  In this article, we introduce the concept of discounted pseudocosts, inspired
by discounted total reward in reinforcement learning, and explore their
application in mixed-integer linear programming (MILP). Traditional pseudocosts
estimate changes in the objective function due to variable bound changes during
the branch-and-bound process. By integrating reinforcement learning concepts,
we propose a novel approach incorporating a forward-looking perspective into
pseudocost estimation. We present the motivation behind discounted pseudocosts
and discuss how they represent the anticipated reward for branching after one
level of exploration in the MILP problem space. Initial experiments on MIPLIB
2017 benchmark instances demonstrate the potential of discounted pseudocosts to
enhance branching strategies and accelerate the solution process for
challenging MILP problems.
