DePICT: Decision-Preserving Interface for Constrained Downstream Tasks

Utkarsh Grover; Ravi Ranjan; Agoritsa Polyzou; Wyatt Mackey; J. Morris Chang; Leonardo Bobadilla; Xiaomin Lin

cs.LGOct 2, 2026

DePICT: Decision-Preserving Interface for Constrained Downstream Tasks

Authors: Utkarsh Grover, Ravi Ranjan, Agoritsa Polyzou, Wyatt Mackey, J. Morris Chang, Leonardo Bobadilla, Xiaomin Lin

Organizations: University of South Florida · Florida International University · DEVCOM Army Research Lab

Abstract

A constrained optimization problem may involve a parameter in its objective and active constraints, yet the final decision may remain insensitive to small changes in that parameter. This raises a fundamental question: which inputs does a decision making system truly depend on? Building on this question, we introduce DePICT, a procedure for constructing decision preserving interfaces by ranking context directions according to the optimizer's solution sensitivity and aggregating them across an operating regime. We study this problem in a high dimensional setting where primitive context parameterizes a constrained task and the downstream agent observes only a selected subset of context directions. For locally regular constrained programs, we derive a Karush Kuhn Tucker (KKT) based characterization of when a context direction is optimizer relevant. Our analysis shows that appearing in the active optimization problem does not necessarily imply that a variable affects the final decision. Some context directions can alter the KKT conditions while leaving the optimal solution unchanged because their effect is absorbed by the dual variables. DePICT is designed to remove exactly these directions. In a controlled diagnosis, it recovers the decision relevant interface exactly and reduces linear predictor regret to 0.009, compared with 0.475 for the strongest competing baseline.

Figures & tables

Figure 1: Controlled results. Knapsack (top row) and shortest path (bottom row) under matched MLP and linear predictors. All the values are mean over 10 seeds.

Figure 2: Edge-regime solver-mediated tasks. Warcraft shortest path (top row) and FF25 portfolio allocation (bottom row) under matched linear and MLP predictors. All the values are mean over 10 seeds.

Figure 3: Layer-2 annihilation diagnostic. Controlled knapsack (top) and FF25 portfolio (bottom) compare recovery of irreducible directions and Layer-2 nuisance variables. Mean over 10 seeds.

Figure 4: Perturbation stability on controlled knapsack. Decision match, Jaccard overlap, and regret are reported across interface budgets

m\in\{20,40,60\}

as the perturbation magnitude

\epsilon

increases.

Figure 5: Interface-selection runtime as context dimension increases. Time comparison across different methods with increasing context dimension for Controlled Knapsack dataset.

Figure 6: DePICT constructs the information interface from the downstream decision.

\theta^{*}(c_{t})\in\arg\min_{\theta}f(\theta;c_{t})\quad\mathrm{s.t.}\quad m_{i}(\theta;c_{t})\geq 0.

Algorithm 2 Detailed DePICT Interface Construction

	Knapsack						Shortest Path
Method	$m$	Regret $\downarrow$	Obj. $\uparrow$	Feas. $\downarrow$	Prec. $\uparrow$	F1 $\uparrow$	$m$	Regret $\downarrow$	Obj. $\uparrow$	Feas. $\downarrow$	Path $\uparrow$	F1 $\uparrow$
Nonlinear predictor (MLP)
Random	60	3.1588	8.5163	2.70e-04	0.2833	0.2720	160	2.9469	-8.1239	7.35e-06	0.7593	0.3920
Mutual Information Peng et al. (2005)	60	0.2394	11.4357	1.40e-04	0.9833	0.9440	160	0.8043	-5.9812	8.19e-06	0.8452	0.8125
LASSO Tibshirani (1996)	60	0.3115	11.3636	3.51e-04	0.8667	0.8320	160	1.2531	-6.4300	6.15e-06	0.8156	0.5966
FD Ranking Lin et al. (2023)	60	2.0047	9.6704	6.07e-04	0.6500	0.6240	160	2.7098	-7.8867	8.46e-06	0.7657	0.4602

Table 1: Full controlled KKT-regime results corresponding to Figure 1 . DePICT recovers the oracle interface exactly while preserving downstream decision quality under matched linear and MLP predictors. Lower regret and feasibility violation are better; higher objective value, path match, precision, and support F1 are better. Values are averaged over 10 independent seeds.

