Delayed Reward Bernoulli Bandits: Optimal Policy and Predictive Meta-Algorithm PARDI
Bibliographic record
Abstract
Bernoulli multi-armed bandits are a reinforcement learning model used to optimize the sequences of decisions with binary outcomes. Well-known bandit algorithms, including the optimal policy, assume that before a decision is made the outcomes of previous decisions are known. This assumption is often not satisfied in real-life scenarios. As demonstrated in this article, if decision outcomes are affected by delays, the performance of existing algorithms can be severely affected. We present the first practically applicable method to compute statistically optimal decisions in the presence of outcome delays. Our method has a predictive component abstracted out into a meta-algorithm, predictive algorithm reducing delay impact (PARDI), which significantly reduces the impact of delays on commonly used algorithms. We demonstrate empirically that PARDI-enhanced Whittle index is nearly optimal for a wide range of Bernoulli bandit parameters and delays. In a wide spectrum of experiments, it performed better than any other suboptimal algorithm, e.g., UCB1-tuned and Thompson sampling. PARDI-enhanced Whittle index can be used when computational requirements of the optimal policy are too high.
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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 | 0.010 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 0.000 |
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".