arXiv subjects

Donghwan Lee

Publications and source records attributed to Donghwan Lee.

At least 73 records · Page 4Linked to original sources

arXiv2024

Lossless Convexification and Duality

The main goal of this paper is to investigate strong duality of non-convex semidefinite programming problems (SDPs). In the optimization community, it is well-known that a convex optimization problem satisfies strong duality if the Slater's condition holds. However, this result cannot be directly generalized to non-convex problems. In this paper, we prove that a class of non-convex SDPs with special structures satisfies strong duality under the Slater's condition. Such a class of SDPs arises in SDP-based control analysis and design approaches. Throughout the paper, several examples are given to support the proposed results. We expect that the proposed analysis can potentially deepen our understanding of non-convex SDPs arising in the control community, and promote their analysis based on KKT conditions.

math.OC↗

arXiv2024

Analysis of Off-Policy Multi-Step TD-Learning with Linear Function Approximation

This paper analyzes multi-step TD-learning algorithms within the `deadly triad' scenario, characterized by linear function approximation, off-policy learning, and bootstrapping. In particular, we prove that n-step TD-learning algorithms converge to a solution as the sampling horizon n increases sufficiently. The paper is divided into two parts. In the first part, we comprehensively examine the fundamental properties of their model-based deterministic counterparts, including projected value iteration, gradient descent algorithms, and the control theoretic approach, which can be viewed as prototype deterministic algorithms whose analysis plays a pivotal role in understanding and developing their model-free reinforcement learning counterparts. In particular, we prove that these algorithms converge to meaningful solutions when n is sufficiently large. Based on these findings, two n-step TD-learning algorithms are proposed and analyzed, which can be seen as the model-free reinforcement learning counterparts of the gradient and control theoretic algorithms.

eess.SY↗

arXiv2024

New Versions of Gradient Temporal Difference Learning

Sutton, Szepesvári and Maei introduced the first gradient temporal-difference (GTD) learning algorithms compatible with both linear function approximation and off-policy training. The goal of this paper is (a) to propose some variants of GTDs with extensive comparative analysis and (b) to establish new theoretical analysis frameworks for the GTDs. These variants are based on convex-concave saddle-point interpretations of GTDs, which effectively unify all the GTDs into a single framework, and provide simple stability analysis based on recent results on primal-dual gradient dynamics. Finally, numerical comparative analysis is given to evaluate these approaches.

cs.LG↗

arXiv2023

Relaxed Conditions for Parameterized Linear Matrix Inequality in the Form of Nested Fuzzy Summations

The aim of this study is to investigate less conservative conditions for parameterized linear matrix inequalities (PLMIs) that are formulated as nested fuzzy summations. Such PLMIs are commonly encountered in stability analysis and control design problems for Takagi-Sugeno (T-S) fuzzy systems. Utilizing the weighted inequality of arithmetic and geometric means (AM-GM inequality), we develop new, less conservative linear matrix inequalities for the PLMIs. This methodology enables us to efficiently handle the product of membership functions that have intersecting indices. Through empirical case studies, we demonstrate that our proposed conditions produce less conservative results compared to existing approaches in the literature.

math.OC↗

arXiv2023

T-Cal: An optimal test for the calibration of predictive models

The prediction accuracy of machine learning methods is steadily increasing, but the calibration of their uncertainty predictions poses a significant challenge. Numerous works focus on obtaining well-calibrated predictive models, but less is known about reliably assessing model calibration. This limits our ability to know when algorithms for improving calibration have a real effect, and when their improvements are merely artifacts due to random noise in finite datasets. In this work, we consider detecting mis-calibration of predictive models using a finite validation dataset as a hypothesis testing problem. The null hypothesis is that the predictive model is calibrated, while the alternative hypothesis is that the deviation from calibration is sufficiently large. We find that detecting mis-calibration is only possible when the conditional probabilities of the classes are sufficiently smooth functions of the predictions. When the conditional class probabilities are Hölder continuous, we propose T-Cal, a minimax optimal test for calibration based on a debiased plug-in estimator of the $\ell_2$-Expected Calibration Error (ECE). We further propose Adaptive T-Cal, a version that is adaptive to unknown smoothness. We verify our theoretical findings with a broad range of experiments, including with several popular deep neural net architectures and several standard post-hoc calibration methods. T-Cal is a practical general-purpose tool, which -- combined with classical tests for discrete-valued predictors -- can be used to test the calibration of virtually any probabilistic classification method.

