High-accuracy log-concave sampling with stochastic queries
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866909045176139776 |
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| author | Chen, Fan Chewi, Sinho Daskalakis, Constantinos Rakhlin, Alexander |
| author_facet | Chen, Fan Chewi, Sinho Daskalakis, Constantinos Rakhlin, Alexander |
| contents | We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/δ)$, where $δ$ is the desired target accuracy -- are achievable using stochastic gradients with subexponential tails. Notably, this exhibits a separation with the problem of convex optimization, where stochasticity (even additive Gaussian noise) in the gradient oracle incurs $\mathrm{poly}(1/δ)$ queries. We also give an information-theoretic argument that light-tailed stochastic gradients are necessary for high accuracy: for example, in the bounded variance case, we show that the minimax-optimal query complexity scales as $Θ(1/δ)$. Our framework also provides similar high accuracy guarantees under stochastic zeroth order (value) queries, and an improved complexity result for sampling from finite-sum potentials. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2602_14342 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | High-accuracy log-concave sampling with stochastic queries Chen, Fan Chewi, Sinho Daskalakis, Constantinos Rakhlin, Alexander Statistics Theory Data Structures and Algorithms Machine Learning Probability We show that high-accuracy guarantees for log-concave sampling -- that is, iteration and query complexities which scale as $\mathrm{poly}\log(1/δ)$, where $δ$ is the desired target accuracy -- are achievable using stochastic gradients with subexponential tails. Notably, this exhibits a separation with the problem of convex optimization, where stochasticity (even additive Gaussian noise) in the gradient oracle incurs $\mathrm{poly}(1/δ)$ queries. We also give an information-theoretic argument that light-tailed stochastic gradients are necessary for high accuracy: for example, in the bounded variance case, we show that the minimax-optimal query complexity scales as $Θ(1/δ)$. Our framework also provides similar high accuracy guarantees under stochastic zeroth order (value) queries, and an improved complexity result for sampling from finite-sum potentials. |
| title | High-accuracy log-concave sampling with stochastic queries |
| topic | Statistics Theory Data Structures and Algorithms Machine Learning Probability |
| url | https://arxiv.org/abs/2602.14342 |