Donghwan Lee

Martin Humenberger, Yohann Cabon, Noé Pion et al.

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.

Hyungtae Lim, Suyong Yeon, Soohyun Ryu et al.

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.

Jaehoon Choi, Dongki Jung, Taejae Lee et al.

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.

Jaehoon Choi, Dongki Jung, Yonghan Lee et al.

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.

Donghwan Lee

Periodic target updates in Q-learning and soft target updates in actor-critic methods are empirically well established stabilization mechanisms, but their precise theoretical explanation is still incomplete. This paper gives a rigorous and exact analysis of these mechanisms for Q-learning with linear function approximation (linear Q-learning) using the exact switched linear system (SLS) dynamics induced by the Bellman maximum and the joint spectral radius (JSR) of the resulting switching matrix families. Although linear Q-learning can fail to converge in general, we prove that, under explicit spectral and step-size conditions, periodic hard target updates and soft target updates can guarantee convergence to the exact projected Q-Bellman solution. The main analysis is carried out for deterministic linear Q-learning, where the target-update mechanism is most transparent. Once the corresponding JSR certificate is established for the mean recursion, the stochastic reinforcement-learning setting can be treated by replacing deterministic modes with sampled stochastic modes and adding the corresponding stochastic-noise analysis.

Behrad Moniri, Donghwan Lee, Hamed Hassani et al.

Feature learning is thought to be one of the fundamental reasons for the success of deep neural networks. It is rigorously known that in two-layer fully-connected neural networks under certain conditions, one step of gradient descent on the first layer can lead to feature learning; characterized by the appearance of a separated rank-one component -- spike -- in the spectrum of the feature matrix. However, with a constant gradient descent step size, this spike only carries information from the linear component of the target function and therefore learning non-linear components is impossible. We show that with a learning rate that grows with the sample size, such training in fact introduces multiple rank-one components, each corresponding to a specific polynomial feature. We further prove that the limiting large-dimensional and large sample training and test errors of the updated neural networks are fully characterized by these spikes. By precisely analyzing the improvement in the training and test errors, we demonstrate that these non-linear features can enhance learning.

Donghwan Lee, Xinmeng Huang, Hamed Hassani et al.

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.

Donghwan Lee, Behrad Moniri, Xinmeng Huang et al.

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.

Xinmeng Huang, Kan Xu, Donghwan Lee et al.

Large and complex datasets are often collected from several, possibly heterogeneous sources. Multitask learning methods improve efficiency by leveraging commonalities across datasets while accounting for possible differences among them. Here, we study multitask linear regression and contextual bandits under sparse heterogeneity, where the source/task-associated parameters are equal to a global parameter plus a sparse task-specific term. We propose a novel two-stage estimator called MOLAR that leverages this structure by first constructing a covariate-wise weighted median of the task-wise linear regression estimates and then shrinking the task-wise estimates towards the weighted median. Compared to task-wise least squares estimates, MOLAR improves the dependence of the estimation error on the data dimension. Extensions of MOLAR to generalized linear models and constructing confidence intervals are discussed in the paper. We then apply MOLAR to develop methods for sparsely heterogeneous multitask contextual bandits, obtaining improved regret guarantees over single-task bandit methods. We further show that our methods are minimax optimal by providing a number of lower bounds. Finally, we support the efficiency of our methods by performing experiments on both synthetic data and the PISA dataset on student educational outcomes from heterogeneous countries.

Xinmeng Huang, Donghwan Lee, Edgar Dobriban et al.

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.

Han-Dong Lim, Donghwan Lee

Temporal-difference (TD) learning is widely regarded as one of the most popular algorithms in reinforcement learning (RL). Despite its widespread use, it has only been recently that researchers have begun to actively study its finite time behavior, including the finite time bound on mean squared error and sample complexity. On the empirical side, experience replay has been a key ingredient in the success of deep RL algorithms, but its theoretical effects on RL have yet to be fully understood. In this paper, we present a simple decomposition of the Markovian noise terms and provide finite-time error bounds for TD-learning with experience replay. Specifically, under the Markovian observation model, we demonstrate that for both the averaged iterate and final iterate cases, the error term induced by a constant step-size can be effectively controlled by the size of the replay buffer and the mini-batch sampled from the experience replay buffer.

