Achieving Logarithmic Regret via Hints in Online Learning of Noisy LQR Systems
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Bibliographic record
Abstract
We consider the problem of online adaptive control of a linear-quadratic system, where the true system transition parameters (matrices A and B) are unknown. The objective is to design and analyze algorithms that generate control policies with sublinear "regret", defined as the difference between the cumulative cost of the policies generated by the algorithm and the cumulative cost of the optimal policy. Recent studies show that when the system parameters are fully unknown, for any algorithm that only uses data from the past system trajectory, there is a choice of system parameters such that the algorithm at best achieves a square root regret, providing a hard fundamental limit on the achievable regret in general. However, it is known that (poly)-logarithmic regret is achievable when only matrix A or only matrix B is unknown. We prove a result, encompassing both of these scenarios, showing that (poly)logarithmic regret is achievable when both of these matrices are unknown, but a hint about them is given to the learner over time. <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">1</sup>
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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 | 0.005 | 0.004 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 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 it