Masahiro Kato

Masahiro Kato

This study investigates the experimental design problem for identifying the arm with the highest expected outcome, referred to as best arm identification (BAI). In our experiments, the number of treatment-allocation rounds is fixed. During each round, a decision-maker allocates an arm and observes a corresponding outcome, which follows a Gaussian distribution with variances that can differ among the arms. At the end of the experiment, the decision-maker recommends one of the arms as an estimate of the best arm. To design an experiment, we first discuss lower bounds for the probability of misidentification. Our analysis highlights that the available information on the outcome distribution, such as means (expected outcomes), variances, and the choice of the best arm, significantly influences the lower bounds. Because available information is limited in actual experiments, we develop a lower bound that is valid under the unknown means and the unknown choice of the best arm, which are referred to as the worst-case lower bound. We demonstrate that the worst-case lower bound depends solely on the variances of the outcomes. Then, under the assumption that the variances are known, we propose the Generalized-Neyman-Allocation (GNA)-empirical-best-arm (EBA) strategy, an extension of the Neyman allocation proposed by Neyman (1934). We show that the GNA-EBA strategy is asymptotically optimal in the sense that its probability of misidentification aligns with the lower bounds as the sample size increases infinitely and the differences between the expected outcomes of the best and other suboptimal arms converge to the same values across arms. We refer to such strategies as asymptotically worst-case optimal.

Masahiro Kato

Riesz regression has garnered attention as a tool in debiased machine learning for causal and structural parameter estimation (Chernozhukov et al., 2021). This study shows that Riesz regression is closely related to direct density-ratio estimation (DRE) in important cases, including average treat- ment effect (ATE) estimation. Specifically, the idea and objective in Riesz regression coincide with the one in least-squares importance fitting (LSIF, Kanamori et al., 2009) in direct density-ratio estimation. While Riesz regression is general in the sense that it can be applied to Riesz representer estimation in a wide class of problems, the equivalence with DRE allows us to directly import exist- ing results in specific cases, including convergence-rate analyses, the selection of loss functions via Bregman-divergence minimization, and regularization techniques for flexible models, such as neural networks. Conversely, insights about the Riesz representer in debiased machine learning broaden the applications of direct density-ratio estimation methods. This paper consolidates our prior results in Kato (2025a) and Kato (2025b).

Masahiro Kato, Akihiro Oga, Wataru Komatsubara et al.

This study designs an adaptive experiment for efficiently estimating average treatment effects (ATEs). In each round of our adaptive experiment, an experimenter sequentially samples an experimental unit, assigns a treatment, and observes the corresponding outcome immediately. At the end of the experiment, the experimenter estimates an ATE using the gathered samples. The objective is to estimate the ATE with a smaller asymptotic variance. Existing studies have designed experiments that adaptively optimize the propensity score (treatment-assignment probability). As a generalization of such an approach, we propose optimizing the covariate density as well as the propensity score. First, we derive the efficient covariate density and propensity score that minimize the semiparametric efficiency bound and find that optimizing both covariate density and propensity score minimizes the semiparametric efficiency bound more effectively than optimizing only the propensity score. Next, we design an adaptive experiment using the efficient covariate density and propensity score sequentially estimated during the experiment. Lastly, we propose an ATE estimator whose asymptotic variance aligns with the minimized semiparametric efficiency bound.

Masahiro Kato

This study investigates treatment effect estimation in the semi-supervised setting, where we can use not only the standard triple of covariates, treatment indicator, and outcome, but also unlabeled auxiliary covariates. For this problem, we develop efficiency bounds and efficient estimators whose asymptotic variance aligns with the efficiency bound. In the analysis, we introduce two different data-generating processes: the one-sample setting and the two-sample setting. The one-sample setting considers the case where we can observe treatment indicators and outcomes for a part of the dataset, which is also called the censoring setting. In contrast, the two-sample setting considers two independent datasets with labeled and unlabeled data, which is also called the case-control setting or the stratified setting. In both settings, we find that by incorporating auxiliary covariates, we can lower the efficiency bound and obtain an estimator with an asymptotic variance smaller than that without such auxiliary covariates.

