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Revisiting the Predictability of Performative, Social Events
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Shows that performative multicalibration (outcome indistinguishability) predictions of social events can be found efficiently via online-to-batch reduction from online multicalibration, yet such predictors can be poor in risk terms.
Problem
Whether social predictions that actively shape outcome distributions (performative prediction) can still be efficiently learned to be valid (calibrated/multicalibrated), and whether such valid predictions are desirable in terms of predictive risk.
Approach
Reduces performative multicalibration under outcome performativity to online multicalibration via an online-to-batch conversion that handles outcome distributions induced by the predictor itself, with no smoothness assumptions on the distribution map; also shows multicalibration implies performative stability for squared loss but can yield arbitrarily poor performative risk.
Key results
- Batch predictor from any online multicalibration algorithm achieves error sqrt(|C|/n)+O(sqrt(log|C|/n)) with runtime O(n·time(n)), requiring no Lipschitz assumptions on the distribution map.
- Performatively multicalibrated predictors w.r.t. benchmark class H are performatively stable (2-epsilon) for squared loss with binary outcomes.
- Constructed example where a perfectly multicalibrated predictor maximizes performative risk, with performative risk gap between worst and best predictor near 0.25 vs 0.01.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Use an online multicalibration algorithm and convert its predictors into a randomized batch predictor | Outcome-performative prediction · General outcome-performative setting | performative multicalibration error: \frac{\mathsf{Regret}_{\mathcal{A}}(n)}{n} + 4\sqrt{\frac{\log(|\mathcal{C}|) + \log(1/\delta)}{n}} | Helped |
| Use K29 with a kernel for a finite collection of functions | K29 batch predictor · Any finite collection | performative multicalibration error: \sqrt{\frac{|\mathcal{C}|}{n}} + 4\sqrt{\frac{\log(|\mathcal{C}|) + \log(1/\delta)}{n}} | Helped |
| Use K29 with a linear kernel | K29 batch predictor · Linear functions | performative multicalibration error: \sqrt{\frac{2}{n}} + 4\sqrt{\frac{\log(|\mathcal{C}|) + \log(1/\delta)}{n}} | Helped |
| Use K29 with the low-degree polynomial kernel | K29 batch predictor · Low-degree Boolean functions | performative multicalibration error: 10\sqrt{\frac{d^s}{n}} + 4\sqrt{\frac{\log(|\mathcal{C}|) + \log(1/\delta)}{n}} | Helped |
| Require performative multicalibration with respect to p - 1/2 and h(x) - 1/2 | Predictor f · Binary outcomes; squared loss | performative stability error: 2\varepsilon | Helped |
| Replace a deterministic forecast with a randomized mixture between 1/2 and 1/2 + α | Outcome-performative predictor · No features; binary outcomes | calibration error: \frac{.01}{2}\big( c(1/2) - c(1/2 +\alpha) \big) | Helped |
| Use the randomized mixture near 1/2 instead of a performatively optimal forecast | Outcome-performative predictor · No features; binary outcomes | squared performative risk: \frac{1}{4} + {\cal O}(\alpha); $.01 | Hurt |
| Use a predictor that is multicalibrated with respect to all bounded continuous tests | Outcome-performative predictor · General benchmark class | squared performative risk: - {\cal O}(\varepsilon) | Hurt |
Surprising findings
- A predictor can be perfectly multicalibrated with respect to all continuous functions yet explain none of the variance in outcomes.
- Performatively multicalibrated predictors can maximize performative risk over benchmark classes, reversing the supervised-learning intuition.
Limitations
- Analysis restricted to stateless outcome performativity; features are not performative.
- Results for stability are stated for binary outcomes only.
- Multicalibration is not sufficient for good predictions; desiderata must be reconsidered via loss choice.
Experimental setup
Metrics: performative multicalibration error squared loss performative risk
Builds on: performative prediction multicalibration outcome indistinguishability K29 algorithm
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