T. Sandholm
Publications
Decision Making under Imperfect Recall: Algorithms and Benchmarks
In game theory, imperfect-recall decision problems model situations in which an agent forgets information it held before. They encompass games such as the ``absentminded driver'' and team games with limited communication. In this paper, we introduce the first benchmark suite for imperfect-recall decision problems. Our benchmarks capture a variety of problem types, including ones concerning privacy in AI systems that elicit sensitive information, and AI safety via testing of agents in simulation. Across 61 problem instances generated using this suite, we evaluate the performance of different algorithms for finding first-order optimal strategies in such problems. In particular, we introduce the family of regret matching (RM) algorithms for nonlinear constrained optimization. This class of parameter-free algorithms has enjoyed tremendous success in solving large two-player zero-sum games, but, surprisingly, they were hitherto relatively unexplored beyond that setting. Our key finding is that RM algorithms consistently outperform commonly employed first-order optimizers such as projected gradient descent, often by orders of magnitude. This establishes, for the first time, the RM family as a formidable approach to large-scale constrained optimization problems.
Learning Potentials for Dynamic Matching and Application to Heart Transplantation
Each year, thousands of patients in need of heart transplants face life-threatening wait times due to organ scarcity. While allocation policies aim to maximize population-level outcomes, current approaches often fail to account for the dynamic arrival of organs and the composition of waitlisted candidates, thereby hampering efficiency. The United States is transitioning from rigid, rule-based allocation to more flexible data-driven models. In this paper, we propose a novel framework for non-myopic policy optimization in general online matching relying on potentials, a concept originally introduced for kidney exchange. We develop scalable and accurate ways of learning potentials that are higher-dimensional and more expressive than prior approaches. Our approach is a form of self-supervised imitation learning: the potentials are trained to mimic an omniscient algorithm that has perfect foresight. We focus on the application of heart transplant allocation and demonstrate, using real historical data, that our policies significantly outperform prior approaches -- including the current US status quo policy and the proposed continuous distribution framework -- in optimizing for population-level outcomes. Our analysis and methods come at a pivotal moment in US policy, as the current heart transplant allocation system is under review. We propose a scalable and theoretically grounded path toward more effective organ allocation.
Near-Optimal Dynamic Matching via Coarsening with Application to Heart Transplantation
Online matching has been a mainstay in domains such as Internet advertising and organ allocation, but practical algorithms often lack strong theoretical guarantees. We take an important step toward addressing this by developing new online matching algorithms based on a coarsening approach. Although coarsening typically implies a loss of granularity, we show that, to the contrary, aggregating offline nodes into capacitated clusters can yield near-optimal theoretical guarantees. We apply our methodology to heart transplant allocation to develop theoretically grounded policies based on structural properties of historical data. Furthermore, in simulations based on real data, our policy closely matches the performance of the omniscient benchmark, achieving competitive ratio 0.91, drastically higher than the US status quo policy's 0.51. Our work bridges the gap between data-driven heuristics and pessimistic theoretical lower bounds.