Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Learning selection strategies in Buchberger's algorithm   Studying the set of exact solutions of a system of polynomial equations
largely depends on a single iterative algorithm, known as Buchberger's
algorithm. Optimized versions of this algorithm are crucial for many computer
algebra systems (e.g., Mathematica, Maple, Sage). We introduce a new approach
to Buchberger's algorithm that uses reinforcement learning agents to perform
S-pair selection, a key step in the algorithm. We then study how the difficulty
of the problem depends on the choices of domain and distribution of
polynomials, about which little is known. Finally, we train a policy model
using proximal policy optimization (PPO) to learn S-pair selection strategies
for random systems of binomial equations. In certain domains, the trained model
outperforms state-of-the-art selection heuristics in total number of polynomial
additions performed, which provides a proof-of-concept that recent developments
in machine learning have the potential to improve performance of algorithms in
symbolic computation.

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The categories of this paper are: hep-ph
36
The categories of this paper are: cmp-lg
37
The categories of this paper are: supr-con
20
The categories of this paper are: acc-phys
33
The categories of this paper are: plasm-ph
31
The categories of this paper are: ao-sci
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
18
The categories of this paper are: econ
26
The categories of this paper are: bayes-an
25
The categories of this paper are: patt-sol
7
The categories of this paper are: hep-th
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex