Information-directed sampling for bandits: a primer
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866915692365742080 |
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| author | Hirling, Annika Nicoletti, Giorgio Celani, Antonio |
| author_facet | Hirling, Annika Nicoletti, Giorgio Celani, Antonio |
| contents | The Multi-Armed Bandit problem provides a fundamental framework for analyzing the tension between exploration and exploitation in sequential learning. This paper explores Information Directed Sampling (IDS) policies, a class of heuristics that balance immediate regret against information gain. We focus on the tractable environment of two-state Bernoulli bandits as a minimal model to rigorously compare heuristic strategies against the optimal policy. We extend the IDS framework to the discounted infinite-horizon setting by introducing a modified information measure and a tuning parameter to modulate the decision-making behavior. We examine two specific problem classes: symmetric bandits and the scenario involving one fair coin. In the symmetric case we show that IDS achieves bounded cumulative regret, whereas in the one-fair-coin scenario the IDS policy yields a regret that scales logarithmically with the horizon, in agreement with classical asymptotic lower bounds. This work serves as a pedagogical synthesis, aiming to bridge concepts from reinforcement learning and information theory for an audience of statistical physicists. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20096 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Information-directed sampling for bandits: a primer Hirling, Annika Nicoletti, Giorgio Celani, Antonio Machine Learning Information Theory The Multi-Armed Bandit problem provides a fundamental framework for analyzing the tension between exploration and exploitation in sequential learning. This paper explores Information Directed Sampling (IDS) policies, a class of heuristics that balance immediate regret against information gain. We focus on the tractable environment of two-state Bernoulli bandits as a minimal model to rigorously compare heuristic strategies against the optimal policy. We extend the IDS framework to the discounted infinite-horizon setting by introducing a modified information measure and a tuning parameter to modulate the decision-making behavior. We examine two specific problem classes: symmetric bandits and the scenario involving one fair coin. In the symmetric case we show that IDS achieves bounded cumulative regret, whereas in the one-fair-coin scenario the IDS policy yields a regret that scales logarithmically with the horizon, in agreement with classical asymptotic lower bounds. This work serves as a pedagogical synthesis, aiming to bridge concepts from reinforcement learning and information theory for an audience of statistical physicists. |
| title | Information-directed sampling for bandits: a primer |
| topic | Machine Learning Information Theory |
| url | https://arxiv.org/abs/2512.20096 |