Han-Dong Lim, Donghwan Lee

Off-policy learning ability is an important feature of reinforcement learning (RL) for practical applications. However, even one of the most elementary RL algorithms, temporal-difference (TD) learning, is known to suffer form divergence issue when the off-policy scheme is used together with linear function approximation. To overcome the divergent behavior, several off-policy TD-learning algorithms, including gradient-TD learning (GTD), and TD-learning with correction (TDC), have been developed until now. In this work, we provide a unified view of such algorithms from a purely control-theoretic perspective, and propose a new convergent algorithm. Our method relies on the backstepping technique, which is widely used in nonlinear control theory. Finally, convergence of the proposed algorithm is experimentally verified in environments where the standard TD-learning is known to be unstable.

Donghwan Lee

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.

Han-Dong Lim, Donghwan Lee

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.

Yeeun Lim, Narim Jeong, Donghwan Lee

Ensuring safety during reinforcement learning (RL) training is critical in real-world applications where unsafe exploration can lead to devastating outcomes. While most safe RL methods mitigate risk through constraints or penalization, they still allow exploration of unsafe states during training. In this work, we adopt a stricter safety requirement that eliminates unsafe state visitation during training. To achieve this goal, we propose a Q-learning-based safe RL framework that leverages a behavior policy supported on a safe set. Under the assumption that the induced trajectories remain within the safe set, this policy enables sufficient exploration within the safe region without requiring near-optimality. We adopt a two-stage framework in which the Q-function and policy are trained separately. Specifically, we introduce a KL-regularized Bellman target that constrains the Q-function to remain close to the behavior policy. We then derive the policy induced from the trained Q-values and propose a parametric policy extraction method to approximate the optimal policy. Our approach provides a unified framework that can be adapted to different action spaces and types of behavior policies. Experimental results demonstrate that the proposed method achieves stable learning and well-calibrated value estimates and yields safer behavior with comparable or better performance than existing baselines.

Donghwan Lee, Han-Dong Lim, Do Wan Kim

The main goal of this paper is to investigate continuous-time distributed dynamic programming (DP) algorithms for networked multi-agent Markov decision problems (MAMDPs). In our study, we adopt a distributed multi-agent framework where individual agents have access only to their own rewards, lacking insights into the rewards of other agents. Moreover, each agent has the ability to share its parameters with neighboring agents through a communication network, represented by a graph. We first introduce a novel distributed DP, inspired by the distributed optimization method of Wang and Elia. Next, a new distributed DP is introduced through a decoupling process. The convergence of the DP algorithms is proved through systems and control perspectives. The study in this paper sets the stage for new distributed temporal different learning algorithms.

Donghwan Lee, Do Wan Kim

Temporal difference (TD) learning is a cornerstone reinforcement learning (RL) method for policy evaluation, where the goal is to estimate the value function of a Markov decision process under a fixed policy. While a substantial body of work has established its convergence and stability properties, more recent efforts have focused on its statistical efficiency through finite-time error bounds. In this paper, we advance this line of research by developing a new finite-time error analysis for tabular TD learning that directly exploits a discrete-time stochastic linear system representation and leverages Schur stability of the associated matrices. Beyond the specific bounds obtained, the proposed framework provides a reusable template for analyzing TD learning and related RL algorithms, and it offers control-theoretic insights that may guide future developments in finite-sample RL theory.

Donghwan Lee, Byeongjin Kim, Geunhee Kim et al.

