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A Submodular Optimization Approach to Accountable Loan Approval
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Describes a deployed automated system at Hyundai Capital Services that builds interpretable loan approval rule lists by greedy submodular (SCSK) optimization over XGBoost-derived atomic rules.
Problem
Loan approval rules must be interpretable and accountable, yet manual construction by risk analysts is slow and limited, while accurate black-box credit scoring models cannot be used directly for underwriting.
Approach
Generate a candidate search space of high-precision, monotone atomic rules from XGBoost tree leaves, then select an ordered rule list by greedy submodular cost submodular knapsack optimization trading off bad rate against loan volume, with an interactive cut-off simulation toolkit.
Key results
- SUBMOD precision 3.5% vs 2.7% for the human-expert BASE rule at 10% ineligible rate, comparable to XGB (3.5%) while remaining interpretable.
- Live override test in Aug-Oct 2021 grew loan volume by 14% while actual bad rate matched predicted (3.70% overall vs 3.71% predicted).
- Search space reduced from roughly 680 million possible atomic rules to about 50,000 candidate rules.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Replace the human-crafted BASE rule with the SUBMOD approval rule at similar ineligible rates | Loan approval rules · Personal loan services data, out-of-time test | precision (%): 2.7% to 3.5% | Helped |
| Replace BASE with SUBMOD | Loan approval rules · Personal loan services data, out-of-time test | recall (%): 52.2 -> 66.2 | Helped |
| Replace BASE with SUBMOD | Loan approval rules · Personal loan services data, out-of-time test | accuracy (%): 89.9 -> 90.2 | Helped |
| Replace BASE with SUBMOD | Loan approval rules · Personal loan services data, out-of-time test | F1-score (%): 5.2 -> 6.6 | Helped |
| Use SUBMOD rather than XGBoost | Loan approval rules · Personal loan services data, out-of-time test | accuracy (%): 90.4 -> 90.2 | Hurt |
| Use SUBMOD rather than DNN | Loan approval rules · Personal loan services data, out-of-time test | precision (%): 3.6 -> 3.5 | Hurt |
| Deploy SUBMOD as an override for customers rejected by BASE | Loan approval system · Live test, Aug-Oct 2021 | volume growth (%): 14% | Helped |
| Apply the optimized rule to customers with credit scores below 700 | Loan approval system · Customers with credit scores below 700 | delinquency rate (percentage points): 2-percentage point | Hurt |
Surprising findings
- Greedy submodular selection naturally placed rules with higher bad rates at the head of the list, matching the manual ordering convention.
- Optimized rules caused a 2-percentage-point rise in delinquency among customers with credit scores below 700, complicating stakeholder support.
Limitations
- Evaluation relies on proprietary data from a single company and only one case study (credit loan service).
- Greedy algorithm has only loose worst-case approximation guarantees.
- Results compared mainly against a single human-expert baseline and do not report formal statistical significance.
Experimental setup
Datasets: Hyundai Capital Services personal loan customer data (proprietary)
Benchmarks: Hyundai Capital Services out-of-time personal loan test data
Metrics: precision recall accuracy F1-score bad rate volume growth
Baselines: BASE (human-expert rule) logistic regression XGBoost deep neural network
Builds on: SCSK/SCSC submodular cost formulations (Iyer and Bilmes) XGBoost falling rule lists
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