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Distributionally Robust Performative Prediction
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Introduces distributionally robust performative prediction, a KL-divergence uncertainty set over distribution maps that yields a distributionally robust performative optimum (DRPO), reformulated via duality into tilted performative risk minimization.
Problem
Performative optimum (PO) minimization relies on a nominal distribution map that is inevitably misspecified, so the resulting model can perform poorly under the true performative risk.
Approach
Define the DRPO as minimizing the worst-case performative risk over a KL-ball of distribution maps around the nominal map; strong duality turns this into an augmented (tilted) performative risk minimization problem, with provable excess-risk bounds relative to the true PO.
Key results
- DRPO/tilted PO reduces worst-case performative risk relative to PO when misspecification is moderate to large (eta in {2/3, 4/3, 2}) in the partially identifiable location experiment.
- Without misspecification (eta=0) the PO is better than the tilted PO, consistent with the theory.
- In the fairness experiment, increasing the tilt narrows the majority-minority performative risk gap at the cost of higher population risk.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use DRPO instead of PO under cost-function misspecification | Credit scoring · Credit scoring, misspecified cost function | worst-case performative risk | Helped |
| Increase the DRPO radius ρ | DRPO · Credit scoring, misspecified cost function | uniformity of performative risk across ε_true | Helped |
| Use DRPO with radius ρ = 0.04 instead of PO | Credit scoring · Credit scoring, ε_true ∈ [0,1] | performative balanced error rate | Helped |
| Increase the DRPO radius ρ | DRPO · Credit scoring, η ∈ {0.6, 0.8, 1.0} | worst-case performative balanced error rate | Helped |
| Use TPO instead of PO | Credit scoring, partially identifiable distribution map · No misspecification (η = 0) | worst-case performative risk | Hurt |
| Use TPO instead of PO | Credit scoring, partially identifiable distribution map · Moderate to large misspecification, η ∈ {2/3, 4/3, 2} | worst-case performative risk | Helped |
| Increase the TPO tilt α | TPO · Credit scoring, partially identifiable distribution map | uniformity of performative risk across ε_true | Helped |
| Increase the TPO tilt α | TPO · Synthetic fairness without demographics | performance gap between majority and minority | Helped |
| Increase the TPO tilt α | TPO · Synthetic fairness without demographics, population | population performative risk | Hurt |
| Use PO instead of TPO | Synthetic fairness without demographics · Population | population performative risk | Helped |
| Use PO instead of TPO | Synthetic fairness without demographics · Majority and minority | performance gap between groups | Hurt |
Surprising findings
- With no misspecification, the PO is strictly better than the DRPO, so robustness has a cost when the nominal map is correct.
Limitations
- Theoretical bounds are upper bounds that may not be tight.
- Wasserstein-based extension left for future work.
- Radius calibration requires extra data or a KL estimate that uses a parametric (Gaussian) approximation.
Experimental setup
Datasets: Kaggle credit scoring dataset (CC-BY 4.0) synthetic classification data
Benchmarks: Kaggle credit scoring (strategic classification) synthetic location-family data synthetic fairness data
Metrics: performative risk worst-case relative improvement performative balanced error rate
Baselines: performative optimum (PO) repeated distributionally robust optimization
Builds on: performative prediction distributionally robust optimization repeated risk minimization
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