Masahiro Kato

The goal of policy learning is to train a policy function that recommends a treatment given covariates to maximize population welfare. There are two major approaches in policy learning: the empirical welfare maximization (EWM) approach and the plug-in approach. The EWM approach is analogous to a classification problem, where one first builds an estimator of the population welfare, which is a functional of policy functions, and then trains a policy by maximizing the estimated welfare. In contrast, the plug-in approach is based on regression, where one first estimates the conditional average treatment effect (CATE) and then recommends the treatment with the highest estimated outcome. This study bridges the gap between the two approaches by showing that both are based on essentially the same optimization problem. In particular, we prove an exact equivalence between EWM and least squares over a reparameterization of the policy class. As a consequence, the two approaches are interchangeable in several respects and share the same theoretical guarantees under common conditions. Leveraging this equivalence, we propose a regularization method for policy learning. The reduction to least squares yields a smooth surrogate that is typically easier to optimize in practice. At the same time, for many natural policy classes the inherent combinatorial hardness of exact EWM generally remains, so the reduction should be viewed as an optimization aid rather than a universal bypass of NP-hardness.

Toshinori Kitamura, Tadashi Kozuno, Masahiro Kato et al.

We study a primal-dual (PD) reinforcement learning (RL) algorithm for online constrained Markov decision processes (CMDPs). Despite its widespread practical use, the existing theoretical literature on PD-RL algorithms for this problem only provides sublinear regret guarantees and fails to ensure convergence to optimal policies. In this paper, we introduce a novel policy gradient PD algorithm with uniform probably approximate correctness (Uniform-PAC) guarantees, simultaneously ensuring convergence to optimal policies, sublinear regret, and polynomial sample complexity for any target accuracy. Notably, this represents the first Uniform-PAC algorithm for the online CMDP problem. In addition to the theoretical guarantees, we empirically demonstrate in a simple CMDP that our algorithm converges to optimal policies, while baseline algorithms exhibit oscillatory performance and constraint violation.

Masahiro Kato, Kentaro Baba, Hibiki Kaibuchi et al.

Portfolio optimization is a critical task in investment. Most existing portfolio optimization methods require information on the distribution of returns of the assets that make up the portfolio. However, such distribution information is usually unknown to investors. Various methods have been proposed to estimate distribution information, but their accuracy greatly depends on the uncertainty of the financial markets. Due to this uncertainty, a model that could well predict the distribution information at one point in time may perform less accurately compared to another model at a different time. To solve this problem, we investigate a method for portfolio optimization based on Bayesian predictive synthesis (BPS), one of the Bayesian ensemble methods for meta-learning. We assume that investors have access to multiple asset return prediction models. By using BPS with dynamic linear models to combine these predictions, we can obtain a Bayesian predictive posterior about the mean rewards of assets that accommodate the uncertainty of the financial markets. In this study, we examine how to construct mean-variance portfolios and quantile-based portfolios based on the predicted distribution information.

Masahiro Kato

This study investigates the estimation and the statistical inference about Conditional Average Treatment Effects (CATEs), which have garnered attention as a metric representing individualized causal effects. In our data-generating process, we assume linear models for the outcomes associated with binary treatments and define the CATE as a difference between the expected outcomes of these linear models. This study allows the linear models to be high-dimensional, and our interest lies in consistent estimation and statistical inference for the CATE. In high-dimensional linear regression, one typical approach is to assume sparsity. However, in our study, we do not assume sparsity directly. Instead, we consider sparsity only in the difference of the linear models. We first use a doubly robust estimator to approximate this difference and then regress the difference on covariates with Lasso regularization. Although this regression estimator is consistent for the CATE, we further reduce the bias using the techniques in double/debiased machine learning (DML) and debiased Lasso, leading to $\sqrt{n}$-consistency and confidence intervals. We refer to the debiased estimator as the triple/debiased Lasso (TDL), applying both DML and debiased Lasso techniques. We confirm the soundness of our proposed method through simulation studies.

