Bayesian optimal control of smoothly parameterized systems
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Bibliographic record
Abstract
We study Bayesian optimal control of a general class of smoothly parameterized Markov deci-sion problems (MDPs). We propose a lazy ver-sion of the so-called posterior sampling method, a method that goes back to Thompson and Strens, more recently studied by Osband, Russo and van Roy. While Osband et al. derived a bound on the (Bayesian) regret of this method for undis-counted total cost episodic, finite state and ac-tion problems, we consider the continuing, av-erage cost setting with no cardinality restric-tions on the state or action spaces. While in the episodic setting, it is natural to switch to a new policy at the episode-ends, in the continu-ing average cost framework we must introduce switching points explicitly and in a principled fashion, or the regret could grow linearly. Our lazy method introduces these switching points based on monitoring the uncertainty left about the unknown parameter. To develop a suitable and easy-to-compute uncertainty measure, we in-troduce a new “average local smoothness ” con-dition, which is shown to be satisfied in com-mon examples. Under this, and some additional mild conditions, we derive rate-optimal bounds on the regret of our algorithm. Our general ap-proach allows us to use a single algorithm and a single analysis for a wide range of problems, such as finite MDPs or linear quadratic regula-tion, both being instances of smoothly parame-terized MDPs. The effectiveness of our method is illustrated by means of a simulated example. 1
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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 | 0.004 | 0.005 |
| 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 | 0.001 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| 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