Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality
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arXiv
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| Autores principales: | , , |
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| Formato: | Preprint |
| Publicado: |
2022
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| _version_ | 1866913349352030208 |
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| author | Cutler, Joshua Díaz, Mateo Drusvyatskiy, Dmitriy |
| author_facet | Cutler, Joshua Díaz, Mateo Drusvyatskiy, Dmitriy |
| contents | We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction and its multiplayer extensions. We show that under mild assumptions, the deviation between the average iterate of the algorithm and the solution is asymptotically normal, with a covariance that clearly decouples the effects of the gradient noise and the distributional shift. Moreover, building on the work of Hájek and Le Cam, we show that the asymptotic performance of the algorithm with averaging is locally minimax optimal. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2207_04173 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality Cutler, Joshua Díaz, Mateo Drusvyatskiy, Dmitriy Optimization and Control Machine Learning 90C15, 90C25 We analyze a stochastic approximation algorithm for decision-dependent problems, wherein the data distribution used by the algorithm evolves along the iterate sequence. The primary examples of such problems appear in performative prediction and its multiplayer extensions. We show that under mild assumptions, the deviation between the average iterate of the algorithm and the solution is asymptotically normal, with a covariance that clearly decouples the effects of the gradient noise and the distributional shift. Moreover, building on the work of Hájek and Le Cam, we show that the asymptotic performance of the algorithm with averaging is locally minimax optimal. |
| title | Stochastic Approximation with Decision-Dependent Distributions: Asymptotic Normality and Optimality |
| topic | Optimization and Control Machine Learning 90C15, 90C25 |
| url | https://arxiv.org/abs/2207.04173 |