arXiv subjects

Junya Honda

Publications and source records attributed to Junya Honda.

At least 19 recordsLinked to original sources

arXiv2026

SAVER: Stochastic Adaptive Variance-Driven Exploration and Reconstruction for Low-Dose Computed Tomography

Computed Tomography (CT) is indispensable in clinical diagnostics, yet minimizing radiation dose without compromising image quality remains a critical challenge. Conventional low-dose protocols often rely on fixed, uniform angular sampling, independent of the underlying structural complexity of organs of individual patients. We propose ``Stochastic Adaptive Variance-Driven Exploration and Reconstruction'' (SAVER), an adaptive data acquisition framework that selects projection angles in real-time based on the statistical variance of acquired data. Utilizing a Softmax-based stochastic scheduling scheme with simulated annealing, SAVER prioritizes directions with high structural information while maintaining necessary exploration. Numerical experiments across 8 diverse phantoms demonstrate that SAVER achieves consistently higher reconstruction fidelity than conventional random sampling, particularly for objects with high structural anisotropy. Furthermore, the proposed method exhibits robust performance under significant measurement noise. By dynamically reallocating radiation dose to the most informative projections, SAVER provides a mathematically-grounded approach to maximize diagnostic quality per unit of radiation dose, marking a shift toward sample-dependent, data-driven CT acquisition.

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arXiv2026

Adaptive Learning Rates with Surrogate Probability for Follow-the-Perturbed-Leader

Follow-the-regularized-leader framework has shown effectiveness and flexibility in online learning problems, where the choice of learning rates are known to be crucial. Recently, adaptive learning rates defined in terms of the arm-selection probabilities, obtained by solving convex optimization, have achieved improved best-of-both-worlds (BOBW) guarantees in various bandit problems. In contrast, BOBW guarantees for its computationally efficient alternative, follow-the-perturbed-leader (FTPL), remain relatively limited since its optimization-free nature ironically makes the design of adaptive, probability-dependent learning rates non-trivial. To address this challenge, we propose an adaptive learning rate for FTPL by introducing surrogate probability functions that can be computed only from the available quantities, without requiring the exact probabilities. Based on these learning rates with surrogate functions, we provide the BOBW guarantee for FTPL with Pareto perturbations for any shape parameter $\alpha >1$, generalizing prior results restricted to specific choices of $\alpha=2$. We further show the BOBW guarantees for FTPL with adaptive learning rates in the bandit problem with expert advices. Our approach preserves the computational simplicity of FTPL while enabling probability-dependent adaptivity, and the surrogate-based methodology may be of independent interest in other algorithmic frameworks beyond FTPL and learning rate designs.

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arXiv2026

Rate-optimal Design for Anytime Best Arm Identification

We consider the best arm identification problem, where the goal is to identify the arm with the highest mean reward from a set of $K$ arms under a limited sampling budget. This problem models many practical scenarios such as A/B testing. We consider a class of algorithms for this problem, which is provably minimax optimal up to a constant factor. This idea is a generalization of existing works in fixed-budget best arm identification, which are limited to a particular choice of risk measures. Based on the framework, we propose Almost Tracking, a closed-form algorithm that has a provable guarantee on the popular risk measure $H_1$. Unlike existing algorithms, Almost Tracking does not require the total budget in advance nor does it need to discard a significant part of samples, which gives a practical advantage. Through experiments on synthetic and real-world datasets, we show that our algorithm outperforms existing anytime algorithms as well as fixed-budget algorithms.

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arXiv2026

A Further Efficient Algorithm with Best-of-Both-Worlds Guarantees for $m$-Set Semi-Bandit Problem

This paper studies the optimality and complexity of Follow-the-Perturbed-Leader (FTPL) policy in $m$-set semi-bandit problems. FTPL has been studied extensively as a promising candidate of an efficient algorithm with favorable regret for adversarial combinatorial semi-bandits. Nevertheless, the optimality of FTPL has still been unknown unlike Follow-the-Regularized-Leader (FTRL) whose optimality has been proved for various tasks of online learning. In this paper, we extend the analysis of FTPL with geometric resampling (GR) to $m$-set semi-bandits, which is a special case of combinatorial semi-bandits, showing that FTPL with Fréchet and Pareto distributions with certain parameters achieves the best possible regret of $O(\sqrt{mdT})$ in adversarial setting. We also show that FTPL with Fréchet and Pareto distributions with a certain parameter achieves a logarithmic regret for stochastic setting, meaning the Best-of-Both-Worlds optimality of FTPL for $m$-set semi-bandit problems. Furthermore, we extend the conditional geometric resampling to $m$-set semi-bandits for efficient loss estimation in FTPL, reducing the computational complexity from $O(d^2)$ of the original geometric resampling to $O(md(\log(d/m)+1))$ without sacrificing the regret performance.