Masahiro Kato

This study investigates minimax and Bayes optimal strategies in fixed-budget best-arm identification. We consider an adaptive procedure consisting of a sampling phase followed by a recommendation phase, and we design an adaptive experiment within this framework to efficiently identify the best arm, defined as the one with the highest expected outcome. In our proposed strategy, the sampling phase consists of two stages. The first stage is a pilot phase, in which we allocate each arm uniformly in equal proportions to eliminate clearly suboptimal arms and estimate outcome variances. In the second stage, arms are allocated in proportion to the variances estimated during the first stage. After the sampling phase, the procedure enters the recommendation phase, where we select the arm with the highest sample mean as our estimate of the best arm. We prove that this single strategy is simultaneously asymptotically minimax and Bayes optimal for the simple regret, with upper bounds that coincide exactly with our lower bounds, including the constant terms.

Masahiro Kato, Yuki Ikeda, Kentaro Baba et al.

In this study, we propose a method for identifying potential customers in targeted marketing by applying learning from positive and unlabeled data (PU learning). We consider a scenario in which a company sells a product and can observe only the customers who purchased it. Decision-makers seek to market products effectively based on whether people have loyalty to the company. Individuals with loyalty are those who are likely to remain interested in the company even without additional advertising. Consequently, those loyal customers would likely purchase from the company if they are interested in the product. In contrast, people with lower loyalty may overlook the product or buy similar products from other companies unless they receive marketing attention. Therefore, by focusing marketing efforts on individuals who are interested in the product but do not have strong loyalty, we can achieve more efficient marketing. To achieve this goal, we consider how to learn, from limited data, a classifier that identifies potential customers who (i) have interest in the product and (ii) do not have loyalty to the company. Although our algorithm comprises a single-stage optimization, its objective function implicitly contains two losses derived from standard PU learning settings. For this reason, we refer to our approach as double PU learning. We verify the validity of the proposed algorithm through numerical experiments, confirming that it functions appropriately for the problem at hand.

Masahiro Kato, Fumiaki Kozai, Ryo Inokuchi

The estimation of average treatment effects (ATEs), defined as the difference in expected outcomes between treatment and control groups, is a central topic in causal inference. This study develops semiparametric efficient estimators for ATE in a setting where only a treatment group and an unlabeled group, consisting of units whose treatment status is unknown, are observed. This scenario constitutes a variant of learning from positive and unlabeled data (PU learning) and can be viewed as a special case of ATE estimation with missing data. For this setting, we derive the semiparametric efficiency bounds, which characterize the lowest achievable asymptotic variance for regular estimators. We then construct semiparametric efficient ATE estimators that attain these bounds. Our results contribute to the literature on causal inference with missing data and weakly supervised learning.

Masahiro Kato

This study proposes a debiasing method for smooth nonparametric estimators. While machine learning techniques such as random forests and neural networks have demonstrated strong predictive performance, their theoretical properties remain relatively underexplored. In particular, many modern algorithms lack guarantees of pointwise and uniform risk convergence, as well as asymptotic normality. These properties are essential for statistical inference and robust estimation and have been well-established for classical methods such as Nadaraya-Watson regression. To ensure these properties for various nonparametric regression estimators, we introduce a model-free debiasing method. By incorporating a correction term that estimates the conditional expected residual of the original estimator, or equivalently, its estimation error, into the initial nonparametric regression estimator, we obtain a debiased estimator that satisfies pointwise and uniform risk convergence, along with asymptotic normality, under mild smoothness conditions. These properties facilitate statistical inference and enhance robustness to covariate shift, making the method broadly applicable to a wide range of nonparametric regression problems.

Masahiro Kato

This study investigates an asymptotically minimax optimal algorithm in the two-armed fixed-budget best-arm identification (BAI) problem. Given two treatment arms, the objective is to identify the arm with the highest expected outcome through an adaptive experiment. We focus on the Neyman allocation, where treatment arms are allocated following the ratio of their outcome standard deviations. Our primary contribution is to prove the minimax optimality of the Neyman allocation for the simple regret, defined as the difference between the expected outcomes of the true best arm and the estimated best arm. Specifically, we first derive a minimax lower bound for the expected simple regret, which characterizes the worst-case performance achievable under the location-shift distributions, including Gaussian distributions. We then show that the simple regret of the Neyman allocation asymptotically matches this lower bound, including the constant term, not just the rate in terms of the sample size, under the worst-case distribution. Notably, our optimality result holds without imposing locality restrictions on the distribution, such as the local asymptotic normality. Furthermore, we demonstrate that the Neyman allocation reduces to the uniform allocation, i.e., the standard randomized controlled trial, under Bernoulli distributions.

