A PDE approach for regret bounds under partial monitoring
Authors: Erhan Bayraktar, Ibrahim Ekren, Xin Zhang
JMLR 2023 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Theoretical | In this paper, we study a learning problem in which a forecaster only observes partial information. By properly rescaling the problem, we heuristically derive a limiting PDE on Wasserstein space which characterizes the asymptotic behavior of the regret of the forecaster. Using a verification type argument, we show that the problem of obtaining regret bounds and efficient algorithms can be tackled by finding appropriate smooth sub/supersolutions of this parabolic PDE. |
| Researcher Affiliation | Academia | Erhan Bayraktar EMAIL Department of Mathematics University of Michigan Ann Arbor, MI 48109-1043, USA; Ibrahim Ekren EMAIL Department of Mathematics University of Michigan Ann Arbor, MI 48109-1043, USA; Xin Zhang EMAIL Department of Mathematics University of Vienna Vienna, 1090 , Austria |
| Pseudocode | No | The paper describes algorithms conceptually, such as the multiplicative weights algorithm, and strategies like β n(m) := DmΦ (tn, m, [ em]) (16), but these are embedded within the text or as mathematical expressions rather than structured pseudocode blocks or clearly labeled algorithm sections. |
| Open Source Code | No | The paper does not contain any explicit statements about releasing code, nor does it provide links to any code repositories or mention code in supplementary materials. |
| Open Datasets | No | This paper is theoretical and focuses on mathematical derivations for a learning problem. It does not use any empirical datasets for experiments or evaluation, and therefore does not provide any access information for datasets. |
| Dataset Splits | No | This paper is theoretical and does not involve empirical experiments with datasets. Consequently, there is no mention of dataset splits for training, validation, or testing. |
| Hardware Specification | No | The paper is theoretical and describes mathematical models and derivations; it does not involve any computational experiments that would require specific hardware. Therefore, no hardware specifications are mentioned. |
| Software Dependencies | No | This paper is theoretical and focuses on mathematical derivations and analysis. It does not describe any computational implementation or experiments that would require specific software or library versions. |
| Experiment Setup | No | The paper is theoretical and does not present any experimental results or empirical studies. Therefore, there are no details regarding experimental setup, hyperparameters, or training configurations. |