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arXiv2025

Revisiting Follow-the-Perturbed-Leader with Unbounded Perturbations in Bandit Problems

Follow-the-Regularized-Leader (FTRL) policies have achieved Best-of-Both-Worlds (BOBW) results in various settings through hybrid regularizers, whereas analogous results for Follow-the-Perturbed-Leader (FTPL) remain limited due to inherent analytical challenges. To advance the analytical foundations of FTPL, we revisit classical FTRL-FTPL duality for unbounded perturbations and establish BOBW results for FTPL under a broad family of asymmetric unbounded Fréchet-type perturbations, including hybrid perturbations combining Gumbel-type and Fréchet-type tails. These results not only extend the BOBW results of FTPL but also offer new insights into designing alternative FTPL policies competitive with hybrid regularization approaches. Motivated by earlier observations in two-armed bandits, we further investigate the connection between the $1/2$-Tsallis entropy and a Fréchet-type perturbation. Our numerical observations suggest that it corresponds to a symmetric Fréchet-type perturbation, and based on this, we establish the first BOBW guarantee for symmetric unbounded perturbations in the two-armed setting. In contrast, in general multi-armed bandits, we find an instance in which symmetric Fréchet-type perturbations violate the key condition for standard BOBW analysis, which is a problem not observed with asymmetric or nonnegative Fréchet-type perturbations. Although this example does not rule out alternative analyses achieving BOBW results, it suggests the limitations of directly applying the relationship observed in two-armed cases to the general case and thus emphasizes the need for further investigation to fully understand the behavior of FTPL in broader settings.

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arXiv2025

Thompson Exploration with Best Challenger Rule in Best Arm Identification

This paper studies the fixed-confidence best arm identification (BAI) problem in the bandit framework in the canonical single-parameter exponential models. For this problem, many policies have been proposed, but most of them require solving an optimization problem at every round and/or are forced to explore an arm at least a certain number of times except those restricted to the Gaussian model. To address these limitations, we propose a novel policy that combines Thompson sampling with a computationally efficient approach known as the best challenger rule. While Thompson sampling was originally considered for maximizing the cumulative reward, we demonstrate that it can be used to naturally explore arms in BAI without forcing it. We show that our policy is asymptotically optimal for any two-armed bandit problems and achieves near optimality for general $K$-armed bandit problems for $K\geq 3$. Nevertheless, in numerical experiments, our policy shows competitive performance compared to asymptotically optimal policies in terms of sample complexity while requiring less computation cost. In addition, we highlight the advantages of our policy by comparing it to the concept of $β$-optimality, a relaxed notion of asymptotic optimality commonly considered in the analysis of a class of policies including the proposed one.

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arXiv2025

Note on Follow-the-Perturbed-Leader in Combinatorial Semi-Bandit Problems

This paper studies the optimality and complexity of Follow-the-Perturbed-Leader (FTPL) policy in size-invariant combinatorial semi-bandit problems. Recently, Honda et al. (2023) and Lee et al. (2024) showed that FTPL achieves Best-of-Both-Worlds (BOBW) optimality in standard multi-armed bandit problems with Fréchet-type distributions. However, the optimality of FTPL in combinatorial semi-bandit problems remains unclear. In this paper, we consider the regret bound of FTPL with geometric resampling (GR) in size-invariant semi-bandit setting, showing that FTPL respectively achieves $O\left(\sqrt{m^2 d^\frac{1}αT}+\sqrt{mdT}\right)$ regret with Fréchet distributions, and the best possible regret bound of $O\left(\sqrt{mdT}\right)$ with Pareto distributions in adversarial setting. Furthermore, we extend the conditional geometric resampling (CGR) to size-invariant semi-bandit setting, which reduces the computational complexity from $O(d^2)$ of original GR to $O\left(md\left(\log(d/m)+1\right)\right)$ without sacrificing the regret performance of FTPL.