Masahiro Kato

This study introduces a debiasing method for regression estimators, including high-dimensional and nonparametric regression estimators. For example, nonparametric regression methods allow for the estimation of regression functions in a data-driven manner with minimal assumptions; however, these methods typically fail to achieve $\sqrt{n}$-consistency in their convergence rates, and many, including those in machine learning, lack guarantees that their estimators asymptotically follow a normal distribution. To address these challenges, we propose a debiasing technique for nonparametric estimators by adding a bias-correction term to the original estimators, extending the conventional one-step estimator used in semiparametric analysis. Specifically, for each data point, we estimate the conditional expected residual of the original nonparametric estimator, which can, for instance, be computed using kernel (Nadaraya-Watson) regression, and incorporate it as a bias-reduction term. Our theoretical analysis demonstrates that the proposed estimator achieves $\sqrt{n}$-consistency and asymptotic normality under a mild convergence rate condition for both the original nonparametric estimator and the conditional expected residual estimator. Notably, this approach remains model-free as long as the original estimator and the conditional expected residual estimator satisfy the convergence rate condition. The proposed method offers several advantages, including improved estimation accuracy and simplified construction of confidence intervals.

Junpei Komiyama, Kaito Ariu, Masahiro Kato et al.

We consider best arm identification in the multi-armed bandit problem. Assuming certain continuity conditions of the prior, we characterize the rate of the Bayesian simple regret. Differing from Bayesian regret minimization (Lai, 1987), the leading term in the Bayesian simple regret derives from the region where the gap between optimal and suboptimal arms is smaller than $\sqrt{\frac{\log T}{T}}$. We propose a simple and easy-to-compute algorithm with its leading term matching with the lower bound up to a constant factor; simulation results support our theoretical findings.

Kaito Ariu, Masahiro Kato, Junpei Komiyama et al.

We consider the "policy choice" problem -- otherwise known as best arm identification in the bandit literature -- proposed by Kasy and Sautmann (2021) for adaptive experimental design. Theorem 1 of Kasy and Sautmann (2021) provides three asymptotic results that give theoretical guarantees for exploration sampling developed for this setting. We first show that the proof of Theorem 1 (1) has technical issues, and the proof and statement of Theorem 1 (2) are incorrect. We then show, through a counterexample, that Theorem 1 (3) is false. For the former two, we correct the statements and provide rigorous proofs. For Theorem 1 (3), we propose an alternative objective function, which we call posterior weighted policy regret, and derive the asymptotic optimality of exploration sampling.

Masahiro Kato, Kaito Ariu

We study the best-arm identification problem with fixed confidence when contextual (covariate) information is available in stochastic bandits. Although we can use contextual information in each round, we are interested in the marginalized mean reward over the contextual distribution. Our goal is to identify the best arm with a minimal number of samplings under a given value of the error rate. We show the instance-specific sample complexity lower bounds for the problem. Then, we propose a context-aware version of the "Track-and-Stop" strategy, wherein the proportion of the arm draws tracks the set of optimal allocations and prove that the expected number of arm draws matches the lower bound asymptotically. We demonstrate that contextual information can be used to improve the efficiency of the identification of the best marginalized mean reward compared with the results of Garivier & Kaufmann (2016). We experimentally confirm that context information contributes to faster best-arm identification.

Riku Togashi, Masahiro Kato, Mayu Otani et al.

Learning from implicit feedback is challenging because of the difficult nature of the one-class problem: we can observe only positive examples. Most conventional methods use a pairwise ranking approach and negative samplers to cope with the one-class problem. However, such methods have two main drawbacks particularly in large-scale applications; (1) the pairwise approach is severely inefficient due to the quadratic computational cost; and (2) even recent model-based samplers (e.g. IRGAN) cannot achieve practical efficiency due to the training of an extra model. In this paper, we propose a learning-to-rank approach, which achieves convergence speed comparable to the pointwise counterpart while performing similarly to the pairwise counterpart in terms of ranking effectiveness. Our approach estimates the probability densities of positive items for each user within a rich class of distributions, viz. \emph{exponential family}. In our formulation, we derive a loss function and the appropriate negative sampling distribution based on maximum likelihood estimation. We also develop a practical technique for risk approximation and a regularisation scheme. We then discuss that our single-model approach is equivalent to an IRGAN variant under a certain condition. Through experiments on real-world datasets, our approach outperforms the pointwise and pairwise counterparts in terms of effectiveness and efficiency.

