Multi-Treatment-DML: Causal Estimation for Multi-Dimensional Continuous Treatments with Monotonicity Constraints in Personal Loan Risk Optimization

Abstract: Optimizing credit limits, interest rates, and loan terms is crucial for managing borrower risk and lifetime value (LTV) in personal loan platform. However, counterfactual estimation of these continuous, multi-dimensional treatments faces significant challenges: randomized trials are often prohibited by risk controls and long repayment cycles, forcing reliance on biased observational data. Existing causal methods primarily handle binary/discrete treatments and struggle with continuous, multi-dimensional settings. Furthermore, financial domain knowledge mandates provably monotonic treatment-outcome relationships (e.g., risk increases with credit limit).To address these gaps, we propose Multi-Treatment-DML, a novel framework leveraging Double Machine Learning (DML) to: (i) debias observational data for causal effect estimation; (ii) handle arbitrary-dimensional continuous treatments; and (iii) enforce monotonic constraints between treatments and outcomes, guaranteeing adherence to domain requirements.Extensive experiments on public benchmarks and real-world industrial datasets demonstrate the effectiveness of our approach. Furthermore, online A/B testing conducted on a realworld personal loan platform, confirms the practical superiority of Multi-Treatment-DML in real-world loan operations.