stat.ML↗

arXiv2023

On the Local Quadratic Stability of T-S Fuzzy Systems in the Vicinity of the Origin

The main goal of this paper is to introduce new local stability conditions for continuous-time Takagi-Sugeno (T-S) fuzzy systems. These stability conditions are based on linear matrix inequalities (LMIs) in combination with quadratic Lyapunov functions. Moreover, they integrate information on the membership functions at the origin and effectively leverage the linear structure of the underlying nonlinear system in the vicinity of the origin. As a result, the proposed conditions are proved to be less conservative compared to existing methods using fuzzy Lyapunov functions in the literature. Moreover, we establish that the proposed methods offer necessary and sufficient conditions for the local exponential stability of T-S fuzzy systems. The paper also includes discussions on the inherent limitations associated with fuzzy Lyapunov approaches. To demonstrate the theoretical results, we provide comprehensive examples that elucidate the core concepts and validate the efficacy of the proposed conditions.

eess.SY↗

arXiv2023

Control Theoretic Analysis of Temporal Difference Learning

The goal of this manuscript is to conduct a controltheoretic analysis of Temporal Difference (TD) learning algorithms. TD-learning serves as a cornerstone in the realm of reinforcement learning, offering a methodology for approximating the value function associated with a given policy in a Markov Decision Process. Despite several existing works that have contributed to the theoretical understanding of TD-learning, it is only in recent years that researchers have been able to establish concrete guarantees on its statistical efficiency. In this paper, we introduce a finite-time, control-theoretic framework for analyzing TD-learning, leveraging established concepts from the field of linear systems control. Consequently, this paper provides additional insights into the mechanics of TD learning and the broader landscape of reinforcement learning, all while employing straightforward analytical tools derived from control theory.

cs.AI↗

arXiv2023

Finite-Time Analysis of Minimax Q-Learning for Two-Player Zero-Sum Markov Games: Switching System Approach

The objective of this paper is to investigate the finite-time analysis of a Q-learning algorithm applied to two-player zero-sum Markov games. Specifically, we establish a finite-time analysis of both the minimax Q-learning algorithm and the corresponding value iteration method. To enhance the analysis of both value iteration and Q-learning, we employ the switching system model of minimax Q-learning and the associated value iteration. This approach provides further insights into minimax Q-learning and facilitates a more straightforward and insightful convergence analysis. We anticipate that the introduction of these additional insights has the potential to uncover novel connections and foster collaboration between concepts in the fields of control theory and reinforcement learning communities.

eess.SY↗

arXiv2023

TMO: Textured Mesh Acquisition of Objects with a Mobile Device by using Differentiable Rendering

We present a new pipeline for acquiring a textured mesh in the wild with a single smartphone which offers access to images, depth maps, and valid poses. Our method first introduces an RGBD-aided structure from motion, which can yield filtered depth maps and refines camera poses guided by corresponding depth. Then, we adopt the neural implicit surface reconstruction method, which allows for high-quality mesh and develops a new training process for applying a regularization provided by classical multi-view stereo methods. Moreover, we apply a differentiable rendering to fine-tune incomplete texture maps and generate textures which are perceptually closer to the original scene. Our pipeline can be applied to any common objects in the real world without the need for either in-the-lab environments or accurate mask images. We demonstrate results of captured objects with complex shapes and validate our method numerically against existing 3D reconstruction and texture mapping methods.

cs.CV↗

arXiv2023

Demystifying Disagreement-on-the-Line in High Dimensions

Evaluating the performance of machine learning models under distribution shift is challenging, especially when we only have unlabeled data from the shifted (target) domain, along with labeled data from the original (source) domain. Recent work suggests that the notion of disagreement, the degree to which two models trained with different randomness differ on the same input, is a key to tackle this problem. Experimentally, disagreement and prediction error have been shown to be strongly connected, which has been used to estimate model performance. Experiments have led to the discovery of the disagreement-on-the-line phenomenon, whereby the classification error under the target domain is often a linear function of the classification error under the source domain; and whenever this property holds, disagreement under the source and target domain follow the same linear relation. In this work, we develop a theoretical foundation for analyzing disagreement in high-dimensional random features regression; and study under what conditions the disagreement-on-the-line phenomenon occurs in our setting. Experiments on CIFAR-10-C, Tiny ImageNet-C, and Camelyon17 are consistent with our theory and support the universality of the theoretical findings.

