arXiv subjects

Bongsoo Yi

Publications and source records attributed to Bongsoo Yi.

7 recordsLinked to original sources

arXiv2025

Optimal graph joining with applications to isomorphism detection and identification

We introduce an optimal transport based approach for comparing undirected graphs with non-negative edge weights and general vertex labels, and we study connections between the resulting linear program and the graph isomorphism problem. Our approach is based on the notion of a joining of two graphs $G$ and $H$, which is a product graph that preserves their marginal structure. Given $G$ and $H$ and a vertex-based cost function $c$, the optimal graph joining (OGJ) problem finds a joining of $G$ and $H$ minimizing degree weighted cost. The OGJ problem can be written as a linear program with a convex polyhedral solution set. We establish several basic properties of the OGJ problem, and present theoretical results connecting the OGJ problem to the graph isomorphism problem. In particular, we examine a variety of conditions on graph families that are sufficient to ensure that for every pair of graphs $G$ and $H$ in the family (i) $G$ and $H$ are isomorphic if and only if their optimal joining cost is zero, and (ii) if $G$ and $H$ are isomorphic, the the extreme points of the solution set of the OGJ problem are deterministic joinings corresponding to the isomorphisms from $G$ to $H$.

math.CO↗

arXiv2025

Single Index Bandits: Generalized Linear Contextual Bandits with Unknown Reward Functions

Generalized linear bandits have been extensively studied due to their broad applicability in real-world online decision-making problems. However, these methods typically assume that the expected reward function is known to the users, an assumption that is often unrealistic in practice. Misspecification of this link function can lead to the failure of all existing algorithms. In this work, we address this critical limitation by introducing a new problem of generalized linear bandits with unknown reward functions, also known as single index bandits. We first consider the case where the unknown reward function is monotonically increasing, and propose two novel and efficient algorithms, STOR and ESTOR, that achieve decent regrets under standard assumptions. Notably, our ESTOR can obtain the nearly optimal regret bound $\tilde{O}_T(\sqrt{T})$ in terms of the time horizon $T$. We then extend our methods to the high-dimensional sparse setting and show that the same regret rate can be attained with the sparsity index. Next, we introduce GSTOR, an algorithm that is agnostic to general reward functions, and establish regret bounds under a Gaussian design assumption. Finally, we validate the efficiency and effectiveness of our algorithms through experiments on both synthetic and real-world datasets.

stat.ML↗

arXiv2025

Quantum Lipschitz Bandits

The Lipschitz bandit is a key variant of stochastic bandit problems where the expected reward function satisfies a Lipschitz condition with respect to an arm metric space. With its wide-ranging practical applications, various Lipschitz bandit algorithms have been developed, achieving the cumulative regret lower bound of order $\tilde O(T^{(d_z+1)/(d_z+2)})$ over time horizon $T$. Motivated by recent advancements in quantum computing and the demonstrated success of quantum Monte Carlo in simpler bandit settings, we introduce the first quantum Lipschitz bandit algorithms to address the challenges of continuous action spaces and non-linear reward functions. Specifically, we first leverage the elimination-based framework to propose an efficient quantum Lipschitz bandit algorithm named Q-LAE. Next, we present novel modifications to the classical Zooming algorithm, which results in a simple quantum Lipschitz bandit method, Q-Zooming. Both algorithms exploit the computational power of quantum methods to achieve an improved regret bound of $\tilde O(T^{d_z/(d_z+1)})$. Comprehensive experiments further validate our improved theoretical findings, demonstrating superior empirical performance compared to existing Lipschitz bandit methods.

cs.LG↗

arXiv2024

Improving Clean Accuracy via a Tangent-Space Perspective on Adversarial Training

Adversarial training has proven effective in improving the robustness of deep neural networks against adversarial attacks. However, this enhanced robustness often comes at the cost of a substantial drop in accuracy on clean data. In this paper, we address this limitation by introducing Tangent Direction Guided Adversarial Training (TART), a novel method that enhances clean accuracy by exploiting the geometry of the data manifold. We argue that adversarial examples with large components in the normal direction can overly distort the decision boundary and degrade clean accuracy. TART addresses this issue by estimating the tangent direction of adversarial examples and adaptively modulating the perturbation bound based on the norm of their tangential component. To the best of our knowledge, TART is the first adversarial defense framework that explicitly incorporates the concept of tangent space and direction into adversarial training. Extensive experiments on both synthetic and benchmark datasets demonstrate that TART consistently improves clean accuracy while maintaining robustness against adversarial attacks.

cs.LG↗

arXiv2024

Biased Dueling Bandits with Stochastic Delayed Feedback

The dueling bandit problem, an essential variation of the traditional multi-armed bandit problem, has become significantly prominent recently due to its broad applications in online advertising, recommendation systems, information retrieval, and more. However, in many real-world applications, the feedback for actions is often subject to unavoidable delays and is not immediately available to the agent. This partially observable issue poses a significant challenge to existing dueling bandit literature, as it significantly affects how quickly and accurately the agent can update their policy on the fly. In this paper, we introduce and examine the biased dueling bandit problem with stochastic delayed feedback, revealing that this new practical problem will delve into a more realistic and intriguing scenario involving a preference bias between the selections. We present two algorithms designed to handle situations involving delay. Our first algorithm, requiring complete delay distribution information, achieves the optimal regret bound for the dueling bandit problem when there is no delay. The second algorithm is tailored for situations where the distribution is unknown, but only the expected value of delay is available. We provide a comprehensive regret analysis for the two proposed algorithms and then evaluate their empirical performance on both synthetic and real datasets.

cs.LG↗

arXiv2024

Alignment and Comparison of Directed Networks via Transition Couplings of Random Walks

We describe and study a transport based procedure called NetOTC (network optimal transition coupling) for the comparison and alignment of two networks. The networks of interest may be directed or undirected, weighted or unweighted, and may have distinct vertex sets of different sizes. Given two networks and a cost function relating their vertices, NetOTC finds a transition coupling of their associated random walks having minimum expected cost. The minimizing cost quantifies the difference between the networks, while the optimal transport plan itself provides alignments of both the vertices and the edges of the two networks. Coupling of the full random walks, rather than their marginal distributions, ensures that NetOTC captures local and global information about the networks, and preserves edges. NetOTC has no free parameters, and does not rely on randomization. We investigate a number of theoretical properties of NetOTC and present experiments establishing its empirical performance.

cs.LG↗

arXiv2022

A Gift from Label Smoothing: Robust Training with Adaptive Label Smoothing via Auxiliary Classifier under Label Noise

As deep neural networks can easily overfit noisy labels, robust training in the presence of noisy labels is becoming an important challenge in modern deep learning. While existing methods address this problem in various directions, they still produce unpredictable sub-optimal results since they rely on the posterior information estimated by the feature extractor corrupted by noisy labels. Lipschitz regularization successfully alleviates this problem by training a robust feature extractor, but it requires longer training time and expensive computations. Motivated by this, we propose a simple yet effective method, called ALASCA, which efficiently provides a robust feature extractor under label noise. ALASCA integrates two key ingredients: (1) adaptive label smoothing based on our theoretical analysis that label smoothing implicitly induces Lipschitz regularization, and (2) auxiliary classifiers that enable practical application of intermediate Lipschitz regularization with negligible computations. We conduct wide-ranging experiments for ALASCA and combine our proposed method with previous noise-robust methods on several synthetic and real-world datasets. Experimental results show that our framework consistently improves the robustness of feature extractors and the performance of existing baselines with efficiency. Our code is available at https://github.com/jongwooko/ALASCA.

cs.LG↗