Bayesian optimal control of smoothly parameterized systems
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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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 | 0.002 | 0.009 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.001 | 0.002 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.003 | 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".