# Instruction-Level Design of Local Optimisers using Push GP

## TL;DR

This paper presents a genetic programming approach to automatically design local optimisers expressed in the Push language, capable of efficiently navigating various continuous landscapes to find optima.

## Contribution

It introduces a novel method for evolving local optimisation algorithms using Push GP, enabling flexible exploration of optimisation landscapes.

## Key findings

- Evolved optimisers effectively reach optima using short paths.
- Optimisers learn landscape features and utilize mathematical functions for exploration.
- The approach demonstrates adaptability across different landscape types.

## Abstract

This work uses genetic programming to explore the design space of local optimisation algorithms. Optimisers are expressed in the Push programming language, a stack-based language with a wide range of typed primitive instructions. The evolutionary framework provides the evolving optimisers with an outer loop and information about whether a solution has improved, but otherwise they are relatively unconstrained in how they explore optimisation landscapes. To test the utility of this approach, optimisers were evolved on four different types of continuous landscape, and the search behaviours of the evolved optimisers analysed. By making use of mathematical functions such as tangents and logarithms to explore different neighbourhoods, and also by learning features of the landscapes, it was observed that the evolved optimisers were often able to reach the optima using relatively short paths.