A Differentially Private Approach for Budgeted Combinatorial Multi-Armed Bandits
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Bibliographic record
Abstract
As a fundamental tool for sequential decision-making, the Combinatorial Multi-Armed Bandits model (CMAB) has been extensively analyzed and applied in various online applications. However, the privacy concerns in budgeted CMAB are rarely investigated thus far. Few bandit algorithms have adequately addressed the privacy-preserving budgeted CMAB setting. Motivated by this, we study this setting using differential privacy as the formal measure of privacy. In this setting, playing an arm yields both a random reward and a random cost, and these values are kept private. In addition, multiple arms can be played in each round. The objective of the decision-maker is to minimize regret while subject to a budget constraint on the cumulative cost of all played arms. We demonstrate an exploration-exploitation-balanced bandit policy, which preserves the privacy of both rewards and costs under budgeted CMAB settings. This policy is proven differentially private and achieves an upper bound on regret. Furthermore, to provide incentives for the differentially private bandit policy so as to ensure that the reported costs are truthful, we introduce the concept of truthfulness and incorporate a payment mechanism that has been proven to be <inline-formula><tex-math notation="LaTeX">$\sigma$</tex-math></inline-formula>-truthful. Numerical simulations based on multiple real-world datasets validate the theoretical findings and demonstrate the effectiveness of our policy compared to state-of-the-art policies.
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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.001 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it