On the Sample Complexity of Batch Reinforcement Learning with Policy-Induced Data.
Bibliographic record
Abstract
We study the fundamental question of the sample complexity of learning a good policy in finite Markov decision processes (MDPs) when the data available for learning is obtained by following a logging policy that must be chosen without knowledge of the underlying MDP. Our main results show that the sample complexity, the minimum number of transitions necessary and sufficient to obtain a good policy, is an exponential function of the relevant quantities when the planning horizon $H$ is finite. In particular, we prove that the sample complexity of obtaining $\epsilon$-optimal policies is at least $\Omega(\mathrm{A}^{\min(\mathrm{S}-1, H+1)})$ for $\gamma$-discounted problems, where $\mathrm{S}$ is the number of states, $\mathrm{A}$ is the number of actions, and $H$ is the effective horizon defined as $H=\lfloor \tfrac{\ln(1/\epsilon)}{\ln(1/\gamma)} \rfloor$; and it is at least $\Omega(\mathrm{A}^{\min(\mathrm{S}-1, H)}/\varepsilon^2)$ for finite horizon problems, where $H$ is the planning horizon of the problem. This lower bound is essentially matched by an upper bound. For the average-reward setting we show that there is no algorithm finding $\epsilon$-optimal policies with a finite amount of data.
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How this classification was reachedexpand
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 | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.005 | 0.007 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".