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arXiv2025

Optimal Regret of Bernoulli Bandits under Global Differential Privacy

As sequential learning algorithms are increasingly applied to real life, ensuring data privacy while maintaining their utilities emerges as a timely question. In this context, regret minimisation in stochastic bandits under $ε$-global Differential Privacy (DP) has been widely studied. Unlike bandits without DP, there is a significant gap between the best-known regret lower and upper bound in this setting, though they "match" in order. Thus, we revisit the regret lower and upper bounds of $ε$-global DP algorithms for Bernoulli bandits and improve both. First, we prove a tighter regret lower bound involving a novel information-theoretic quantity characterising the hardness of $ε$-global DP in stochastic bandits. Our lower bound strictly improves on the existing ones across all $ε$ values. Then, we choose two asymptotically optimal bandit algorithms, i.e. DP-KLUCB and DP-IMED, and propose their DP versions using a unified blueprint, i.e., (a) running in arm-dependent phases, and (b) adding Laplace noise to achieve privacy. For Bernoulli bandits, we analyse the regrets of these algorithms and show that their regrets asymptotically match our lower bound up to a constant arbitrary close to 1. This refutes the conjecture that forgetting past rewards is necessary to design optimal bandit algorithms under global DP. At the core of our algorithms lies a new concentration inequality for sums of Bernoulli variables under Laplace mechanism, which is a new DP version of the Chernoff bound. This result is universally useful as the DP literature commonly treats the concentrations of Laplace noise and random variables separately, while we couple them to yield a tighter bound.

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arXiv2025

Multi-Player Approaches for Dueling Bandits

Various approaches have emerged for multi-armed bandits in distributed systems. The multiplayer dueling bandit problem, common in scenarios with only preference-based information like human feedback, introduces challenges related to controlling collaborative exploration of non-informative arm pairs, but has received little attention. To fill this gap, we demonstrate that the direct use of a Follow Your Leader black-box approach matches the lower bound for this setting when utilizing known dueling bandit algorithms as a foundation. Additionally, we analyze a message-passing fully distributed approach with a novel Condorcet-winner recommendation protocol, resulting in expedited exploration in many cases. Our experimental comparisons reveal that our multiplayer algorithms surpass single-player benchmark algorithms, underscoring their efficacy in addressing the nuanced challenges of the multiplayer dueling bandit setting.

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arXiv2025

Efficient Adaptive Experimental Design for Average Treatment Effect Estimation

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.

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arXiv2025

Exploration by Optimization with Hybrid Regularizers: Logarithmic Regret with Adversarial Robustness in Partial Monitoring

Partial monitoring is a generic framework of online decision-making problems with limited feedback. To make decisions from such limited feedback, it is necessary to find an appropriate distribution for exploration. Recently, a powerful approach for this purpose, \emph{exploration by optimization} (ExO), was proposed, which achieves optimal bounds in adversarial environments with follow-the-regularized-leader for a wide range of online decision-making problems. However, a naive application of ExO in stochastic environments significantly degrades regret bounds. To resolve this issue in locally observable games, we first establish a new framework and analysis for ExO with a hybrid regularizer. This development allows us to significantly improve existing regret bounds of best-of-both-worlds (BOBW) algorithms, which achieves nearly optimal bounds both in stochastic and adversarial environments. In particular, we derive a stochastic regret bound of $O(\sum_{a \neq a^*} k^2 m^2 \log T / Δ_a)$, where $k$, $m$, and $T$ are the numbers of actions, observations and rounds, $a^*$ is an optimal action, and $Δ_a$ is the suboptimality gap for action $a$. This bound is roughly $Θ(k^2 \log T)$ times smaller than existing BOBW bounds. In addition, for globally observable games, we provide a new BOBW algorithm with the first $O(\log T)$ stochastic bound.