Masahiro Kato

Adaptive experiments, including efficient average treatment effect estimation and multi-armed bandit algorithms, have garnered attention in various applications, such as social experiments, clinical trials, and online advertisement optimization. This paper considers estimating the mean outcome of an action from samples obtained in adaptive experiments. In causal inference, the mean outcome of an action has a crucial role, and the estimation is an essential task, where the average treatment effect estimation and off-policy value estimation are its variants. In adaptive experiments, the probability of choosing an action (logging policy) is allowed to be sequentially updated based on past observations. Due to this logging policy depending on the past observations, the samples are often not independent and identically distributed (i.i.d.), making developing an asymptotically normal estimator difficult. A typical approach for this problem is to assume that the logging policy converges in a time-invariant function. However, this assumption is restrictive in various applications, such as when the logging policy fluctuates or becomes zero at some periods. To mitigate this limitation, we propose another assumption that the average logging policy converges to a time-invariant function and show the doubly robust (DR) estimator's asymptotic normality. Under the assumption, the logging policy itself can fluctuate or be zero for some actions. We also show the empirical properties by simulations.

Riku Togashi, Masahiro Kato, Mayu Otani et al.

Learning from implicit user feedback is challenging as we can only observe positive samples but never access negative ones. Most conventional methods cope with this issue by adopting a pairwise ranking approach with negative sampling. However, the pairwise ranking approach has a severe disadvantage in the convergence time owing to the quadratically increasing computational cost with respect to the sample size; it is problematic, particularly for large-scale datasets and complex models such as neural networks. By contrast, a pointwise approach does not directly solve a ranking problem, and is therefore inferior to a pairwise counterpart in top-K ranking tasks; however, it is generally advantageous in regards to the convergence time. This study aims to establish an approach to learn personalised ranking from implicit feedback, which reconciles the training efficiency of the pointwise approach and ranking effectiveness of the pairwise counterpart. The key idea is to estimate the ranking of items in a pointwise manner; we first reformulate the conventional pointwise approach based on density ratio estimation and then incorporate the essence of ranking-oriented approaches (e.g. the pairwise approach) into our formulation. Through experiments on three real-world datasets, we demonstrate that our approach not only dramatically reduces the convergence time (one to two orders of magnitude faster) but also significantly improving the ranking performance.

Masahiro Kato, Zhenghang Cui, Yoshihiro Fukuhara

This paper proposes a classification framework with a rejection option to mitigate the performance deterioration caused by adversarial examples. While recent machine learning algorithms achieve high prediction performance, they are empirically vulnerable to adversarial examples, which are slightly perturbed data samples that are wrongly classified. In real-world applications, adversarial attacks using such adversarial examples could cause serious problems. To this end, various methods are proposed to obtain a classifier that is robust against adversarial examples. Adversarial training is one of them, which trains a classifier to minimize the worst-case loss under adversarial attacks. In this paper, in order to acquire a more reliable classifier against adversarial attacks, we propose the method of Adversarial Training with a Rejection Option (ATRO). Applying the adversarial training objective to both a classifier and a rejection function simultaneously, classifiers trained by ATRO can choose to abstain from classification when it has insufficient confidence to classify a test data point. We examine the feasibility of the framework using the surrogate maximum hinge loss and establish a generalization bound for linear models. Furthermore, we empirically confirmed the effectiveness of ATRO using various models and real-world datasets.

Masahiro Kato, Yusuke Kaneko

The goal of off-policy evaluation (OPE) is to evaluate a new policy using historical data obtained via a behavior policy. However, because the contextual bandit algorithm updates the policy based on past observations, the samples are not independent and identically distributed (i.i.d.). This paper tackles this problem by constructing an estimator from a martingale difference sequence (MDS) for the dependent samples. In the data-generating process, we do not assume the convergence of the policy, but the policy uses the same conditional probability of choosing an action during a certain period. Then, we derive an asymptotically normal estimator of the value of an evaluation policy. As another advantage of our method, the batch-based approach simultaneously solves the deficient support problem. Using benchmark and real-world datasets, we experimentally confirm the effectiveness of the proposed method.