Fine-grained classification of marine animals supports ecology, biodiversity and habitat conservation, and evidence-based policy-making. However, existing methods often overlook contextual interactions from the surrounding environment and insufficiently incorporate the hierarchical structure of marine biological taxonomy. To address these challenges, we propose MATANet (Multi-context Attention and Taxonomy-Aware Network), a novel model designed for fine-grained marine species classification. MATANet mimics expert strategies by using taxonomy and environmental context to interpret ambiguous features of underwater animals. It consists of two key components: a Multi-Context Environmental Attention Module (MCEAM), which learns relationships between regions of interest (ROIs) and their surrounding environments, and a Hierarchical Separation-Induced Learning Module (HSLM), which encodes taxonomic hierarchy into the feature space. MATANet combines instance and environmental features with taxonomic structure to enhance fine-grained classification. Experiments on the FathomNet2025, FAIR1M, and LifeCLEF2015-Fish datasets demonstrate state-of-the-art performance. The source code is available at: https://github.com/dhlee-work/fathomnet-cvpr2025-ssl

Donghwan Lee

This paper develops a sign-separated finite-time error analysis for constant step-size Q-learning. Starting from the switching-system representation, the error is decomposed into its componentwise negative and positive parts. The negative part is dominated by a lower comparison linear time-invariant (LTI) system associated with a fixed optimal policy, whereas the positive part is controlled by a linear switching system. The resulting bounds show that the negative-side LTI certificate is no slower than the positive-side switching certificate and may produce a faster exponential envelope. The analysis identifies a max-induced asymmetry in Q-learning error dynamics. This asymmetry is connected to overestimation: positive action-wise errors can be selected and propagated by the Bellman maximum, whereas negative errors admit an optimal-policy lower comparison. Finite-time bounds are provided for both deterministic and stochastic constant-step-size recursions.

Donghwan Lee, Han-Dong Lim

This paper develops a switching-system interpretation of Q-learning with linear function approximation (LFA) based on the joint spectral radius (JSR). We derive an exact linear switched model for the mean dynamics and relate convergence to stability of the corresponding switched system. The same construction is then used for stochastic linear Q-learning with independent and identically distributed (i.i.d.) observations and with Markovian observations. Although exact JSR computation is difficult in general, the certificate captures products of switching modes and can be less conservative than one-step norm bounds. The framework also yields a JSR-based view of regularized Q-learning with LFA. The resulting analysis connects projected Bellman equations, finite-difference stochastic-policy switching, and switched-system stability in a single parameter-space formulation.

Han-Dong Lim, Donghwan Lee

The goal of this paper is to investigate distributed temporal difference (TD) learning for a networked multi-agent Markov decision process. The proposed approach is based on distributed optimization algorithms, which can be interpreted as primal-dual Ordinary differential equation (ODE) dynamics subject to null-space constraints. Based on the exponential convergence behavior of the primal-dual ODE dynamics subject to null-space constraints, we examine the behavior of the final iterate in various distributed TD-learning scenarios, considering both constant and diminishing step-sizes and incorporating both i.i.d. and Markovian observation models. Unlike existing methods, the proposed algorithm does not require the assumption that the underlying communication network structure is characterized by a doubly stochastic matrix.

Donghwan Lee

This paper develops a joint spectral radius (JSR) framework for analyzing rank-one deflated Q-value iteration (Q-VI) in discounted Markov decision process control. Focusing on an all-ones residual correction, we interpret the resulting algorithm through the geometry of switching systems and, to the best of our knowledge, give the first JSR-based convergence analysis of deflated Q-VI for policy optimization problems. Our analysis reveals that the standard Q-VI switching system model has JSR exactly the discount factor $γ\in (0,1)$, since all admissible subsystems share the all-ones vector as an invariant direction. By passing to the quotient space that removes this direction, we obtain a projected switching system model whose JSR governs the relevant error dynamics and may be strictly smaller than $γ$. Therefore, the deflated Q-VI admits a potentially sharper convergence-rate characterization than the ambient-space $γ$-bound. Finally, we prove that the correction is equivalent to a scalar recentering of standard Q-VI. Hence, the projected trajectory, and therefore the greedy-policy sequence, is unchanged relative to standard Q-VI initialized from the same point. The benefit of deflation is not a change in the induced decision-making problem, but a more precise JSR-based description of the convergence geometry after the redundant all-ones component is removed.

Sanghyun Jo, Donghwan Lee, Eunji Jung et al.

