Yasushi Kawase

Shunta Akiyama, Mitsuaki Obara, Yasushi Kawase

Lotteries are a prevalent form of gambling between a seller and buyers. Designing a lottery requires a model of how buyers make decisions when confronted with uncertain outcomes. Cumulative prospect theory (CPT) is a descriptive model that captures people's propensity to overestimate extreme events and their different attitudes toward gains and losses. In this study, we design a lottery that maximizes the seller's profit when the buyers' decision-making adheres to the CPT framework. The main difficulty is the nonconvexity of the CPT framework, which we overcome by reformulating the problem as a three-level optimization problem and characterizing its optimal solution. Based on the analysis, we propose a linear-time algorithm that computes the optimal lottery. Furthermore, we present an efficient algorithm applicable to a broader setting with a ticket price constraint. This is the first study to employ the CPT framework in designing an optimal lottery with more than two outcomes.

Tsubasa Harada, Yasushi Kawase, Hanna Sumita

We study the repeated optimal stopping problem, which generalizes the classical optimal stopping problem with an unknown distribution to a setting where the same problem is solved repeatedly over $T$ rounds. In this framework, we aim to design algorithms that guarantee a competitive ratio in each round while also achieving sublinear regret across all rounds. Our primary contribution is a general algorithmic framework that achieves these objectives simultaneously for a wide array of repeated optimal stopping problems. The core idea is to dynamically select an algorithm for each round, choosing between two candidates: (1) an empirically optimal algorithm derived from the history of observations, and (2) a sample-based algorithm with a proven competitive ratio guarantee. Based on this approach, we design an algorithm that performs no worse than the baseline sample-based algorithm in every round, while ensuring that the total regret is bounded by $\tilde{O}(\sqrt{T})$. We demonstrate the broad applicability of our framework to canonical problems, including the prophet inequality, the secretary problem, and their variants under adversarial, random, and i.i.d. input models. For example, for the repeated prophet inequality problem, our method achieves a $1/2$-competitive ratio from the second round on and an $\tilde{O}(\sqrt{T})$ regret. Furthermore, we establish a regret lower bound of $Ω(\sqrt{T})$ even in the i.i.d. model, confirming that our algorithm's performance is almost optimal with respect to the number of rounds.

Yasushi Kawase, Yuko Kuroki, Atsushi Miyauchi

Aggregating responses from crowd workers is a fundamental task in the process of crowdsourcing. In cases where a few experts are overwhelmed by a large number of non-experts, most answer aggregation algorithms such as the majority voting fail to identify the correct answers. Therefore, it is crucial to extract reliable experts from the crowd workers. In this study, we introduce the notion of "expert core", which is a set of workers that is very unlikely to contain a non-expert. We design a graph-mining-based efficient algorithm that exactly computes the expert core. To answer the aggregation task, we propose two types of algorithms. The first one incorporates the expert core into existing answer aggregation algorithms such as the majority voting, whereas the second one utilizes information provided by the expert core extraction algorithm pertaining to the reliability of workers. We then give a theoretical justification for the first type of algorithm. Computational experiments using synthetic and real-world datasets demonstrate that our proposed answer aggregation algorithms outperform state-of-the-art algorithms.