Masahiro Kato, Kenshi Abe, Kaito Ariu et al.

Off-policy evaluation (OPE) is the problem of estimating the value of a target policy from samples obtained via different policies. Recently, applying OPE methods for bandit problems has garnered attention. For the theoretical guarantees of an estimator of the policy value, the OPE methods require various conditions on the target policy and policy used for generating the samples. However, existing studies did not carefully discuss the practical situation where such conditions hold, and the gap between them remains. This paper aims to show new results for bridging the gap. Based on the properties of the evaluation policy, we categorize OPE situations. Then, among practical applications, we mainly discuss the best policy selection. For the situation, we propose a meta-algorithm based on existing OPE estimators. We investigate the proposed concepts using synthetic and open real-world datasets in experiments.

Masahiro Kato, Shota Yasui, Kenichiro McAlinn

The doubly robust (DR) estimator, which consists of two nuisance parameters, the conditional mean outcome and the logging policy (the probability of choosing an action), is crucial in causal inference. This paper proposes a DR estimator for dependent samples obtained from adaptive experiments. To obtain an asymptotically normal semiparametric estimator from dependent samples with non-Donsker nuisance estimators, we propose adaptive-fitting as a variant of sample-splitting. We also report an empirical paradox that our proposed DR estimator tends to show better performances compared to other estimators utilizing the true logging policy. While a similar phenomenon is known for estimators with i.i.d. samples, traditional explanations based on asymptotic efficiency cannot elucidate our case with dependent samples. We confirm this hypothesis through simulation studies.

Masahiro Kato, Kei Nakagawa, Kenshi Abe et al.

This study investigates the mean-variance (MV) trade-off in reinforcement learning (RL), an instance of the sequential decision-making under uncertainty. Our objective is to obtain MV-efficient policies whose means and variances are located on the Pareto efficient frontier with respect to the MV trade-off; under the condition, any increase in the expected reward would necessitate a corresponding increase in variance, and vice versa. To this end, we propose a method that trains our policy to maximize the expected quadratic utility, defined as a weighted sum of the first and second moments of the rewards obtained through our policy. We subsequently demonstrate that the maximizer indeed qualifies as an MV-efficient policy. Previous studies that employed constrained optimization to address the MV trade-off have encountered computational challenges. However, our approach is more computationally efficient as it eliminates the need for gradient estimation of variance, a contributing factor to the double sampling issue observed in existing methodologies. Through experimentation, we validate the efficacy of our approach.

Masahiro Kato

This study addresses the problem of off-policy evaluation (OPE) from dependent samples obtained via the bandit algorithm. The goal of OPE is to evaluate a new policy using historical data obtained from behavior policies generated by the bandit algorithm. Because the bandit algorithm updates the policy based on past observations, the samples are not independent and identically distributed (i.i.d.). However, several existing methods for OPE do not take this issue into account and are based on the assumption that samples are i.i.d. In this study, we address this problem by constructing an estimator from a standardized martingale difference sequence. To standardize the sequence, we consider using evaluation data or sample splitting with a two-step estimation. This technique produces an estimator with asymptotic normality without restricting a class of behavior policies. In an experiment, the proposed estimator performs better than existing methods, which assume that the behavior policy converges to a time-invariant policy.

Masahiro Kato, Takeshi Teshima

Density ratio estimation (DRE) is at the core of various machine learning tasks such as anomaly detection and domain adaptation. In existing studies on DRE, methods based on Bregman divergence (BD) minimization have been extensively studied. However, BD minimization when applied with highly flexible models, such as deep neural networks, tends to suffer from what we call train-loss hacking, which is a source of overfitting caused by a typical characteristic of empirical BD estimators. In this paper, to mitigate train-loss hacking, we propose a non-negative correction for empirical BD estimators. Theoretically, we confirm the soundness of the proposed method through a generalization error bound. Through our experiments, the proposed methods show a favorable performance in inlier-based outlier detection.