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arXiv2024

A General Recipe for the Analysis of Randomized Multi-Armed Bandit Algorithms

In this paper we propose a general methodology to derive regret bounds for randomized multi-armed bandit algorithms. It consists in checking a set of sufficient conditions on the sampling probability of each arm and on the family of distributions to prove a logarithmic regret. As a direct application we revisit two famous bandit algorithms, Minimum Empirical Divergence (MED) and Thompson Sampling (TS), under various models for the distributions including single parameter exponential families, Gaussian distributions, bounded distributions, or distributions satisfying some conditions on their moments. In particular, we prove that MED is asymptotically optimal for all these models, but also provide a simple regret analysis of some TS algorithms for which the optimality is already known. We then further illustrate the interest of our approach, by analyzing a new Non-Parametric TS algorithm (h-NPTS), adapted to some families of unbounded reward distributions with a bounded h-moment. This model can for instance capture some non-parametric families of distributions whose variance is upper bounded by a known constant.

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arXiv2024

Learning with Posterior Sampling for Revenue Management under Time-varying Demand

This paper discusses the revenue management (RM) problem to maximize revenue by pricing items or services. One challenge in this problem is that the demand distribution is unknown and varies over time in real applications such as airline and retail industries. In particular, the time-varying demand has not been well studied under scenarios of unknown demand due to the difficulty of jointly managing the remaining inventory and estimating the demand. To tackle this challenge, we first introduce an episodic generalization of the RM problem motivated by typical application scenarios. We then propose a computationally efficient algorithm based on posterior sampling, which effectively optimizes prices by solving linear programming. We derive a Bayesian regret upper bound of this algorithm for general models where demand parameters can be correlated between time periods, while also deriving a regret lower bound for generic algorithms. Our empirical study shows that the proposed algorithm performs better than other benchmark algorithms and comparably to the optimal policy in hindsight. We also propose a heuristic modification of the proposed algorithm, which further efficiently learns the pricing policy in the experiments.

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arXiv2024

Adaptive Learning Rate for Follow-the-Regularized-Leader: Competitive Analysis and Best-of-Both-Worlds

Follow-The-Regularized-Leader (FTRL) is known as an effective and versatile approach in online learning, where appropriate choice of the learning rate is crucial for smaller regret. To this end, we formulate the problem of adjusting FTRL's learning rate as a sequential decision-making problem and introduce the framework of competitive analysis. We establish a lower bound for the competitive ratio and propose update rules for learning rate that achieves an upper bound within a constant factor of this lower bound. Specifically, we illustrate that the optimal competitive ratio is characterized by the (approximate) monotonicity of components of the penalty term, showing that a constant competitive ratio is achievable if the components of the penalty term form a monotonically non-increasing sequence, and derive a tight competitive ratio when penalty terms are $ξ$-approximately monotone non-increasing. Our proposed update rule, referred to as \textit{stability-penalty matching}, also facilitates constructing the Best-Of-Both-Worlds (BOBW) algorithms for stochastic and adversarial environments. In these environments our result contributes to achieve tighter regret bound and broaden the applicability of algorithms for various settings such as multi-armed bandits, graph bandits, linear bandits, and contextual bandits.

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arXiv2024

Follow-the-Perturbed-Leader with Fréchet-type Tail Distributions: Optimality in Adversarial Bandits and Best-of-Both-Worlds

This paper studies the optimality of the Follow-the-Perturbed-Leader (FTPL) policy in both adversarial and stochastic $K$-armed bandits. Despite the widespread use of the Follow-the-Regularized-Leader (FTRL) framework with various choices of regularization, the FTPL framework, which relies on random perturbations, has not received much attention, despite its inherent simplicity. In adversarial bandits, there has been conjecture that FTPL could potentially achieve $\mathcal{O}(\sqrt{KT})$ regrets if perturbations follow a distribution with a Fréchet-type tail. Recent work by Honda et al. (2023) showed that FTPL with Fréchet distribution with shape $α=2$ indeed attains this bound and, notably logarithmic regret in stochastic bandits, meaning the Best-of-Both-Worlds (BOBW) capability of FTPL. However, this result only partly resolves the above conjecture because their analysis heavily relies on the specific form of the Fréchet distribution with this shape. In this paper, we establish a sufficient condition for perturbations to achieve $\mathcal{O}(\sqrt{KT})$ regrets in the adversarial setting, which covers, e.g., Fréchet, Pareto, and Student-$t$ distributions. We also demonstrate the BOBW achievability of FTPL with certain Fréchet-type tail distributions. Our results contribute not only to resolving existing conjectures through the lens of extreme value theory but also potentially offer insights into the effect of the regularization functions in FTRL through the mapping from FTPL to FTRL.