Object removal differs from common inpainting, since it must prevent the masked target from reappearing and reconstruct the occluded background with structural and contextual fidelity, rather than merely filling a hole plausibly. Recent dataset-free approaches that redirect self-attention inside the mask fail in two ways: non-target foregrounds are often misinterpreted as background, which regenerates unwanted objects, and direct attention manipulation disrupts fine details and hinders coherent integration of background cues. We propose EraseLoRA, a novel dataset-free framework that replaces attention surgery with background-aware reasoning and test-time adaptation. First, Background-aware Foreground Exclusion (BFE), uses a multimodal large-language models to separate target foreground, non-target foregrounds, and clean background from a single image-mask pair without paired supervision, producing reliable background cues while excluding distractors. Second, Background-aware Reconstruction with Subtype Aggregation (BRSA), performs test-time optimization that treats inferred background subtypes as complementary pieces and enforces their consistent integration through reconstruction and alignment objectives, preserving local detail and global structure without explicit attention intervention. We validate EraseLoRA as a plug-in to pretrained diffusion models and across benchmarks for object removal, demonstrating consistent improvements over dataset-free baselines and competitive results against dataset-driven methods. The code will be made available upon publication.

Donghwan Lee

Dynamic programming is one of the most fundamental methodologies for solving Markov decision problems. Among its many variants, Q-value iteration (Q-VI) is particularly important due to its conceptual simplicity and its classical contraction-based convergence guarantee. Despite the central role of this contraction property, it does not fully reveal the geometric structure of the Q-VI trajectory. In particular, when one is interested not only in the final limit $Q^*$ but also in when the induced greedy policy becomes effectively optimal, the standard contraction argument provides only a coarse characterization. To formalize this notion, we denote by $\mathcal X^*$ the set of $Q$-functions whose corresponding tie-broken greedy policies are optimal, referred to as the practically optimal solution set (POS). In this paper, we revisit discounted Q-VI through the lens of switching system theory and derive new geometric insights into its behavior. In particular, we show that although Q-VI does not reach $Q^*$ in finite time in general, it identifies the optimal action class in finite time. Furthermore, we prove that the distance from the iterate to a particular subset of $\mathcal X^*$ decays exponentially at a rate governed by the joint spectral radius (JSR) of a restricted switching family. This rate can be strictly faster than the standard $γ$ rate when the restricted JSR is strictly smaller than $γ$, while the convergence of the entire $Q$-function to $Q^*$ can still be dominated by the slower $γ$ mode, where $γ$ denotes the discount factor. These results reveal a two-stage geometric behavior of Q-VI: a fast convergence toward $\mathcal X_1$, followed by a slower convergence toward $Q^*$ in general.

Donghwan Lee, Do Wan Kim

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.

Hyunjun Na, Donghwan Lee

Deterministic policy gradient (DPG) is widely utilized for continuous control; however, it inherently relies on the differentiability of the critic with respect to the action during policy updates. This assumption is violated in practical control problems involving sparse or discrete rewards, leading to ill-defined policy gradients and unstable learning. To address these challenges, we propose a principled alternative based on a smoothed Bellman equation formulated via Gaussian smoothing. Specifically, we define a novel action-value function based on a smoothed Bellman equation and derive the soft deterministic policy gradient (Soft-DPG). Our formulation eliminates explicit dependence on critic action-gradients and ensures that the gradient remains well-defined even for non-smooth Q-functions. We instantiate this framework into a deep reinforcement learning algorithm, which we call soft deep deterministic policy gradient (Soft DDPG). Empirical evaluations on standard continuous control benchmarks and their discretized-reward variants show that Soft DDPG remains competitive in dense-reward settings and provides clear gains in most discretized-reward environments, where standard DDPG is more sensitive to irregular critic landscapes.

Hyukjun Yang, Han-Dong Lim, Donghwan Lee

In reinforcement learning (RL), Q-learning is a fundamental algorithm whose convergence is guaranteed in the tabular setting. However, this convergence guarantee does not hold under linear function approximation. To overcome this limitation, a significant line of research has introduced regularization techniques to ensure stable convergence under function approximation. In this work, we propose a new algorithm, periodic regularized Q-learning (PRQ). We first introduce regularization at the level of the projection operator and explicitly construct a regularized projected value iteration (RP-VI), subsequently extending it to a sample-based RL algorithm. By appropriately regularizing the projection operator, the resulting projected value iteration becomes a contraction. By extending this regularized projection into the stochastic setting, we establish the PRQ algorithm and provide a rigorous theoretical analysis that proves finite-time convergence guarantees for PRQ under linear function approximation.

