# Optimizing Social Utility in Sequential Experiments

arXiv: https://arxiv.org/abs/2605.06520 · HTML: https://mlsanity.com/paper/2605.06520/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 13 of its 79 references that are in the map.
- First posted on arXiv 7 May 2026.

## Builds on (most cited first, 13 of 13)

- [A Tutorial on Thompson Sampling](https://mlsanity.com/paper/1707.02038/) (2017)
- [Estimating means of bounded random variables by betting](https://mlsanity.com/paper/2010.09686/) (2020)
- [Game-theoretic statistics and safe anytime-valid inference](https://mlsanity.com/paper/2210.01948/) (2022)
- [Principal-Agent Hypothesis Testing](https://mlsanity.com/paper/2205.06812/) (2022)
- [Instance-Log-Optimality of Portfolio-Based E-Processes and their Sequential Hypothesis Tests](https://mlsanity.com/paper/2504.02818/) (2025)
- [Minimax-Bayes Reinforcement Learning](https://mlsanity.com/paper/2302.10831/) (2023)
- [Sharp Results for Hypothesis Testing with Risk-Sensitive Agents](https://mlsanity.com/paper/2412.16452/) (2024)
- [Towards Anytime-Valid Statistical Watermarking](https://mlsanity.com/paper/2602.17608/) (2026)
- [Post-Hoc Large-Sample Statistical Inference](https://mlsanity.com/paper/2603.08002/) (2026)
- [Instance-Adaptive Hypothesis Tests with Heterogeneous Agents](https://mlsanity.com/paper/2510.21178/) (2025)
- [Anytime Detection of Strategic Deviations in Multi-Agent Systems](https://mlsanity.com/paper/2601.05427/) (2026)
- [Bayesian Learning Approach to Model Predictive Control](https://mlsanity.com/paper/2203.02720/) (2022)
- [Optimal Stopping for Sequential Bayesian Experimental Design](https://mlsanity.com/paper/2509.21734/) (2025)

## Abstract (arXiv)

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.