Optimizing Social Utility in Sequential Experiments

2026-05-07

AI Summary

This study addresses the high costs of traditional large-scale randomized controlled trials (RCTs) in high-stakes domains such as drug development, which often deter investment in high-uncertainty, high-social-value “moonshot” projects. The authors propose a novel statistical protocol that integrates sequential RCTs with partial cost subsidies from regulators. For the first time, they jointly model this interaction as a belief Markov decision process and efficiently compute the optimal policy using dynamic programming and divide-and-conquer algorithms. Theoretical analysis reveals that social welfare is a piecewise-linear convex function of the subsidy level, enabling precise identification of the socially optimal subsidy. Simulations based on publicly available antibiotic development data demonstrate that the proposed protocol improves social welfare by over 35% compared to conventional non-sequential approaches.

Abstract

Regulatory approval of products in high-stakes domains such as drug development requires statistical evidence of safety and efficacy through large-scale randomized controlled trials. However, the high financial cost of these trials may deter developers who lack absolute certainty in their product's efficacy, ultimately stifling the development of `moonshot' products that could offer high social utility. To address this inefficiency, in this paper, we introduce a statistical protocol for experimentation where the product developer (the agent) conducts a randomized controlled trial sequentially and the regulator (the principal) partially subsidizes its cost. By modeling the protocol using a belief Markov decision process, we show that the agent's optimal strategy can be found efficiently using dynamic programming. Further, we show that the social utility is a piecewise linear and convex function over the subsidy level the principal selects, and thus the socially optimal subsidy can also be found efficiently using divide-and-conquer. Simulation experiments using publicly available data on antibiotic development and approval demonstrate that our statistical protocol can be used to increase social utility by more than $35$$\%$ relative to standard, non-sequential protocols.

Problem

• sequential experiments
• social utility
• randomized controlled trials
• regulatory approval
• subsidy

Innovation

• sequential experimentation
• subsidy mechanism
• belief Markov decision process
• social utility optimization
• dynamic programming