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Ken Kobayashi

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10 papers

2 author rows

TMLR Journal 2026 Journal Article

Hierarchical Time Series Forecasting with Robust Reconciliation

Shuhei Aikawa
Aru Suzuki
Kei Yoshitake
Kanata Teshigawara
Iwabuchi Akira
Ken Kobayashi
Kazuhide Nakata

This paper focuses on forecasting hierarchical time-series data, where each higher-level observation equals the sum of its corresponding lower-level time series. In such contexts, the forecast values should be coherent, meaning that the forecast value of each parent series exactly matches the sum of the forecast values of its child series. Existing hierarchical forecasting methods typically generate base forecasts independently for each series and then apply a reconciliation procedure to adjust them so that the resulting forecast values are coherent across the hierarchy. These methods generally derive an optimal reconciliation, using a covariance matrix of the forecast error. In practice, however, the true covariance matrix is unknown and has to be estimated from finite samples in advance. This gap between the true and estimated covariance matrix may degrade forecast performance. To address this issue, we propose a robust optimization framework for hierarchical reconciliation that accounts for uncertainty in the estimated covariance matrix. We first introduce an uncertainty set for the estimated covariance matrix and formulate a reconciliation problem that minimizes the worst-case average of weighted squared residuals over this uncertainty set. We show that our problem can be cast as a semidefinite optimization problem. Numerical experiments demonstrate that the proposed robust reconciliation method achieved better forecast performance than existing hierarchical forecasting methods, which indicates the effectiveness of integrating uncertainty into the reconciliation process.

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ICML Conference 2025 Conference Paper

Algorithmic Recourse for Long-Term Improvement

Kentaro Kanamori
Ken Kobayashi
Satoshi Hara 0001
Takuya Takagi

Algorithmic recourse aims to provide a recourse action for altering an unfavorable prediction given by a model into a favorable one (e. g. , loan approval). In practice, it is also desirable to ensure that an action makes the real-world outcome better (e. g. , loan repayment). We call this requirement improvement. Unfortunately, existing methods cannot ensure improvement unless we know the true oracle. To address this issue, we propose a framework for suggesting improvement-oriented actions from a long-term perspective. Specifically, we introduce a new online learning task of assigning actions to a given sequence of instances. We assume that we can observe delayed feedback on whether the past suggested action achieved improvement. Using the feedback, we estimate an action that can achieve improvement for each instance. To solve this task, we propose two approaches based on contextual linear bandit and contextual Bayesian optimization. Experimental results demonstrated that our approaches could assign improvement-oriented actions to more instances than the existing methods.

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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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NeurIPS Conference 2025 Conference Paper

Learning Gradient Boosted Decision Trees with Algorithmic Recourse

Kentaro Kanamori
Ken Kobayashi
Takuya Takagi

This paper proposes a new algorithm for learning gradient boosted decision trees while ensuring the existence of recourse actions. Algorithmic recourse aims to provide a recourse action for altering the undesired prediction result given by a model. While existing studies often focus on extracting valid and executable actions from a given learned model, such reasonable actions do not always exist for models optimized solely for predictive accuracy. To address this issue, recent studies proposed a framework for learning a model while guaranteeing the existence of reasonable actions with high probability. However, these methods can not be applied to gradient boosted decision trees, which are renowned as one of the most popular models for tabular datasets. We propose an efficient gradient boosting algorithm that takes recourse guarantee into account, while maintaining the same time complexity as the standard ones. We also propose a post-processing method for refining a learned model under the constraint of a recourse guarantee and provide a PAC-style analysis of the refined model. Experimental results demonstrated that our method successfully provided reasonable actions to more instances than the baselines without significantly degrading accuracy and computational efficiency.

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ICML Conference 2024 Conference Paper

Learning Decision Trees and Forests with Algorithmic Recourse

Kentaro Kanamori
Takuya Takagi
Ken Kobayashi
Yuichi Ike

This paper proposes a new algorithm for learning accurate tree-based models while ensuring the existence of recourse actions. Algorithmic Recourse (AR) aims to provide a recourse action for altering the undesired prediction result given by a model. Typical AR methods provide a reasonable action by solving an optimization task of minimizing the required effort among executable actions. In practice, however, such actions do not always exist for models optimized only for predictive performance. To alleviate this issue, we formulate the task of learning an accurate classification tree under the constraint of ensuring the existence of reasonable actions for as many instances as possible. Then, we propose an efficient top-down greedy algorithm by leveraging the adversarial training techniques. We also show that our proposed algorithm can be applied to the random forest, which is known as a popular framework for learning tree ensembles. Experimental results demonstrated that our method successfully provided reasonable actions to more instances than the baselines without significantly degrading accuracy and computational efficiency.