Figure 7: Seed variability across representative regret comparisons. Bars report mean regret and error bars report

\pm 1

standard deviation over 10 independent seeds. Panels cover controlled knapsack, controlled shortest path, Warcraft shortest path, and FF25 portfolio allocation under representative linear-predictor settings. Lower is better.

	Warcraft Shortest Path				FF25 Portfolio
Method	Regret $\downarrow$	Obj. $\uparrow$	Feas. $\downarrow$	Path $\uparrow$	$m$	Regret $\downarrow$	Obj. $\uparrow$	Sharpe $\uparrow$	Turnover $\downarrow$
Nonlinear predictor (MLP)
Random	12.7335	-50.6898	3.15e-05	0.8278	40	0.0040	-0.0040	0.4539	0.1042
Mutual Information	12.0701	-49.0297	2.44e-05	0.8348	40	0.0041	-0.0029	0.4743	0.1030
LASSO	12.7771	-50.7333	3.41e-05	0.8272	40	0.0033	-0.0018	0.4537	0.1001
FD Ranking	12.3340	-50.1533	3.09e-05	0.8298	40	0.0033	-0.0037	0.4515	0.0899

Table 2: Solver-mediated decision-task evaluation on Warcraft shortest path and FF25 portfolio optimization. Warcraft reports shortest-path regret, objective value, feasibility violation, and path-match rate. FF25 reports common-reference portfolio regret, common-reference objective, realized Sharpe, and turnover at matched budget

m=40

from the provided runs. Lower regret, feasibility violation, and turnover are better; higher objective, path match, and Sharpe are better.

Linear
	10 Tasks		15 Tasks		20 Tasks
Method	Cost $\downarrow$	Regret $\downarrow$	Cost $\downarrow$	Regret $\downarrow$	Cost $\downarrow$	Regret $\downarrow$
Correlation Screening	187.794	34.294	324.866	42.349	395.948	46.654
Elastic Net	188.453	34.954	324.417	41.900	407.354	58.060
FD Ranking	188.453	34.954	324.417	41.900	407.354	58.060
Full	203.783	50.284	359.248	76.731	452.739	103.445

Table 3: Energy-cost-aware scheduling edge-regime evaluation. We report all comparison methods at budget

m=5

across task sizes and predictor families. Lower cost and regret are better. All methods have zero feasibility violation and zero solver failure rate. The benchmark is solver-mediated and discrete, so it is used as an edge-regime stress test rather than a direct validation of the fixed-active-set KKT theory.

Method	$m$	Irr. Recall $\uparrow$	L2 FPR $\downarrow$	L1 FPR $\downarrow$	F1 $\uparrow$	Regret $\downarrow$
Full	200	1.000	1.000	1.000	0.182	1.788
Random	20	0.100	0.100	0.100	0.100	1.954
Mutual Information Peng et al. (2005)	20	0.300	0.700	0.000	0.300	0.478
LASSO Tibshirani (1996)	20	0.100	0.000	0.113	0.100	2.667
FD Ranking Lin et al. (2023)	20	0.400	0.500	0.013	0.400	0.565
PFMM Sharma et al. (2024)	20	0.400	0.500	0.013	0.400	0.475

Table 4: Full Layer-2 diagnostic on controlled knapsack and FF25 under the linear predictor. For knapsack, higher irreducible recall and support F1 are better, while lower Layer-2/Layer-1 false-positive rate and regret are better. For FF25, lower Layer-2/Layer-1 false-positive rate, regret, and turnover are better, while higher Sharpe is better.

Figure 8: Seed variability for the controlled diagnostic. Bars report means and error bars report

\pm 1

standard deviation over 10 independent seeds. DePICT maintains near-zero Layer-2 diagnostic regret, exact or near-exact knapsack support recovery, and the lowest knapsack regret under the linear predictor. Lower regret is better; higher support F1 is better.

Figure 9: Jacobian-ranking stability under context perturbations on controlled knapsack. Exact top- $m$ identity decreases with $\epsilon$ , but Jaccard overlap remains high and regret inflation stays near zero, supporting the spectral-gap view that high-overlap interfaces can remain decision-stable even when exact rankings change.

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Abstract

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