Research map / Learning theory and algorithms / Prediction and decision losses
The Relative Value of Prediction in Algorithmic Decision Making
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Theoretical analysis of when expanding access beats improving prediction in algorithmic targeting, deriving the prediction-access ratio under linear and probit regression models.
Problem
Deciding whether to improve a predictor or expand access to scarce goods/interventions in algorithmic decision making for welfare maximization, and when a predictor is "good enough" for decisions.
Approach
Defines the prediction-access ratio (PAR) comparing marginal welfare gains from expanding access versus improving prediction (via explained variance), and derives closed-form or bounded expressions under Gaussian linear and probit welfare models, showing prediction's relative value is small when access is scarce.
Key results
- Under the linear model, the prediction-access ratio is approximately gamma_s/alpha, so it grows as access alpha shrinks.
- Under the probit model, the ratio scales as alpha^(-1/gamma_t^2), larger than in the linear case, so expanding access is more favored even for low predictive power.
- Numerical simulations show the cost-benefit threshold is of the form gamma_s proportional to alpha in the linear model.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Expand access rather than improve prediction | Linear regression targeting · Linear regression model | prediction-access ratio (PAR): \frac{1}{4} \cdot \frac{1}{\alpha} \left( \frac{\mu}{\norm{\beta} \Phi^{-1}(1-\alpha)}+ \gamma_s\right) \frac{\Delta_\al | Helped |
| Expand access rather than improve prediction | Probit regression targeting · Probit regression model | prediction-access ratio (PAR): \widetilde{\Theta}\left(\frac{\gamma_t}{b} \alpha^{-1 / \gamma_{t}^2}\right) | Helped |
Surprising findings
- Under the probit model, expanding access can be more cost-efficient than improving prediction for small alpha regardless of how well the predictor explains outcomes.
Limitations
- Analysis assumes welfare improvements are positive for most of the population (alpha < b) and interventions are goods, not harms.
- Assumes costs are known and the planner correctly specifies the prediction problem and observes the treatment effects directly.
- Results rely on Gaussian linear and probit models and bounds only hold for small alpha and small improvements.
Experimental setup
Metrics: prediction-access ratio welfare value
Builds on: prediction policy problems contextual bandits with knapsacks
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