# Optimal Transport for Correctional Learning

arXiv: https://arxiv.org/abs/2304.01701 · HTML: https://mlsanity.com/paper/2304.01701/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 31 references that are in the map.
- First posted on arXiv 4 Apr 2023.

## Builds on (most cited first, 12 of 12)

- [Computational Optimal Transport](https://mlsanity.com/paper/1803.00567/) (2018)
- [Learning with a Wasserstein Loss](https://mlsanity.com/paper/1506.05439/) (2015)
- [Fast Optimal Transport Averaging of Neuroimaging Data](https://mlsanity.com/paper/1503.08596/) (2015)
- [Reinforcement learning with human advice: a survey](https://mlsanity.com/paper/2005.11016/) (2020)
- [Optimal Transport for Parameter Identification of Chaotic Dynamics via Invariant Measures](https://mlsanity.com/paper/2104.15138/) (2021)
- [Online Domain Adaptation for Occupancy Mapping](https://mlsanity.com/paper/2007.00164/) (2020)
- [An Optimal Transport Formulation of the Ensemble Kalman Filter](https://mlsanity.com/paper/1910.02338/) (2019)
- [Cooperative System Identification via Correctional Learning](https://mlsanity.com/paper/2012.05161/) (2020)
- [A Statistical Decision-Theoretical Perspective on the Two-Stage Approach to Parameter Estimation](https://mlsanity.com/paper/2204.00036/) (2022)
- [Renaissance Robot: Optimal Transport Policy Fusion for Learning Diverse Skills](https://mlsanity.com/paper/2207.00978/) (2022)
- [State tracking of linear ensembles via optimal mass transport](https://mlsanity.com/paper/1803.02296/) (2018)
- [A Teacher-Student Markov Decision Process-based Framework for Online Correctional Learning](https://mlsanity.com/paper/2111.07818/) (2021)

## Abstract (arXiv)

The contribution of this paper is a generalized formulation of correctional learning using optimal transport, which is about how to optimally transport one mass distribution to another. Correctional learning is a framework developed to enhance the accuracy of parameter estimation processes by means of a teacher-student approach. In this framework, an expert agent, referred to as the teacher, modifies the data used by a learning agent, known as the student, to improve its estimation process. The objective of the teacher is to alter the data such that the student's estimation error is minimized, subject to a fixed intervention budget. Compared to existing formulations of correctional learning, our novel optimal transport approach provides several benefits. It allows for the estimation of more complex characteristics as well as the consideration of multiple intervention policies for the teacher. We evaluate our approach on two theoretical examples, and on a human-robot interaction application in which the teacher's role is to improve the robots performance in an inverse reinforcement learning setting.