Optimal e-variables under constraints
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arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2026
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| _version_ | 1866908989702275072 |
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| author | Saha, Aytijhya Ramdas, Aaditya |
| author_facet | Saha, Aytijhya Ramdas, Aaditya |
| contents | E-variables enable safe and anytime-valid inference, with log-optimal e-variables given by the likelihood ratio of the least favorable distributions (LFDs) when they exist in composite settings. While this unconstrained theory is well understood, one may need/wish to impose additional structural constraints, including differential privacy, quantization, boundedness, or moment restrictions. We show that under these constraints, log-optimal constrained e-variables can often be constructed by a simple \emph{optimize-then-constrain} principle: first compute the unconstrained log-optimal e-variable, then impose the constraint via an appropriate transformation. Thus, the constrained growth-rate optimization problem does not require solving for a different LFD pair; the constrained optimal solution is just a post-processing of the unconstrained optimal solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_21680 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Optimal e-variables under constraints Saha, Aytijhya Ramdas, Aaditya Methodology E-variables enable safe and anytime-valid inference, with log-optimal e-variables given by the likelihood ratio of the least favorable distributions (LFDs) when they exist in composite settings. While this unconstrained theory is well understood, one may need/wish to impose additional structural constraints, including differential privacy, quantization, boundedness, or moment restrictions. We show that under these constraints, log-optimal constrained e-variables can often be constructed by a simple \emph{optimize-then-constrain} principle: first compute the unconstrained log-optimal e-variable, then impose the constraint via an appropriate transformation. Thus, the constrained growth-rate optimization problem does not require solving for a different LFD pair; the constrained optimal solution is just a post-processing of the unconstrained optimal solution. |
| title | Optimal e-variables under constraints |
| topic | Methodology |
| url | https://arxiv.org/abs/2604.21680 |