Risk level dependent Minimax Quantile lower bounds for Interactive Statistical Decision Making
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arXiv
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| Hauptverfasser: | , , , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914079148343296 |
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| author | Bongole, Raghav Zamani, Amirreza Oechtering, Tobias J. Skoglund, Mikael |
| author_facet | Bongole, Raghav Zamani, Amirreza Oechtering, Tobias J. Skoglund, Mikael |
| contents | Minimax risk and regret focus on expectation, missing rare failures critical in safety-critical bandits and reinforcement learning. Minimax quantiles capture these tails. Three strands of prior work motivate this study: minimax-quantile bounds restricted to non-interactive estimation; unified interactive analyses that focus on expected risk rather than risk level specific quantile bounds; and high-probability bandit bounds that still lack a quantile-specific toolkit for general interactive protocols. To close this gap, within the interactive statistical decision making framework, we develop high-probability Fano and Le Cam tools and derive risk level explicit minimax-quantile bounds, including a quantile-to-expectation conversion and a tight link between strict and lower minimax quantiles. Instantiating these results for the two-armed Gaussian bandit immediately recovers optimal-rate bounds. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_05808 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Risk level dependent Minimax Quantile lower bounds for Interactive Statistical Decision Making Bongole, Raghav Zamani, Amirreza Oechtering, Tobias J. Skoglund, Mikael Information Theory Artificial Intelligence Minimax risk and regret focus on expectation, missing rare failures critical in safety-critical bandits and reinforcement learning. Minimax quantiles capture these tails. Three strands of prior work motivate this study: minimax-quantile bounds restricted to non-interactive estimation; unified interactive analyses that focus on expected risk rather than risk level specific quantile bounds; and high-probability bandit bounds that still lack a quantile-specific toolkit for general interactive protocols. To close this gap, within the interactive statistical decision making framework, we develop high-probability Fano and Le Cam tools and derive risk level explicit minimax-quantile bounds, including a quantile-to-expectation conversion and a tight link between strict and lower minimax quantiles. Instantiating these results for the two-armed Gaussian bandit immediately recovers optimal-rate bounds. |
| title | Risk level dependent Minimax Quantile lower bounds for Interactive Statistical Decision Making |
| topic | Information Theory Artificial Intelligence |
| url | https://arxiv.org/abs/2510.05808 |