Donghwan Lee

Q-learning is one of the most fundamental algorithms in reinforcement learning. We analyze constant-stepsize Q-learning through a direct stochastic switching system representation. The key observation is that the Bellman maximization error can be represented exactly by a stochastic policy. Therefore, the Q-learning error admits a switched linear conditional-mean recursion with martingale-difference noise. The intrinsic drift rate is the joint spectral radius (JSR) of the direct switching family, which can be strictly smaller than the standard row-sum rate. Using this representation, we derive a finite-time final-iterate bound via a JSR-induced Lyapunov function and then give a computable quadratic-certificate version.

HyeAnn Lee, Donghwan Lee

The goal of this paper is to propose a new Q-learning algorithm with a dummy adversarial player, which is called dummy adversarial Q-learning (DAQ), that can effectively regulate the overestimation bias in standard Q-learning. With the dummy player, the learning can be formulated as a two-player zero-sum game. The proposed DAQ unifies several Q-learning variations to control overestimation biases, such as maxmin Q-learning and minmax Q-learning (proposed in this paper) in a single framework. The proposed DAQ is a simple but effective way to suppress the overestimation bias thourgh dummy adversarial behaviors and can be easily applied to off-the-shelf reinforcement learning algorithms to improve the performances. A finite-time convergence of DAQ is analyzed from an integrated perspective by adapting an adversarial Q-learning. The performance of the suggested DAQ is empirically demonstrated under various benchmark environments.

Taeho Lee, Donghwan Lee

Reinforcement learning (RL) has achieved remarkable success in a wide range of control and decision-making tasks. However, RL agents often exhibit unstable or degraded performance when deployed in environments subject to unexpected external disturbances and model uncertainties. Consequently, ensuring reliable performance under such conditions remains a critical challenge. In this paper, we propose minimax deep deterministic policy gradient (MMDDPG), a framework for learning disturbance-resilient policies in continuous control tasks. The training process is formulated as a minimax optimization problem between a user policy and an adversarial disturbance policy. In this problem, the user learns a robust policy that minimizes the objective function, while the adversary generates disturbances that maximize it. To stabilize this interaction, we introduce a fractional objective that balances task performance and disturbance magnitude. This objective prevents excessively aggressive disturbances and promotes robust learning. Experimental evaluations in MuJoCo environments demonstrate that the proposed MMDDPG achieves significantly improved robustness against both external force perturbations and model parameter variations.

Hyunjun Na, Donghwan Lee

Gradient temporal-difference (GTD) learning algorithms are widely used for off-policy policy evaluation with function approximation. However, existing convergence analyses rely on the restrictive assumption that the so-called feature interaction matrix (FIM) is nonsingular. In practice, the FIM can become singular and leads to instability or degraded performance. In this paper, we propose a regularized optimization objective by reformulating the mean-square projected Bellman error (MSPBE) minimization. This formulation naturally yields a regularized GTD algorithms, referred to as R-GTD, which guarantees convergence to a unique solution even when the FIM is singular. We establish theoretical convergence guarantees and explicit error bounds for the proposed method, and validate its effectiveness through empirical experiments.

Narim Jeong, Donghwan Lee

Soft Q-learning is a variation of Q-learning designed to solve entropy regularized Markov decision problems where an agent aims to maximize the entropy regularized value function. Despite its empirical success, there have been limited theoretical studies of soft Q-learning to date. This paper aims to offer a novel and unified finite-time, control-theoretic analysis of soft Q-learning algorithms. We focus on two types of soft Q-learning algorithms: one utilizing the log-sum-exp operator and the other employing the Boltzmann operator. By using dynamical switching system models, we derive novel finite-time error bounds for both soft Q-learning algorithms. We hope that our analysis will deepen the current understanding of soft Q-learning by establishing connections with switching system models and may even pave the way for new frameworks in the finite-time analysis of other reinforcement learning algorithms.

