Who Am i?

We typically think of an algorithm as a set of instructions that are carefully created so that we get a desired output for a given input. However, many algorithms contain decision points where a choice must be made from a set of possible instructions, and it isn’t always clear which instruction is the best.

An important example of an algorithm with decision points is Buchberger’s algorithm which is used to solve a range of problems in computational algebra. In Buchberger’s algorithm, one of the key decision points is pair selection.

The decisions made during pair selection don’t affect the correctness of the output of Buchberger’s algorithm but do affect the amount of computation that it takes to arrive at the output.

Devising a way to perform pair selection optimally is therefore an open area of research. In most commercial or open-source implementations of the algorithm, heuristic solutions are used that select pairs based on simple rules that can be applied generally.

Reinforcement learning is particularly suited to decision making in Buchberger’s algorithm because of the extremely large number of possible states and actions which means that using exact solution methods such as dynamic programming are typically infeasible.

My project involves building on previous work demonstrating that reinforcement learning can be effective for decision making in Buchberger’s algorithm.

My aims are to extend the work from the proof of concept to more challenging inputs and by doing this identify and research solutions for the issues that arise when extending the current methodology.