EpiPivot: Learning to Control the Simplex Method under Epistemic Uncertainty

The simplex method is one of the most widely used algorithms for linear programming, but its practical efficiency is highly sensitive to pivot selection and difficult to predict due to structural uncertainty in the search process. We propose EpiPivot, which casts pivot selection as a controllable decision process under epistemic uncertainty. EpiPivot identifies this uncertainty as two-dimensional: temporal dependence across the optimization trajectory and joint uncertainty across candidate pivot rules, and addresses both through temporal attention and an Epistemic Neural Network with shared latent sampling. At decision time, Thompson sampling combines these uncertainty-aware predictions into robust pivot choices. EpiPivot achieves significant improvements over classical and learning-based baselines, reducing pivot cost by up to 79\% over the best-performing classical rule on large-scale instances where most classical rules fail to converge within the time limit.