Donghwan Lee

Convergence of Q-learning has been the focus of extensive research over the past several decades. Recently, an asymptotic convergence analysis for Q-learning was introduced using a switching system framework. This approach applies the so-called ordinary differential equation (ODE) approach to prove the convergence of the asynchronous Q-learning modeled as a continuous-time switching system, where notions from switching system theory are used to prove its asymptotic stability without using explicit Lyapunov arguments. However, to prove stability, restrictive conditions, such as quasi-monotonicity, must be satisfied for the underlying switching systems, which makes it hard to easily generalize the analysis method to other reinforcement learning algorithms, such as the smooth Q-learning variants. In this paper, we present a more general and unified convergence analysis that improves upon the switching system approach and can analyze Q-learning and its smooth variants. The proposed analysis is motivated by previous work on the convergence of synchronous Q-learning based on $p$-norm serving as a Lyapunov function. However, the proposed analysis addresses more general ODE models that can cover both asynchronous Q-learning and its smooth versions with simpler frameworks.

Hyukjun Yang, Han-Dong Lim, Donghwan Lee

The problem of solving Markov decision processes under function approximation remains a fundamental challenge, even under linear function approximation settings. A key difficulty arises from a geometric mismatch: while the Bellman optimality operator is contractive in the Linfty-norm, commonly used objectives such as projected value iteration and Bellman residual minimization rely on L2-based formulations. To enable gradient-based optimization, we consider a soft formulation of Bellman residual minimization and extend it to a generalized weighted Lp -norm. We show that this formulation aligns the optimization objective with the contraction geometry of the Bellman operator as p increases, and derive corresponding performance error bounds. Our analysis provides a principled connection between residual minimization and Bellman contraction, leading to improved control of error propagation while remaining compatible with gradient-based optimization.

Narim Jeong, Donghwan Lee

Reinforcement learning has been successful both empirically and theoretically in single-agent settings, but extending these results to multi-agent reinforcement learning in general-sum Markov games remains challenging. This paper studies the convergence of Stackelberg Q-value iteration in two-player general-sum Markov games from a control-theoretic perspective. We introduce a relaxed policy condition tailored to the Stackelberg setting and model the learning dynamics as a switching system. By constructing upper and lower comparison systems, we establish finite-time error bounds for the Q-functions and characterize their convergence properties. Our results provide a novel control-theoretic perspective on Stackelberg learning. Moreover, to the best of the authors' knowledge, this paper offers the first finite-time convergence guarantees for Q-value iteration in general-sum Markov games under Stackelberg interactions.

Jongchan Park, Mingyu Park, Donghwan Lee

Offline reinforcement learning (RL) aims to learn a policy from a static dataset without further interactions with the environment. Collecting sufficiently large datasets for offline RL is exhausting since this data collection requires colossus interactions with environments and becomes tricky when the interaction with the environment is restricted. Hence, how an agent learns the best policy with a minimal static dataset is a crucial issue in offline RL, similar to the sample efficiency problem in online RL. In this paper, we propose a simple yet effective plug-and-play pretraining method to initialize a feature of a Q-network to enhance data efficiency in offline RL. Specifically, we introduce a shared Q-network structure that outputs predictions of the next state and Q-value. We pretrain the shared Q-network through a supervised regression task that predicts a next state and trains the shared Q-network using diverse offline RL methods. Through extensive experiments, we empirically demonstrate that our method enhances the performance of existing popular offline RL methods on the D4RL, Robomimic and V-D4RL benchmarks. Furthermore, we show that our method significantly boosts data-efficient offline RL across various data qualities and data distributions trough D4RL and ExoRL benchmarks. Notably, our method adapted with only 10% of the dataset outperforms standard algorithms even with full datasets.

Donghwan Lee, Hyukjun Yang

Markov decision problems are most commonly solved via dynamic programming. Another approach is Bellman residual minimization, which directly minimizes the squared Bellman residual objective function. However, compared to dynamic programming, this approach has received relatively less attention, mainly because it is often less efficient in practice and can be more difficult to extend to model-free settings such as reinforcement learning. Nonetheless, Bellman residual minimization has several advantages that make it worth investigating, such as more stable convergence with function approximation for value functions. While Bellman residual methods for policy evaluation have been widely studied, methods for policy optimization (control tasks) have been scarcely explored. In this paper, we establish foundational results for the control Bellman residual minimization for policy optimization.

