Research map / Learning theory and algorithms / Prediction and decision losses
The Hidden Cost of Waiting for Accurate Predictions
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Models how timing of prediction-driven resource allocation trades off noisier early predictions against more accurate later ones, showing ranking loss can worsen over time due to inequality-driven population attrition and deriving optimal one-time and over-time allocation conditions.
Problem
When a planner allocates a fixed budget to prevent undesirable outcomes using predictions that improve with observations, but individuals with high failure probability drop out over time, it is unclear whether waiting for more accurate predictions improves ranking and allocation welfare.
Approach
A stylized Bernoulli-observation model with failure-driven attrition shows the ranking risk can increase over time because the change-in-population effect (high-risk individuals fail out) grows with inequality (variance of failure probabilities), yielding conditions on when early allocation is optimal and an efficient algorithm for optimal over-time allocation.
Key results
- Theory shows ranking risk can only improve at step t if Var[p]/(1-E[p])^2 minus O(1/sqrt(t)) is below C/t, so higher inequality makes later ranking worse.
- One-time allocation: optimal allocation time t* is at most T/2 + O((G/4 + (gamma+1/gamma)/4 + 1)((gamma+1) ln(N/B) + 1)) for fully effective treatments, shifting earlier with higher inequality or larger budget.
- An algorithm finds the optimal over-time allocation in O(T^3 2^T) steps, independent of population size and budget.
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| wait for more observations while high-risk individuals fail out of the active population | Bayes-optimal ranking · Active population over time | ranking risk | Mixed |
| increase inequality in failure probabilities | Bayes-optimal ranking · Active population over time | ranking risk | Hurt |
| allocate earlier under high inequality or a larger budget | One-time resource allocation · One-time allocation | social welfare | Helped |
| increase the budget | Optimal over-time allocation · Semi-synthetic NELS-based simulation | allocation timing | Helped |
| increase inequality by moving the prior toward a uniform distribution | Optimal over-time allocation · Semi-synthetic priors, B/N = 10% | allocation timing | Helped |
Surprising findings
- Average ranking loss can worsen over time even though individual prediction accuracy improves, due to high-risk individuals failing out of the active pool.
Limitations
- Stylized model with generic assumptions on failure probabilities and observation models
- Ignores heterogeneous costs, starting conditions, and costly observation for vulnerable individuals
- Approximations (normal approximation of ranking risk) underlie the ranking results
Experimental setup
Datasets: National Education Longitudinal Study (NELS) 1988
Metrics: pairwise zero-one ranking risk expected utility of allocation
Builds on: Bayes optimal ranking rotting bandits
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