Tropical Bi-Objective Pseudolinear Optimization as Parametric Mean-Payoff Games

What the math gives to ML

The paper develops an explicit parametric method for two-objective optimization with max-affine objectives and two-sided max-plus constraints. Its transferable asset is the conversion of feasibility into linear inequalities induced by graph cycles, followed by a Newton continuation method that traces an entire piecewise-linear Pareto frontier rather than repeatedly solving scalarized problems. This is most promising for small neural control vectors such as adapter gains, activation clipping parameters, or routing thresholds around a frozen ReLU network, where local behavior is max-affine. The main experiment should test whether frontier tracing reaches the same robustness-versus-accuracy envelope with substantially fewer network evaluations than scalarization grids or bisection.