stat.ML↗

arXiv2022

Collaborative Learning of Discrete Distributions under Heterogeneity and Communication Constraints

In modern machine learning, users often have to collaborate to learn the distribution of the data. Communication can be a significant bottleneck. Prior work has studied homogeneous users -- i.e., whose data follow the same discrete distribution -- and has provided optimal communication-efficient methods for estimating that distribution. However, these methods rely heavily on homogeneity, and are less applicable in the common case when users' discrete distributions are heterogeneous. Here we consider a natural and tractable model of heterogeneity, where users' discrete distributions only vary sparsely, on a small number of entries. We propose a novel two-stage method named SHIFT: First, the users collaborate by communicating with the server to learn a central distribution; relying on methods from robust statistics. Then, the learned central distribution is fine-tuned to estimate their respective individual distribution. We show that SHIFT is minimax optimal in our model of heterogeneity and under communication constraints. Further, we provide experimental results using both synthetic data and $n$-gram frequency estimation in the text domain, which corroborate its efficiency.

stat.ML↗

arXiv2022

A Discrete-Time Switching System Analysis of Q-learning

This paper develops a novel control-theoretic framework to analyze the non-asymptotic convergence of Q-learning. We show that the dynamics of asynchronous Q-learning with a constant step-size can be naturally formulated as a discrete-time stochastic affine switching system. Moreover, the evolution of the Q-learning estimation error is over- and underestimated by trajectories of two simpler dynamical systems. Based on these two systems, we derive a new finite-time error bound of asynchronous Q-learning when a constant stepsize is used. Our analysis also sheds light on the overestimation phenomenon of Q-learning. We further illustrate and validate the analysis through numerical simulations.

math.OC↗

arXiv2022

Block Double-Submission Attack: Block Withholding Can Be Self-Destructive

Proof-of-Work (PoW) is a Sybil control mechanism adopted in blockchain-based cryptocurrencies. It prevents the attempt of malicious actors to manipulate distributed ledgers. Bitcoin has successfully suppressed double-spending by accepting the longest PoW chain. Nevertheless, PoW encountered several major security issues surrounding mining competition. One of them is a Block WithHolding (BWH) attack that can exploit a widespread and cooperative environment called a mining pool. This attack takes advantage of untrustworthy relationships between mining pools and participating agents. Moreover, detecting or responding to attacks is challenging due to the nature of mining pools. In this paper, however, we suggest that BWH attacks also have a comparable trust problem. Because a BWH attacker cannot have complete control over BWH agents, they can betray the belonging mining pool and seek further benefits by trading with victims. We prove that this betrayal is not only valid in all attack parameters but also provides double benefits; finally, it is the best strategy for BWH agents. Furthermore, our study implies that BWH attacks may encounter self-destruction of their own revenue, contrary to their intention.

cs.CR↗

arXiv2022

Finite-Time Analysis of Asynchronous Q-learning under Diminishing Step-Size from Control-Theoretic View

Q-learning has long been one of the most popular reinforcement learning algorithms, and theoretical analysis of Q-learning has been an active research topic for decades. Although researches on asymptotic convergence analysis of Q-learning have a long tradition, non-asymptotic convergence has only recently come under active study. The main goal of this paper is to investigate new finite-time analysis of asynchronous Q-learning under Markovian observation models via a control system viewpoint. In particular, we introduce a discrete-time time-varying switching system model of Q-learning with diminishing step-sizes for our analysis, which significantly improves recent development of the switching system analysis with constant step-sizes, and leads to $\mathcal{O}\left( \sqrt{\frac{\log k}{k}} \right)$ convergence rate that is comparable to or better than most of the state of the art results in the literature. In the mean while, a technique using the similarly transformation is newly applied to avoid the difficulty in the analysis posed by diminishing step-sizes. The proposed analysis brings in additional insights, covers different scenarios, and provides new simplified templates for analysis to deepen our understanding on Q-learning via its unique connection to discrete-time switching systems.

