  Efficient numerical optimization methods can improve performance and reduce
the environmental impact of computing in many applications. This work presents
a proof-of-concept study combining primitive state representations and
agent-environment interactions as first-order optimizers in the setting of
budget-limited optimization. Through reinforcement learning (RL) over a set of
training instances of an optimization problem class, optimal policies for
sequential update selection of algorithmic iteration steps are approximated in
generally formulated low-dimensional partial state representations that
consider aspects of progress and resource use. For the investigated case
studies, deployment of the trained agents to unseen instances of the quadratic
optimization problem classes outperformed conventional optimal algorithms with
optimized hyperparameters. The results show that elementary RL methods combined
with succinct partial state representations can be used as heuristics to manage
complexity in RL-based optimization, paving the way for agentic optimization
approaches.
