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Robust Data-driven Prescriptiveness Optimization
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Introduces a distributionally robust version of the coefficient of prescriptiveness (DRPCR) for contextual optimization, solved via bisection over LPs under a nested CVaR ambiguity set, and shows better robustness to mean distribution shift on a contextual shortest path problem.
Problem
Contextual optimization policies trained from data can degrade under distribution shift; the coefficient of prescriptiveness, a unitless performance measure, has so far been used only as an evaluation metric rather than an optimization objective.
Approach
Replace the empirical risk objective of contextual stochastic optimization with a distributionally robust maximization of the coefficient of prescriptiveness (prescriptiveness competitive ratio against a reference static decision), reformulated as a convex problem and solved by bisection on gamma, with each step reduced to LPs under a nested CVaR ambiguity set.
Key results
- DRPCR keeps a positive mean out-of-sample coefficient of prescriptiveness at 60% mean perturbation (0.01 for relaxed policies) while CSO, DRCSO and DRCRO turn negative (around -0.31).
- At 60% perturbation, DRPCR reaches a positive median of 4% and up to 18% at best across instances, per the revised text.
- DRPCR training takes roughly 36 minutes per instance versus about 3 minutes for DRCSO and DRCRO.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of using CSO, DRCSO, or DRCRO | Shortest path, relaxed x · 50% mean perturbation | coefficient of prescriptiveness: -0.13 -> 0.05 | Helped |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of using CSO, DRCSO, or DRCRO | Shortest path, relaxed x · 60% mean perturbation | coefficient of prescriptiveness: -0.31 -> 0.01 | Helped |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of using CSO, DRCSO, or DRCRO | Shortest path, relaxed x · 0% mean perturbation | coefficient of prescriptiveness: 0.45 -> 0.45 | No clear effect |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of CSO | Shortest path, relaxed x · 20% mean perturbation | coefficient of prescriptiveness: 0.30 -> 0.31 | Helped |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of CSO | Shortest path, relaxed x · 30% mean perturbation | coefficient of prescriptiveness: 0.19 -> 0.23 | Helped |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of CSO | Shortest path, relaxed x · 40% mean perturbation | coefficient of prescriptiveness: 0.04 -> 0.13 | Helped |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of CSO | Shortest path, binary x · 20% mean perturbation | coefficient of prescriptiveness: 0.30 -> 0.32 | Helped |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of CSO | Shortest path, binary x · 30% mean perturbation | coefficient of prescriptiveness: 0.19 -> 0.24 | Helped |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of CSO | Shortest path, binary x · 40% mean perturbation | coefficient of prescriptiveness: 0.04 -> 0.15 | Helped |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of CSO | Shortest path, binary x · 50% mean perturbation | coefficient of prescriptiveness: -0.13 -> 0.07 | Helped |
| Optimize the distributionally robust prescriptiveness ratio (DRPCR) instead of CSO | Shortest path, binary x · 60% mean perturbation | coefficient of prescriptiveness: -0.31 -> 0.02 | Helped |
| Impose binary integrality on the policy rather than using relaxed x (ablation) | CSO shortest-path policy · 0% perturbation | coefficient of prescriptiveness: 0.45 -> 0.45 | No clear effect |
Surprising findings
- Forcing integrality on DRCSO and DRCRO slightly improved their out-of-sample performance, which the authors attribute to overfitting by relaxed models.
Limitations
- Training is roughly tenfold slower than DRCSO and DRCRO due to bisection.
- Restricted to nested ambiguity sets; general non-nested sets are not handled.
- Evaluation limited to a single shortest-path application with synthetic data.
Experimental setup
Datasets: synthetic contextual shortest path data (45 nodes, 97 arcs, 200 covariates)
Benchmarks: contextual shortest path with mean perturbation 0% to 60%
Metrics: coefficient of prescriptiveness runtime
Baselines: CSO DRCSO DRCRO
Builds on: coefficient of prescriptiveness distributionally robust contextual optimization nested CVaR risk measures
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