Optimal Policy for Bernoulli Bandits: Computation and Algorithm Gauge
Bibliographic record
Abstract
Bernoulli multi-armed bandits are a reinforcement learning model used to study a variety of choice optimization problems. Often such optimizations concern a finite-time horizon. In principle, statistically optimal policies can be computed via dynamic programming, but doing so is considered infeasible due to prohibitive computational requirements and implementation complexity. Hence, suboptimal algorithms are applied in practice, despite their unknown level of suboptimality. In this article, we demonstrate that optimal policies can be efficiently computed for large time horizons or number of arms thanks to a novel memory organization and indexing scheme. We use optimal policies to gauge the suboptimality of several well-known finite- and infinite-time horizon algorithms including Whittle and Gittins indices, epsilon-greedy, Thompson sampling, and upper-confidence bound (UCB) algorithms. Our simulation study shows that all but one evaluated algorithm perform significantly worse than the optimal policy. The Whittle index offers a nearly optimal strategy for multi-armed Bernoulli bandits despite its suboptimal decisions—up to 10%—compared to an optimal policy table. Lastly, we discuss optimizations of known algorithms. We derive a novel solution from UCB1-tuned. It outperforms other infinite-time horizon algorithms when dealing with many arms.Impact statement—Bernoulli bandits are a reinforcement learning model used to improve decisions with binary outcomes. They have various applications ranging from headline news selection to clinical trials. Existing bandit algorithms are suboptimal. This article provides the first practical computation method, which determines the optimal decisions in Bernoulli bandits. It provides the lowest achievable decision regret (maximum expected benefit). In clinical trials, where an algorithm selects treatments for subsequent patients, our method can substantially reduce the number of unsuccessfully treated patients—by up to 5×. The optimal strategy is also used for new comprehensive evaluations of well-known suboptimal algorithms. This can significantly improve decision effectiveness in various applications.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.003 | 0.023 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.004 | 0.001 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".