financial planners

Abstract: Fairness constraints in predict-then-optimize pipelines are necessarily enforced on predicted outcomes $\hat{y}$, since true outcomes $y$ are unobserved at decision time. We study whether a demographic parity constraint enforced this way continues to hold against $y$, and how the resulting violation scales with prediction error. Using a budget-constrained allocation problem solved as a linear program, we show empirically that the true-outcome fairness gap grows with prediction error $σ$ and saturates, well fit by $c(1 - e^{-σ/τ})$ with $c = 0.1545 \pm 0.0103$ and $τ= 3.9045 \pm 0.3745$; its mean is invariant to sample size while its variance decays at the standard $O(1/\sqrt{n})$ rate. We derive a two-part theoretical bound: a closed-form local sensitivity result showing the gap's first-order response to prediction error depends on only two individuals per group, validated against the solver to within three significant figures; and a universal, error-independent ceiling following from the boundedness of the decision variable, confirmed consistent with but looser than the empirical saturation level. On US Census income data, enforcing demographic parity on a trained predictor's output reduces an unconstrained disparity in true income to roughly one-third of its original size, leaving 34.4% $\pm$ 3.3% (California) and 35.7% $\pm$ 1.8% (Texas) of the disparity intact and undetectable from the predictions alone -- consistent not only in mechanism but in approximate magnitude across two states with different demographics and income distributions, and stable across ten independent train/test splits in each. A fairness constraint that appears fully satisfied at decision time can mask a substantial, systematic violation of the outcome it was meant to protect.

Abstract: Natural-language descriptions of optimization problems may be incomplete or vague about numerical information that a solver requires, including costs, capacities, demands, bounds, and penalties. A language model can translate the description into code, but when a required value is absent it must either stop or guess. We present SAILOR, a proof-of-concept system that detects such unsupported numerical choices, asks the user targeted follow-up questions, and updates the optimization model before returning a solution. Questions are prioritized using uncertainty and solver-derived estimates of how strongly each missing value affects the current model. We evaluate the pipeline on 1,723 instances from seven masked benchmarks using an idealized simulator that returns ground-truth values. Exact objective-value agreement ranges from 27.0% to 87.6% across datasets, with 1.4--5.7 questions per instance on average. These results establish feasibility under controlled branch-and-reveal feedback; they do not measure performance with human users or general structural model repair. Code is available at: https://github.com/sshaghayeghs/SAILOR.