# A Teacher-Student Markov Decision Process-based Framework for Online Correctional Learning

arXiv: https://arxiv.org/abs/2111.07818 · HTML: https://mlsanity.com/paper/2111.07818/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Placed in On-policy and self-distillation for LLMs, one of 12 directions in Knowledge distillation.
- Builds on 5 of its 28 references that are in the map.
- First posted on arXiv 15 Nov 2021.

## Placed in

- Knowledge distillation / [On-policy and self-distillation for LLMs](https://mlsanity.com/distill/on-policy-and-self-distillation-for-llms/)

## Builds on (most cited first, 5 of 5)

- [Differentiable Convex Optimization Layers](https://mlsanity.com/paper/1910.12430/) (2019)
- [End-to-end Training for Whole Image Breast Cancer Diagnosis using An All Convolutional Design](https://mlsanity.com/paper/1711.05775/) (2017)
- [Partially Observed Markov Decision Processes. Problem Sets and Internet Supplement](https://mlsanity.com/paper/1604.08127/) (2016)
- [A Review on Neural Network Models of Schizophrenia and Autism Spectrum Disorder](https://mlsanity.com/paper/1906.10015/) (2019)
- [Cooperative System Identification via Correctional Learning](https://mlsanity.com/paper/2012.05161/) (2020)

## Built on by (most cited first, 1 of 1)

- [Optimal Transport for Correctional Learning](https://mlsanity.com/paper/2304.01701/) (2023)

## Abstract (arXiv)

A classical learning setting typically concerns an agent/student who collects data, or observations, from a system in order to estimate a certain property of interest. Correctional learning is a type of cooperative teacher-student framework where a teacher, who has partial knowledge about the system, has the ability to observe and alter (correct) the observations received by the student in order to improve the accuracy of its estimate. In this paper, we show how the variance of the estimate of the student can be reduced with the help of the teacher. We formulate the corresponding online problem - where the teacher has to decide, at each time instant, whether or not to change the observations due to a limited budget - as a Markov decision process, from which the optimal policy is derived using dynamic programming. We validate the framework in numerical experiments, and compare the optimal online policy with the one from the batch setting.