that cite this one, ranked by how heavily they lean on it.
| Citing paper | Intensity | Mentions | Sections | |
|---|---|---|---|---|
| 1 | Best Arm Identification with Contextual Information under a Small Gap | 0.511 | 2 | 1 |