  Column generation (CG) is a well-established method for solving large-scale
linear programs. It involves iteratively optimizing a subproblem containing a
subset of columns and using its dual solution to generate new columns with
negative reduced costs. This process continues until the dual values converge
to the optimal dual solution to the original problem. A natural phenomenon in
CG is the heavy oscillation of the dual values during iterations, which can
lead to a substantial slowdown in the convergence rate. Stabilization
techniques are devised to accelerate the convergence of dual values by using
information beyond the state of the current subproblem. However, there remains
a significant gap in obtaining more accurate dual values at an earlier stage.
To further narrow this gap, this paper introduces a novel approach consisting
of 1) a machine learning approach for accurate prediction of optimal dual
solutions and 2) an adaptive stabilization technique that effectively
capitalizes on accurate predictions. On the graph coloring problem, we show
that our method achieves a significantly improved convergence rate compared to
traditional methods.
