Achieving Logarithmic Regret via Hints in Online Learning of Noisy LQR Systems
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.1
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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 | 0.006 | 0.033 |
| Meta-epidemiology (narrow) | 0.002 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.001 | 0.003 |
| Scholarly communication | 0.002 | 0.003 |
| Open science | 0.002 | 0.002 |
| Research integrity | 0.002 | 0.003 |
| 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".