The Hidden Cost of Waiting for Accurate Predictions
Authors: Ali Shirali, Ariel Procaccia, Rediet Abebe
ICLR 2025 | Venue PDF | Archive PDF | Plain Text | LLM Run Details
| Reproducibility Variable | Result | LLM Response |
|---|---|---|
| Research Type | Experimental | We examine this tension using a simple mathematical model, where the planner collects observations on individuals to improve predictions over time. We analyze both the ranking induced by these predictions and optimal resource allocation. We show that though individual prediction accuracy improves over time, counter-intuitively, the average ranking loss can worsen. As a result, the planner s ability to improve social welfare can decline. We identify inequality as a driving factor behind this phenomenon. Our findings provide a nuanced perspective and challenge the conventional wisdom that it is preferable to wait for more accurate predictions to ensure the most efficient allocations. ... Using this algorithm, we then demonstrate that the optimal solution can concentrate the allocation around any time-point t, and it behaves consistently with our findings on one-time allocation. ... We first study the effect of budget size. Theorem 4.3 suggests that in case of one-time allocation, the optimal allocation time shifts with ln( N B ). Fig. 1 suggests that a similar trend holds true in the case of over-time allocation: a larger budget favors earlier allocations. ... To simulate this effect, we fix B N at 10% and consider three priors with differing tail decay. Fig. 2 indicates that as the prior approaches a uniform distribution, corresponding to maximum inequality in terms of our definition of G-decaying distributions, optimal allocation significantly favors earlier times. |
| Researcher Affiliation | Academia | Ali Shirali ,1, Ariel Procaccia ,2, and Rediet Abebe ,3 1University of California, Berkeley 2Harvard University 3ELLIS Institute, Max Planck Institute for Intelligent Systems, & T ubingen AI Center |
| Pseudocode | Yes | Algorithm 1 Optimal over-time allocation 1: Uopt 0 2: for ˆt = 1 to T, and q( ) valid sequences (as constructed in Lemma 5.2) do Simulate as Aˆt q(ˆt) are all treated: 3: {N t q(t)}T t=1 SIMULATETRAJ(1, {N 1 0 , N 1 1 }, q( )) 4: Emax 1{q(1) = 0} N 1 1 + PT t=1 N t q(t) maximum expenditure Simulate the difference as if no one in Aˆt q(ˆt) was treated: 5: { N t q(t)}T t=ˆt SIMULATETRAJ(ˆt, {0, . . . , 0, N ˆt q(ˆt), 0, . . . , 0}, q( ) + 1{( ) = ˆt}) 6: E N ˆt q(ˆt) PT t=ˆt+1 N t q(t) decrease from the max. expenditure Find what proportion of Aˆt q(ˆt) to treat: 7: ρ Emax B E proportion of Aˆt q(ˆt) to be left untreated 8: if ρ > 1 or ρ < 0 then continue to the next possible q( ) end if Calculate the total utility: 9: for t = 1 to T and k = q(t) do U t k Ep Pt( |yt=k)[ut(p)] end for 10: U (1 ρ) N ˆt q(ˆt) U ˆt q(ˆt) + P t =ˆt(N t q(t) + ρ N t q(t)) U t q(t) + 1{q(1) = 0} N 1 1 U 1 1 11: if U > Uopt then Uopt U, qopt q, ˆtopt ˆt end if check for optimality 12: end for 13: return Uopt, qopt, ˆtopt |
| Open Source Code | Yes | Code is available at https://github.com/alishirali Git/hidden-costs-of-waiting-for-accurate-predictions. |
| Open Datasets | Yes | To make our simulations more realistic, we choose the initial distribution to reflect real-world data. In particular, we use National Education Longitudinal Study (NELS) of 1988, a longitudinal study with follow-ups at four points throughout the students education. ... 8https://nces.ed.gov/surveys/nels88/ |
| Dataset Splits | No | We estimate the beta distribution parameters in the following manner. Let m0 and m1 be the proportion of the initial pool of individuals who failed right before the first and second steps, respectively. Assuming there has been no intervention at the first step, it follows from the central limit theorem that m0 α α+β and m1 α(α+1) (α+β)(α+β+1) at a fast rate of O(1/ N). By solving for α and β, we can accurately estimate the initial distribution as a Beta distribution. |
| Hardware Specification | No | The paper does not provide specific hardware details used for running its experiments. It focuses on theoretical modeling and algorithmic design with semi-synthetic simulations. |
| Software Dependencies | No | The paper does not explicitly list specific software dependencies with version numbers. It provides a link to a GitHub repository, but the dependencies themselves are not detailed in the paper's text. |
| Experiment Setup | Yes | We illustrate the effect of budget and inequality by simulating one-time allocation for T = 6 and N = 10000 in Fig. 3. Consistent with the theory, a high inequality corresponding to G 2 can make W t+1 W t. Even when this is not the case, a high budget can still favor earlier allocation. ... Our estimation gives α = 0.028 and β = 0.35 for the case of NELS data. ... We first study the effect of budget size. Theorem 4.3 suggests that in case of one-time allocation, the optimal allocation time shifts with ln( N B ). Fig. 1 suggests that a similar trend holds true in the case of over-time allocation: a larger budget favors earlier allocations. ... To simulate this effect, we fix B N at 10% and consider three priors with differing tail decay. Fig. 2 indicates that as the prior approaches a uniform distribution, corresponding to maximum inequality in terms of our definition of G-decaying distributions, optimal allocation significantly favors earlier times. |