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ICLR Conference 2024 Conference Paper

Towards Assessing and Benchmarking Risk-Return Tradeoff of Off-Policy Evaluation

Haruka Kiyohara
Ren Kishimoto
Kosuke Kawakami
Ken Kobayashi
Kazuhide Nakata
Yuta Saito

**Off-Policy Evaluation (OPE)** aims to assess the effectiveness of counterfactual policies using offline logged data and is frequently utilized to identify the top-$k$ promising policies for deployment in online A/B tests. Existing evaluation metrics for OPE estimators primarily focus on the "accuracy" of OPE or that of downstream policy selection, neglecting risk-return tradeoff and *efficiency* in subsequent online policy deployment. To address this issue, we draw inspiration from portfolio evaluation in finance and develop a new metric, called **SharpeRatio@k**, which measures the risk-return tradeoff and efficiency of policy portfolios formed by an OPE estimator under varying online evaluation budgets ($k$). We first demonstrate, in two example scenarios, that our proposed metric can clearly distinguish between conservative and high-stakes OPE estimators and reliably identify the most *efficient* estimator capable of forming superior portfolios of candidate policies that maximize return with minimal risk during online deployment, while existing evaluation metrics produce only degenerate results. To facilitate a quick, accurate, and consistent evaluation of OPE via SharpeRatio@k, we have also implemented the proposed metric in an open-source software. Using SharpeRatio@k and the software, we conduct a benchmark experiment of various OPE estimators regarding their risk-return tradeoff, presenting several future directions for OPE research.

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AAAI Conference 2021 Conference Paper

Ordered Counterfactual Explanation by Mixed-Integer Linear Optimization

Kentaro Kanamori
Takuya Takagi
Ken Kobayashi
Yuichi Ike
Kento Uemura
Hiroki Arimura

Post-hoc explanation methods for machine learning models have been widely used to support decision-making. One of the popular methods is Counterfactual Explanation (CE), also known as Actionable Recourse, which provides a user with a perturbation vector of features that alters the prediction result. Given a perturbation vector, a user can interpret it as an “action” for obtaining one’s desired decision result. In practice, however, showing only a perturbation vector is often insufficient for users to execute the action. The reason is that if there is an asymmetric interaction among features, such as causality, the total cost of the action is expected to depend on the order of changing features. Therefore, practical CE methods are required to provide an appropriate order of changing features in addition to a perturbation vector. For this purpose, we propose a new framework called Ordered Counterfactual Explanation (OrdCE). We introduce a new objective function that evaluates a pair of an action and an order based on feature interaction. To extract an optimal pair, we propose a mixedinteger linear optimization approach with our objective function. Numerical experiments on real datasets demonstrated the effectiveness of our OrdCE in comparison with unordered CE methods.

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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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IJCAI Conference 2020 Conference Paper

DACE: Distribution-Aware Counterfactual Explanation by Mixed-Integer Linear Optimization

Kentaro Kanamori
Takuya Takagi
Ken Kobayashi
Hiroki Arimura

Counterfactual Explanation (CE) is one of the post-hoc explanation methods that provides a perturbation vector so as to alter the prediction result obtained from a classifier. Users can directly interpret the perturbation as an "action" for obtaining their desired decision results. However, an action extracted by existing methods often becomes unrealistic for users because they do not adequately care about the characteristics corresponding to the empirical data distribution such as feature-correlations and outlier risk. To suggest an executable action for users, we propose a new framework of CE for extracting an action by evaluating its reality on the empirical data distribution. The key idea of our proposed method is to define a new cost function based on the Mahalanobis' distance and the local outlier factor. Then, we propose a mixed-integer linear optimization approach to extracting an optimal action by minimizing our cost function. By experiments on real datasets, we confirm the effectiveness of our method in comparison with existing methods for CE.

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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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