Masahiro Kato, Masatoshi Uehara, Shota Yasui

We consider evaluating and training a new policy for the evaluation data by using the historical data obtained from a different policy. The goal of off-policy evaluation (OPE) is to estimate the expected reward of a new policy over the evaluation data, and that of off-policy learning (OPL) is to find a new policy that maximizes the expected reward over the evaluation data. Although the standard OPE and OPL assume the same distribution of covariate between the historical and evaluation data, a covariate shift often exists, i.e., the distribution of the covariate of the historical data is different from that of the evaluation data. In this paper, we derive the efficiency bound of OPE under a covariate shift. Then, we propose doubly robust and efficient estimators for OPE and OPL under a covariate shift by using a nonparametric estimator of the density ratio between the historical and evaluation data distributions. We also discuss other possible estimators and compare their theoretical properties. Finally, we confirm the effectiveness of the proposed estimators through experiments.

Masahiro Kato, Takuya Ishihara, Junya Honda et al.

We study how to efficiently estimate average treatment effects (ATEs) using adaptive experiments. In adaptive experiments, experimenters sequentially assign treatments to experimental units while updating treatment assignment probabilities based on past data. We start by defining the efficient treatment-assignment probability, which minimizes the semiparametric efficiency bound for ATE estimation. Our proposed experimental design estimates and uses the efficient treatment-assignment probability to assign treatments. At the end of the proposed design, the experimenter estimates the ATE using a newly proposed Adaptive Augmented Inverse Probability Weighting (A2IPW) estimator. We show that the asymptotic variance of the A2IPW estimator using data from the proposed design achieves the minimized semiparametric efficiency bound. We also analyze the estimator's finite-sample properties and develop nonparametric and nonasymptotic confidence intervals that are valid at any round of the proposed design. These anytime valid confidence intervals allow us to conduct rate-optimal sequential hypothesis testing, allowing for early stopping and reducing necessary sample size.

Masahiro Kato, Hikaru Kawarazaki

We propose a novel framework of the model specification test in regression using unlabeled test data. In many cases, we have conducted statistical inferences based on the assumption that we can correctly specify a model. However, it is difficult to confirm whether a model is correctly specified. To overcome this problem, existing works have devised statistical tests for model specification. Existing works have defined a correctly specified model in regression as a model with zero conditional mean of the error term over train data only. Extending the definition in conventional statistical tests, we define a correctly specified model as a model with zero conditional mean of the error term over any distribution of the explanatory variable. This definition is a natural consequence of the orthogonality of the explanatory variable and the error term. If a model does not satisfy this condition, the model might lack robustness with regards to the distribution shift. The proposed method would enable us to reject a misspecified model under our definition. By applying the proposed method, we can obtain a model that predicts the label for the unlabeled test data well without losing the interpretability of the model. In experiments, we show how the proposed method works for synthetic and real-world datasets.

Ryuichi Ueda, Masahiro Kato, Atsushi Saito

Differently from animals, robots can record its experience correctly for long time. We propose a novel algorithm that runs a particle filter on the time sequence of the experience. It can be applied to some teach-and-replay tasks. In a task, the trainer controls a robot, and the robot records its sensor readings and its actions. We name the sequence of the record an episode, which is derived from the episodic memory of animals. After that, the robot executes the particle filter so as to find a similar situation with the current one from the episode. If the robot chooses the action taken in the similar situation, it can replay the taught behavior. We name this algorithm the particle filter on episode (PFoE). The robot with PFoE shows not only a simple replay of a behavior but also recovery motion from skids and interruption. In this paper, we evaluate the properties of PFoE with a small mobile robot.

Masahiro Kato, Liyuan Xu, Gang Niu et al.

We consider a problem of learning a binary classifier only from positive data and unlabeled data (PU learning) and estimating the class-prior in unlabeled data under the case-control scenario. Most of the recent methods of PU learning require an estimate of the class-prior probability in unlabeled data, and it is estimated in advance with another method. However, such a two-step approach which first estimates the class prior and then trains a classifier may not be the optimal approach since the estimation error of the class-prior is not taken into account when a classifier is trained. In this paper, we propose a novel unified approach to estimating the class-prior and training a classifier alternately. Our proposed method is simple to implement and computationally efficient. Through experiments, we demonstrate the practical usefulness of the proposed method.