Stochastic Online Instrumental Variable Regression: Regrets for Endogeneity and Bandit Feedback
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| Název: | Stochastic Online Instrumental Variable Regression: Regrets for Endogeneity and Bandit Feedback |
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| Autoři: | Della Vecchia, Riccardo, Basu, Debabrota |
| Přispěvatelé: | Basu, Debabrota |
| Zdroj: | Proceedings of the AAAI Conference on Artificial Intelligence. 39:16190-16198 |
| Publication Status: | Preprint |
| Informace o vydavateli: | Association for the Advancement of Artificial Intelligence (AAAI), 2025. |
| Rok vydání: | 2025 |
| Témata: | FOS: Computer and information sciences, Computer Science - Machine Learning, Bandit / imperfect feedback, Machine Learning (stat.ML), [INFO.INFO-LG] Computer Science [cs]/Machine Learning [cs.LG], 02 engineering and technology, 01 natural sciences, Linear bandits, [STAT.ML] Statistics [stat]/Machine Learning [stat.ML], Machine Learning (cs.LG), Causality, Online linear regression, [INFO.INFO-CY] Computer Science [cs]/Computers and Society [cs.CY], Two-stage regression, Online learning, Statistics - Machine Learning, [SHS.STAT] Humanities and Social Sciences/Methods and statistics, 0202 electrical engineering, electronic engineering, information engineering, Regret Bounds, Instrumental Variables, Econometrics, 0101 mathematics, [SHS.ECO] Humanities and Social Sciences/Economics and Finance, [MATH.MATH-ST] Mathematics [math]/Statistics [math.ST] |
| Popis: | Endogeneity, i.e. the dependence of noise and covariates, is a common phenomenon in real data due to omitted variables, strategic behaviours, measurement errors etc. In contrast, the existing analyses of stochastic online linear regression with unbounded noise and linear bandits depend heavily on exogeneity, i.e. the independence of noise and covariates. Motivated by this gap, we study the over- and just-identified Instrumental Variable (IV) regression, specifically Two-Stage Least Squares, for stochastic online learning, and propose to use an online variant of Two-Stage Least Squares, namely O2SLS. We show that O2SLS achieves O(dx dz log^2(T)) identification and O(γ √dz √T ) oracle regret after T interactions, where dx and dz are the dimensions of covariates and IVs, and γ is the bias due to endogeneity. For γ = 0, i.e. under exogeneity, O2SLS exhibits O(dx^2 log^2 T ) oracle regret, which is of the same order as that of the stochastic online ridge. Then, we leverage O2SLS as an oracle to design OFUL-IV, a stochastic linear bandit algorithm to tackle endogeneity. OFUL-IV yields O(√dx √dz √T ) regret that matches the regret lower bound under exogeneity. For different datasets with endogeneity, we experimentally show efficiencies of O2SLS and OFUL-IV. |
| Druh dokumentu: | Article Conference object |
| Popis souboru: | application/pdf |
| ISSN: | 2374-3468 2159-5399 |
| DOI: | 10.1609/aaai.v39i15.33778 |
| DOI: | 10.48550/arxiv.2302.09357 |
| Přístupová URL adresa: | http://arxiv.org/abs/2302.09357 https://hal.science/hal-03831210v3 https://hal.science/hal-03831210v3/document |
| Rights: | CC BY CC BY NC |
| Přístupové číslo: | edsair.doi.dedup.....ec7e525cf9d1f245ff91a742ae6ac3a2 |
| Databáze: | OpenAIRE |
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Nájsť tento článok vo Web of Science | Abstrakt: | Endogeneity, i.e. the dependence of noise and covariates, is a common phenomenon in real data due to omitted variables, strategic behaviours, measurement errors etc. In contrast, the existing analyses of stochastic online linear regression with unbounded noise and linear bandits depend heavily on exogeneity, i.e. the independence of noise and covariates. Motivated by this gap, we study the over- and just-identified Instrumental Variable (IV) regression, specifically Two-Stage Least Squares, for stochastic online learning, and propose to use an online variant of Two-Stage Least Squares, namely O2SLS. We show that O2SLS achieves O(dx dz log^2(T)) identification and O(γ √dz √T ) oracle regret after T interactions, where dx and dz are the dimensions of covariates and IVs, and γ is the bias due to endogeneity. For γ = 0, i.e. under exogeneity, O2SLS exhibits O(dx^2 log^2 T ) oracle regret, which is of the same order as that of the stochastic online ridge. Then, we leverage O2SLS as an oracle to design OFUL-IV, a stochastic linear bandit algorithm to tackle endogeneity. OFUL-IV yields O(√dx √dz √T ) regret that matches the regret lower bound under exogeneity. For different datasets with endogeneity, we experimentally show efficiencies of O2SLS and OFUL-IV. |
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| ISSN: | 23743468 21595399 |
| DOI: | 10.1609/aaai.v39i15.33778 |