cs.AI↗

arXiv2022

Investigating the Role of Image Retrieval for Visual Localization -- An exhaustive benchmark

Visual localization, i.e., camera pose estimation in a known scene, is a core component of technologies such as autonomous driving and augmented reality. State-of-the-art localization approaches often rely on image retrieval techniques for one of two purposes: (1) provide an approximate pose estimate or (2) determine which parts of the scene are potentially visible in a given query image. It is common practice to use state-of-the-art image retrieval algorithms for both of them. These algorithms are often trained for the goal of retrieving the same landmark under a large range of viewpoint changes which often differs from the requirements of visual localization. In order to investigate the consequences for visual localization, this paper focuses on understanding the role of image retrieval for multiple visual localization paradigms. First, we introduce a novel benchmark setup and compare state-of-the-art retrieval representations on multiple datasets using localization performance as metric. Second, we investigate several definitions of "ground truth" for image retrieval. Using these definitions as upper bounds for the visual localization paradigms, we show that there is still sgnificant room for improvement. Third, using these tools and in-depth analysis, we show that retrieval performance on classical landmark retrieval or place recognition tasks correlates only for some but not all paradigms to localization performance. Finally, we analyze the effects of blur and dynamic scenes in the images. We conclude that there is a need for retrieval approaches specifically designed for localization paradigms. Our benchmark and evaluation protocols are available at https://github.com/naver/kapture-localization.

cs.CV↗

arXiv2022

A Single Correspondence Is Enough: Robust Global Registration to Avoid Degeneracy in Urban Environments

Global registration using 3D point clouds is a crucial technology for mobile platforms to achieve localization or manage loop-closing situations. In recent years, numerous researchers have proposed global registration methods to address a large number of outlier correspondences. Unfortunately, the degeneracy problem, which represents the phenomenon in which the number of estimated inliers becomes lower than three, is still potentially inevitable. To tackle the problem, a degeneracy-robust decoupling-based global registration method is proposed, called Quatro. In particular, our method employs quasi-SO(3) estimation by leveraging the Atlanta world assumption in urban environments to avoid degeneracy in rotation estimation. Thus, the minimum degree of freedom (DoF) of our method is reduced from three to one. As verified in indoor and outdoor 3D LiDAR datasets, our proposed method yields robust global registration performance compared with other global registration methods, even for distant point cloud pairs. Furthermore, the experimental results confirm the applicability of our method as a coarse alignment. Our code is available: https://github.com/url-kaist/quatro.

cs.CV↗

arXiv2022

SelfTune: Metrically Scaled Monocular Depth Estimation through Self-Supervised Learning

Monocular depth estimation in the wild inherently predicts depth up to an unknown scale. To resolve scale ambiguity issue, we present a learning algorithm that leverages monocular simultaneous localization and mapping (SLAM) with proprioceptive sensors. Such monocular SLAM systems can provide metrically scaled camera poses. Given these metric poses and monocular sequences, we propose a self-supervised learning method for the pre-trained supervised monocular depth networks to enable metrically scaled depth estimation. Our approach is based on a teacher-student formulation which guides our network to predict high-quality depths. We demonstrate that our approach is useful for various applications such as mobile robot navigation and is applicable to diverse environments. Our full system shows improvements over recent self-supervised depth estimation and completion methods on EuRoC, OpenLORIS, and ScanNet datasets.

cs.CV↗

arXiv2021

On the Semidefinite Duality of Finite-Horizon LQG Problem

In this paper, our goal is to study fundamental foundations of linear quadratic Gaussian (LQG) control problems for stochastic linear time-invariant systems via Lagrangian duality of semidefinite programming (SDP) problems. In particular, we derive an SDP formulation of the finite-horizon LQG problem, and its Lagrangian duality. Moreover, we prove that Riccati equation for LQG can be derived the KKT optimality condition of the corresponding SDP problem. Besides, the proposed primal problem efficiently decouples the system matrices and the gain matrix. This allows us to develop new convex relaxations of non-convex structured control design problems such as the decentralized control problem. We expect that this work would provide new insights on the LQG problem and may potentially facilitate developments of new formulations of various optimal control problems. Numerical examples are given to demonstrate the effectiveness of the proposed methods.

math.OC↗