Robustness to Incorrect Priors in Infinite Horizon Stochastic Control
Bibliographic record
Abstract
The paper focuses on the continuity properties of stochastic control problems with respect to initial probability measures. The continuity results are used to study the robustness of optimal control policies applied to systems with incorrect prior models. It is shown that for multi-stage optimal cost problems, weak convergence or setwise convergence is not sufficient for continuity and robustness in general, but that the optimal cost is continuous in the priors under the convergence in total variation under mild conditions. We also propose some sufficient conditions for the continuity of the optimal cost under weak convergence of priors. Using these continuity results we find bounds on the mismatch error that occurs due to the application of a control policy which is designed for an incorrectly estimated prior model in terms of a distance measure between true model and the incorrect one. Implications of these results in empirical learning for control will be presented, where almost surely weak convergence of i.i.d. empirical measures occurs but stronger notions of convergence, such as total variation convergence, in general, do not. These lead to practically important results on empirical learning in stochastic control since often, in engineering applications, system models are learned through training 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 | 0.002 | 0.002 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.001 |
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".