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Naoki Hamada

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4 papers

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TMLR Journal 2025 Journal Article

Bézier Flow: a Surface-wise Gradient Descent Method for Multi-objective Optimization

Akiyoshi Sannai
Yasunari Hikima
Ken Kobayashi
Akinori Tanaka
Naoki Hamada

This paper proposes a framework to construct a multi-objective optimization algorithm from a single-objective optimization algorithm by using the Bézier simplex model. Additionally, we extend the stability of optimization algorithms in the sense of Probably Approximately Correct (PAC) learning and define the PAC stability. We prove that it leads to an upper bound on the generalization error with high probability. Furthermore, we show that multi-objective optimization algorithms derived from a gradient descent-based single-objective optimization algorithm are PAC stable. We conducted numerical experiments with synthetic and real multi-objective optimization problem instances and demonstrated that our method achieved lower generalization errors than the existing multi-objective optimization algorithms.

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AAAI Conference 2023 Conference Paper

GenéLive! Generating Rhythm Actions in Love Live!

Atsushi Takada
Daichi Yamazaki
Yudai Yoshida
Nyamkhuu Ganbat
Takayuki Shimotomai
Naoki Hamada
Likun Liu
Taiga Yamamoto

This article presents our generative model for rhythm action games together with applications in business operation. Rhythm action games are video games in which the player is challenged to issue commands at the right timings during a music session. The timings are rendered in the chart, which consists of visual symbols, called notes, flying through the screen. We introduce our deep generative model, GenéLive!, which outperforms the state-of-the-art model by taking into account musical structures through beats and temporal scales. Thanks to its favorable performance, GenéLive! was put into operation at KLab Inc., a Japan-based video game developer, and reduced the business cost of chart generation by as much as half. The application target included the phenomenal "Love Live!", which has more than 10 million users across Asia and beyond, and is one of the few rhythm action franchises that has led the online era of the genre. In this article, we evaluate the generative performance of GenéLive! using production datasets at KLab as well as open datasets for reproducibility, while the model continues to operate in their business. Our code and the model, tuned and trained using a supercomputer, are publicly available.

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AAAI Conference 2020 Conference Paper

Asymptotic Risk of Bézier Simplex Fitting

Akinori Tanaka
Akiyoshi Sannai
Ken Kobayashi
Naoki Hamada

The Bézier simplex ﬁtting is a novel data modeling technique which utilizes geometric structures of data to approximate the Pareto set of multi-objective optimization problems. There are two ﬁtting methods based on different sampling strategies. The inductive skeleton ﬁtting employs a stratiﬁed subsampling from skeletons of a simplex, whereas the all-atonce ﬁtting uses a non-stratiﬁed sampling which treats a simplex as a single object. In this paper, we analyze the asymptotic risks of those Bézier simplex ﬁtting methods and derive the optimal subsample ratio for the inductive skeleton ﬁtting. It is shown that the inductive skeleton ﬁtting with the optimal ratio has a smaller risk when the degree of a Bézier simplex is less than three. Those results are veriﬁed numerically under small to moderate sample sizes. In addition, we provide two complementary applications of our theory: a generalized location problem and a multi-objective hyper-parameter tuning of the group lasso. The former can be represented by a Bézier simplex of degree two where the inductive skeleton ﬁtting outperforms. The latter can be represented by a Bézier simplex of degree three where the all-at-once ﬁtting gets an advantage.

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AAAI Conference 2019 Conference Paper

Bézier Simplex Fitting: Describing Pareto Fronts of´ Simplicial Problems with Small Samples in Multi-Objective Optimization

Ken Kobayashi
Naoki Hamada
Akiyoshi Sannai
Akinori Tanaka
Kenichi Bannai
Masashi Sugiyama

Multi-objective optimization problems require simultaneously optimizing two or more objective functions. Many studies have reported that the solution set of an M-objective optimization problem often forms an (M − 1)-dimensional topological simplex (a curved line for M = 2, a curved triangle for M = 3, a curved tetrahedron for M = 4, etc.). Since the dimensionality of the solution set increases as the number of objectives grows, an exponentially large sample size is needed to cover the solution set. To reduce the required sample size, this paper proposes a Bézier simplex model and its fitting algorithm. These techniques can exploit the simplex structure of the solution set and decompose a high-dimensional surface fitting task into a sequence of low-dimensional ones. An approximation theorem of Bézier simplices is proven. Numerical experiments with synthetic and real-world optimization problems demonstrate that the proposed method achieves an accurate approximation of high-dimensional solution sets with small samples. In practice, such an approximation will be conducted in the postoptimization process and enable a better trade-off analysis.

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