Bumgeun Park, Donghwan Lee

Reinforcement learning (RL) has achieved impressive results across domains, yet learning an optimal policy typically requires extensive interaction data, limiting practical deployment. A common remedy is to leverage priors, such as pre-collected datasets or reference policies, but their utility degrades under task mismatch between training and deployment. While prior work has sought to address this mismatch, it has largely been restricted to in-distribution settings. To address this challenge, we propose Adaptive Policy Backbone (APB), a meta-transfer RL method that inserts lightweight linear layers before and after a shared backbone, thereby enabling parameter-efficient fine-tuning (PEFT) while preserving prior knowledge during adaptation. Our results show that APB improves sample efficiency over standard RL and adapts to out-of-distribution (OOD) tasks where existing meta-RL baselines typically fail.

Donghwan Lee, Hyukjun Yang, Bum Geun Park

There are two primary approaches to solving Markov decision problems (MDPs): dynamic programming based on the Bellman equation and linear programming (LP). Dynamic programming methods are the most widely used and form the foundation of both classical and modern reinforcement learning (RL). By contrast, LP-based methods have been less commonly employed, although they have recently gained attention in contexts such as offline RL. The relative underuse of the LP-based methods stems from the fact that it leads to an inequality-constrained optimization problem, which is generally more challenging to solve effectively compared with Bellman-equation-based methods. The purpose of this paper is to establish a theoretical foundation for solving LP-based MDPs in a more effective and practical manner. Our key idea is to leverage the log-barrier function, widely used in inequality-constrained optimization, to transform the LP formulation of the MDP into an unconstrained optimization problem. This reformulation enables approximate solutions to be obtained easily via gradient descent. While the method may appear simple, to the best of our knowledge, a thorough theoretical interpretation of this approach has not yet been developed. This paper aims to bridge this gap.

Han-Dong Lim, Donghwan Lee

In this paper, we study the theoretical properties of the projected Bellman equation (PBE) and two algorithms to solve this equation: linear Q-learning and approximate value iteration (AVI). We consider two sufficient conditions for the existence of a solution to PBE : strictly negatively row dominating diagonal (SNRDD) assumption and a condition motivated by the convergence of AVI. The SNRDD assumption also ensures the convergence of linear Q-learning, and its relationship with the convergence of AVI is examined. Lastly, several interesting observations on the solution of PBE are provided when using $ε$-greedy policy.

Bum Geun Park, Taeho Lee, Donghwan Lee

This paper introduces Q-learning with gradient target tracking, a novel reinforcement learning framework that provides a learned continuous target update mechanism as an alternative to the conventional hard update paradigm. In the standard deep Q-network (DQN), the target network is a copy of the online network's weights, held fixed for a number of iterations before being periodically replaced via a hard update. While this stabilizes training by providing consistent targets, it introduces a new challenge: the hard update period must be carefully tuned to achieve optimal performance. To address this issue, we propose two gradient-based target update methods: DQN with asymmetric gradient target tracking (AGT2-DQN) and DQN with symmetric gradient target tracking (SGT2-DQN). These methods replace the conventional hard target updates with continuous and structured updates using gradient descent, which effectively eliminates the need for manual tuning. We provide a theoretical analysis proving the convergence of these methods in tabular settings. Additionally, empirical evaluations demonstrate their advantages over standard DQN baselines, which suggest that gradient-based target updates can serve as an effective alternative to conventional target update mechanisms in Q-learning.

Junhyun Park, Chanyu Moon, Donghwan Lee et al.

