Jongyeong Lee

Jongyeong Lee, Junya Honda, Shinji Ito et al.

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 $α>1$, generalizing prior results restricted to specific choices of $α=2$. 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.

Jongyeong Lee, Junya Honda, Chao-Kai Chiang et al.

In the stochastic multi-armed bandit problem, a randomized probability matching policy called Thompson sampling (TS) has shown excellent performance in various reward models. In addition to the empirical performance, TS has been shown to achieve asymptotic problem-dependent lower bounds in several models. However, its optimality has been mainly addressed under light-tailed or one-parameter models that belong to exponential families. In this paper, we consider the optimality of TS for the Pareto model that has a heavy tail and is parameterized by two unknown parameters. Specifically, we discuss the optimality of TS with probability matching priors that include the Jeffreys prior and the reference priors. We first prove that TS with certain probability matching priors can achieve the optimal regret bound. Then, we show the suboptimality of TS with other priors, including the Jeffreys and the reference priors. Nevertheless, we find that TS with the Jeffreys and reference priors can achieve the asymptotic lower bound if one uses a truncation procedure. These results suggest carefully choosing noninformative priors to avoid suboptimality and show the effectiveness of truncation procedures in TS-based policies.

Jongyeong Lee, Chao-Kai Chiang, Masashi Sugiyama

Thompson sampling (TS) has been known for its outstanding empirical performance supported by theoretical guarantees across various reward models in the classical stochastic multi-armed bandit problems. Nonetheless, its optimality is often restricted to specific priors due to the common observation that TS is fairly insensitive to the choice of the prior when it comes to asymptotic regret bounds. However, when the model contains multiple parameters, the optimality of TS highly depends on the choice of priors, which casts doubt on the generalizability of previous findings to other models. To address this gap, this study explores the impact of selecting noninformative priors, offering insights into the performance of TS when dealing with new models that lack theoretical understanding. We first extend the regret analysis of TS to the model of uniform distributions with unknown supports, which would be the simplest non-regular model. Our findings reveal that changing noninformative priors can significantly affect the expected regret, aligning with previously known results in other multiparameter bandit models. Although the uniform prior is shown to be optimal, we highlight the inherent limitation of its optimality, which is limited to specific parameterizations and emphasizes the significance of the invariance property of priors. In light of this limitation, we propose a slightly modified TS-based policy, called TS with Truncation (TS-T), which can achieve the asymptotic optimality for the Gaussian models and the uniform models by using the reference prior and the Jeffreys prior that are invariant under one-to-one reparameterizations. This policy provides an alternative approach to achieving optimality by employing fine-tuned truncation, which would be much easier than hunting for optimal priors in practice.

Jongyeong Lee, Junya Honda, Masashi Sugiyama

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.

Botao Chen, Jongyeong Lee, Chansoo Kim et al.

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.

Jongyeong Lee, Junya Honda, Shinji Ito et al.

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.

Jongyeong Lee, Junya Honda, Shinji Ito et al.

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.

Chaiwon Kim, Jongyeong Lee, Min-hwan Oh

We study the decoupled multi-armed bandit (MAB) problem, where the learner selects one arm for exploration and one arm for exploitation in each round. The loss of the explored arm is observed but not counted, while the loss of the exploited arm is incurred without being observed. We propose a policy within the Follow-the-Perturbed-Leader (FTPL) framework using Pareto perturbations. Our policy achieves (near-)optimal regret regardless of the environment, i.e., Best-of-Both-Worlds (BOBW): constant regret in the stochastic regime, improving upon the optimal bound of the standard MABs, and minimax optimal regret in the adversarial regime. Moreover, the practicality of our policy stems from avoiding both the convex optimization step required by the previous BOBW policy, Decoupled-Tsallis-INF (Rouyer & Seldin, 2020), and the resampling step that is typically necessary in FTPL. Consequently, it achieves substantial computational improvement, about $20$ times faster than Decoupled-Tsallis-INF, while also demonstrating better empirical performance in both regimes. Finally, we empirically show that our approach outperforms a pure exploration policy, and that naively combining a pure exploration with a standard exploitation policy is suboptimal.

Nontawat Charoenphakdee, Jongyeong Lee, Masashi Sugiyama

When minimizing the empirical risk in binary classification, it is a common practice to replace the zero-one loss with a surrogate loss to make the learning objective feasible to optimize. Examples of well-known surrogate losses for binary classification include the logistic loss, hinge loss, and sigmoid loss. It is known that the choice of a surrogate loss can highly influence the performance of the trained classifier and therefore it should be carefully chosen. Recently, surrogate losses that satisfy a certain symmetric condition (aka., symmetric losses) have demonstrated their usefulness in learning from corrupted labels. In this article, we provide an overview of symmetric losses and their applications. First, we review how a symmetric loss can yield robust classification from corrupted labels in balanced error rate (BER) minimization and area under the receiver operating characteristic curve (AUC) maximization. Then, we demonstrate how the robust AUC maximization method can benefit natural language processing in the problem where we want to learn only from relevant keywords and unlabeled documents. Finally, we conclude this article by discussing future directions, including potential applications of symmetric losses for reliable machine learning and the design of non-symmetric losses that can benefit from the symmetric condition.

Nontawat Charoenphakdee, Jongyeong Lee, Yiping Jin et al.

We consider a document classification problem where document labels are absent but only relevant keywords of a target class and unlabeled documents are given. Although heuristic methods based on pseudo-labeling have been considered, theoretical understanding of this problem has still been limited. Moreover, previous methods cannot easily incorporate well-developed techniques in supervised text classification. In this paper, we propose a theoretically guaranteed learning framework that is simple to implement and has flexible choices of models, e.g., linear models or neural networks. We demonstrate how to optimize the area under the receiver operating characteristic curve (AUC) effectively and also discuss how to adjust it to optimize other well-known evaluation metrics such as the accuracy and F1-measure. Finally, we show the effectiveness of our framework using benchmark datasets.

Jongyeong Lee, Nontawat Charoenphakdee, Seiichi Kuroki et al.

Appropriately evaluating the discrepancy between domains is essential for the success of unsupervised domain adaptation. In this paper, we first point out that existing discrepancy measures are less informative when complex models such as deep neural networks are used, in addition to the facts that they can be computationally highly demanding and their range of applications is limited only to binary classification. We then propose a novel domain discrepancy measure, called the paired hypotheses discrepancy (PHD), to overcome these shortcomings. PHD is computationally efficient and applicable to multi-class classification. Through generalization error bound analysis, we theoretically show that PHD is effective even for complex models. Finally, we demonstrate the practical usefulness of PHD through experiments.

Nontawat Charoenphakdee, Jongyeong Lee, Masashi Sugiyama

This paper aims to provide a better understanding of a symmetric loss. First, we emphasize that using a symmetric loss is advantageous in the balanced error rate (BER) minimization and area under the receiver operating characteristic curve (AUC) maximization from corrupted labels. Second, we prove general theoretical properties of symmetric losses, including a classification-calibration condition, excess risk bound, conditional risk minimizer, and AUC-consistency condition. Third, since all nonnegative symmetric losses are non-convex, we propose a convex barrier hinge loss that benefits significantly from the symmetric condition, although it is not symmetric everywhere. Finally, we conduct experiments to validate the relevance of the symmetric condition.