On Learning Whittle Index Policy for Restless Bandits With Scalable Regret
Bibliographic record
Abstract
Reinforcement learning is an attractive approach to learn good resource allocation and scheduling policies based on data when the system model is unknown. However, the cumulative regret of most RL algorithms scales as ˜ O(S$\rm{\sqrt{AB}}$), where S is the size of the state space, A is the size of the action space, T is the horizon, and the ˜ O(·) notation hides logarithmic terms. Due to the linear dependence on the size of the state space, these regret bounds are prohibitively large for resource allocation and scheduling problems. In this paper, we present a model based RL algorithm for such problems which has scalable regret. In particular, we consider a restless bandit model, and propose a Thompson-sampling based learning algorithm which is tuned to the underlying structure of the model. We present two characterizations of the regret of the proposed algorithm with respect to the Whittle index policy. First, we show that for a restless bandit with n arms and at most m activations at each time, the regret scales either as ˜ O($\rm{mn\sqrt{T}}$) or ˜ O($\rm{n^2\sqrt{T}}$) depending on the reward model. Second, under an additional technical assumption, we show that the regret scales as ˜ O($\rm{n^{1.5}\sqrt{T}}$) or ˜ O(max{$\rm{m\sqrt{T}}$,n}$\rm{\sqrt{T}}$). We present numerical examples to illustrate the salient features of the algorithm.
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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 | 0.005 | 0.021 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.003 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.004 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.003 | 0.004 |
| 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".