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Plug-in Performative Optimization
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Proposes plug-in performative optimization: fit a possibly misspecified distribution-map model from exploratory deployments, then optimize the performative risk under the fitted model, with excess-risk bounds separating misspecification and fast parametric statistical error.
Problem
Learning predictors with low performative risk when the distribution map from deployed predictors to data is unknown and only observed at deployed models; model-agnostic methods converge slowly.
Approach
Use a parametric distribution atlas (possibly misspecified) fitted by ERM on exploration data, then compute the plug-in performative optimum under the fitted map with no further data collection; the excess risk splits into an irreducible misspecification term plus a fast O~(1/sqrt(n)) statistical term.
Key results
- In the well-specified strategic regression setting (rho=2), plug-in performative optimization quickly reaches near-zero excess risk, while DFO decreases slowly.
- In the location-family experiment, plug-in excess risk approaches zero for s=0 and stabilizes at a nonzero level for misspecified s>0, while PerfGD and DFO reduce slowly and greedy SGD plateaus at a suboptimal value.
- Excess risk bound: PR(theta_hat) - PR(theta_PO) <= c*MisspecErr + O~(1/sqrt(n)), where the bandit baseline of Jagadeesan et al. has O~(n^{-1/(d+1)}).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use plug-in performative optimization instead of DFO | Location family · Location family, s=0 | excess risk | Helped |
| Use a linear feedback model when the true map includes a quadratic term with s>0 | Plug-in performative optimization · Location family, s>0 | excess risk | Mixed |
| Use plug-in performative optimization instead of DFO | Location family · Location family | excess risk | Helped |
| Use plug-in performative optimization instead of greedy SGD | Location family · Location family | excess risk | Helped |
| Use plug-in performative optimization with a correctly specified response model | Strategic regression · Strategic regression, ρ=2 | excess risk | Helped |
| Use a response model with linear utility and quadratic cost when the true response has ρ≠2 | Plug-in performative optimization · Strategic regression, ρ∈{2.5, 3} | excess risk | Mixed |
| Use plug-in performative optimization instead of DFO | Strategic regression · Strategic regression | excess risk | Helped |
| Use plug-in performative optimization instead of greedy SGD | Strategic regression · Strategic regression | excess risk | Helped |
| Use plug-in performative optimization instead of greedy SGD | Strategic regression · Strategic regression | test accuracy | Mixed |
Surprising findings
- Misspecified models still yield lower excess risk than model-agnostic bandit-style methods at finite sample sizes, provided misspecification is not too extreme.
Limitations
- Performance degrades when the chosen distribution atlas is highly misspecified; practical gains depend on prior knowledge for choosing the atlas.
- Analysis relies on regularity assumptions (strong convexity, subexponential gradients) on the ERM problem.
- Experiments are limited to simulated and one real credit dataset with simple linear/quadratic models.
Experimental setup
Datasets: synthetic location-family data synthetic strategic regression base data credit dataset (actionable-recourse processed version)
Benchmarks: location-family simulations strategic regression simulations credit dataset
Metrics: excess risk test accuracy
Baselines: derivative-free optimization (DFO) greedy SGD PerfGD
Builds on: performative prediction PerfGD M-estimation
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