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arXiv2024

Stability-penalty-adaptive follow-the-regularized-leader: Sparsity, game-dependency, and best-of-both-worlds

Adaptivity to the difficulties of a problem is a key property in sequential decision-making problems to broaden the applicability of algorithms. Follow-the-regularized-leader (FTRL) has recently emerged as one of the most promising approaches for obtaining various types of adaptivity in bandit problems. Aiming to further generalize this adaptivity, we develop a generic adaptive learning rate, called stability-penalty-adaptive (SPA) learning rate for FTRL. This learning rate yields a regret bound jointly depending on stability and penalty of the algorithm, into which the regret of FTRL is typically decomposed. With this result, we establish several algorithms with three types of adaptivity: sparsity, game-dependency, and best-of-both-worlds (BOBW). Despite the fact that sparsity appears frequently in real problems, existing sparse multi-armed bandit algorithms with $k$-arms assume that the sparsity level $s \leq k$ is known in advance, which is often not the case in real-world scenarios. To address this issue, we first establish $s$-agnostic algorithms with regret bounds of $\tilde{O}(\sqrt{sT})$ in the adversarial regime for $T$ rounds, which matches the existing lower bound up to a logarithmic factor. Meanwhile, BOBW algorithms aim to achieve a near-optimal regret in both the stochastic and adversarial regimes. Leveraging the SPA learning rate and the technique for $s$-agnostic algorithms combined with a new analysis to bound the variation in FTRL output in response to changes in a regularizer, we establish the first BOBW algorithm with a sparsity-dependent bound. Additionally, we explore partial monitoring and demonstrate that the proposed SPA learning rate framework allows us to achieve a game-dependent bound and the BOBW simultaneously.

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arXiv2024

The Survival Bandit Problem

We introduce and study a new variant of the multi-armed bandit problem (MAB), called the survival bandit problem (S-MAB). While in both problems, the objective is to maximize the so-called cumulative reward, in this new variant, the procedure is interrupted if the cumulative reward falls below a preset threshold. This simple yet unexplored extension of the MAB follows from many practical applications. For example, when testing two medicines against each other on voluntary patients, people's health are at stake, and it is necessary to be able to interrupt experiments if serious side effects occur or if the disease syndromes are not dissipated by the treatment. From a theoretical perspective, the S-MAB is the first variant of the MAB where the procedure may or may not be interrupted. We start by formalizing the S-MAB and we define its objective as the minimization of the so-called survival regret, which naturally generalizes the regret of the MAB. Then, we show that the objective of the S-MAB is considerably more difficult than the MAB, in the sense that contrary to the MAB, no policy can achieve a reasonably small (i.e., sublinear) survival regret. Instead, we minimize the survival regret in the sense of Pareto, i.e., we seek a policy whose cumulative reward cannot be improved for some problem instance without being sacrificed for another one. For that purpose, we identify two key components in the survival regret: the regret given no ruin (which corresponds to the regret in the MAB), and the probability that the procedure is interrupted, called the probability of ruin. We derive a lower bound on the probability of ruin, as well as policies whose probability of ruin matches the lower bound. Finally, based on a doubling trick on those policies, we derive a policy which minimizes the survival regret in the sense of Pareto, giving an answer to an open problem by Perotto et al. (COLT 2019).

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arXiv2023

Finite-time Analysis of Globally Nonstationary Multi-Armed Bandits

We consider nonstationary multi-armed bandit problems where the model parameters of the arms change over time. We introduce the adaptive resetting bandit (ADR-bandit), a bandit algorithm class that leverages adaptive windowing techniques from literature on data streams. We first provide new guarantees on the quality of estimators resulting from adaptive windowing techniques, which are of independent interest. Furthermore, we conduct a finite-time analysis of ADR-bandit in two typical environments: an abrupt environment where changes occur instantaneously and a gradual environment where changes occur progressively. We demonstrate that ADR-bandit has nearly optimal performance when abrupt or gradual changes occur in a coordinated manner that we call global changes. We demonstrate that forced exploration is unnecessary when we assume such global changes. Unlike the existing nonstationary bandit algorithms, ADR-bandit has optimal performance in stationary environments as well as nonstationary environments with global changes. Our experiments show that the proposed algorithms outperform the existing approaches in synthetic and real-world environments.

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