Atsushi Iwasaki

Hakuei Yamada, Junpei Komiyama, Kenshi Abe et al.

This work addresses learning online fair division under uncertainty, where a central planner sequentially allocates items without precise knowledge of agents' values or utilities. Departing from conventional online algorithm, the planner here relies on noisy, estimated values obtained after allocating items. We introduce wrapper algorithms utilizing \textit{dual averaging}, enabling gradual learning of both the type distribution of arriving items and agents' values through bandit feedback. This approach enables the algorithms to asymptotically achieve optimal Nash social welfare in linear Fisher markets with agents having additive utilities. We establish regret bounds in Nash social welfare and empirically validate the superior performance of our proposed algorithms across synthetic and empirical datasets.

Kenshi Abe, Junpei Komiyama, Atsushi Iwasaki

This paper considers the capacity expansion problem in two-sided matchings, where the policymaker is allowed to allocate some extra seats as well as the standard seats. In medical residency match, each hospital accepts a limited number of doctors. Such capacity constraints are typically given in advance. However, such exogenous constraints can compromise the welfare of the doctors; some popular hospitals inevitably dismiss some of their favorite doctors. Meanwhile, it is often the case that the hospitals are also benefited to accept a few extra doctors. To tackle the problem, we propose an anytime method that the upper confidence tree searches the space of capacity expansions, each of which has a resident-optimal stable assignment that the deferred acceptance method finds. Constructing a good search tree representation significantly boosts the performance of the proposed method. Our simulation shows that the proposed method identifies an almost optimal capacity expansion with a significantly smaller computational budget than exact methods based on mixed-integer programming.