# Well-posedness for degenerate elliptic PDE arising in optimal learning strategies

## TL;DR

This paper establishes a comparison principle for a specific degenerate elliptic PDE that appears in optimal learning strategies, using a novel approach that leverages the operator's degeneracy.

## Contribution

It introduces a direct method to prove comparison principles for degenerate elliptic PDEs without boundary conditions, relevant to optimal learning.

## Key findings

- Comparison principle proven for the PDE
- Method exploits degeneracy to construct diverging barriers
- Applicable to PDEs in optimal learning contexts

## Abstract

We derive a comparison principle for a degenerate elliptic partial differential equation without boundary conditions which arises naturally in optimal learning strategies. Our argument is direct and exploits the degeneracy of the differential operator to construct (logarithmically) diverging barriers.