Contrastive Language-Image Pre-Training (CLIP) has enabled zero-shot classification in radiology, reducing reliance on manual annotations. However, conventional contrastive learning struggles with normal case detection due to its strict intra-sample alignment, which disrupts normal sample clustering and leads to high false positives (FPs) and false negatives (FNs). To address these issues, we propose OFF-CLIP, a contrastive learning refinement that improves normal detection by introducing an off-diagonal term loss to enhance normal sample clustering and applying sentence-level text filtering to mitigate FNs by removing misaligned normal statements from abnormal reports. OFF-CLIP can be applied to radiology CLIP models without requiring any architectural modifications. Experimental results show that OFF-CLIP significantly improves normal classification, achieving a 0.61 Area under the curve (AUC) increase on VinDr-CXR over CARZero, the state-of-the-art zero-shot classification baseline, while maintaining or improving abnormal classification performance. Additionally, OFF-CLIP enhances zero-shot grounding by improving pointing game accuracy, confirming better anomaly localization. These results demonstrate OFF-CLIP's effectiveness as a robust and efficient enhancement for medical vision-language models.

Taeho Lee, Donghwan Lee

Practical control systems pose significant challenges in identifying optimal control policies due to uncertainties in the system model and external disturbances. While $H_\infty$ control techniques are commonly used to design robust controllers that mitigate the effects of disturbances, these methods often require complex and computationally intensive calculations. To address this issue, this paper proposes a reinforcement learning algorithm called robust deterministic policy gradient (RDPG), which formulates the $H_\infty$ control problem as a two-player zero-sum dynamic game. In this formulation, one player (the user) aims to minimize the cost, while the other player (the adversary) seeks to maximize it. We then employ deterministic policy gradient (DPG) and its deep reinforcement learning counterpart to train a robust control policy with effective disturbance attenuation. In particular, for practical implementation, we introduce an algorithm called robust deep deterministic policy gradient (RDDPG), which employs a deep neural network architecture and integrates techniques from the twin-delayed deep deterministic policy gradient (TD3) to enhance stability and learning efficiency. To evaluate the proposed algorithm, we implement it on an unmanned aerial vehicle (UAV) tasked with following a predefined path in a disturbance-prone environment. The experimental results demonstrate that the proposed method outperforms other control approaches in terms of robustness against disturbances, enabling precise real-time tracking of moving targets even under severe disturbance conditions.

Han-Dong Lim, Donghwan Lee

This paper analyzes multi-step temporal difference (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, 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, in the second part, two $n$-step TD-learning algorithms are proposed and analyzed, which can be seen as the model-free reinforcement learning counterparts of the model-based deterministic algorithms.

Hyunjun Na, Donghwan Lee

$Q$-learning is one of the most fundamental reinforcement learning (RL) algorithms. Despite its widespread success in various applications, it is prone to overestimation bias in the $Q$-learning update. To address this issue, double $Q$-learning employs two independent $Q$-estimators which are randomly selected and updated during the learning process. This paper proposes a modified double $Q$-learning, called simultaneous double $Q$-learning (SDQ), with its finite-time analysis. SDQ eliminates the need for random selection between the two $Q$-estimators, and this modification allows us to analyze double $Q$-learning through the lens of a novel switching system framework facilitating efficient finite-time analysis. Empirical studies demonstrate that SDQ converges faster than double $Q$-learning while retaining the ability to mitigate the maximization bias. Finally, we derive a finite-time expected error bound for SDQ.

Han-Dong Lim, Donghwan Lee

Multi-agent reinforcement learning (MARL) has witnessed a remarkable surge in interest, fueled by the empirical success achieved in applications of single-agent reinforcement learning (RL). In this study, we consider a distributed Q-learning scenario, wherein a number of agents cooperatively solve a sequential decision making problem without access to the central reward function which is an average of the local rewards. In particular, we study finite-time analysis of a distributed Q-learning algorithm, and provide a new sample complexity result of $\tilde{\mathcal{O}}\left( \min\left\{\frac{1}{ε^2}\frac{t_{\text{mix}}}{(1-γ)^6 d_{\min}^4 } ,\frac{1}ε\frac{\sqrt{|\gS||\gA|}}{(1-σ_2(\boldsymbol{W}))(1-γ)^4 d_{\min}^3} \right\}\right)$ under tabular lookup

Donghwan Lee

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.

Han-Dong Lim, HyeAnn Lee, Donghwan Lee

Reinforcement learning has witnessed significant advancements, particularly with the emergence of model-based approaches. Among these, $Q$-learning has proven to be a powerful algorithm in model-free settings. However, the extension of $Q$-learning to a model-based framework remains relatively unexplored. In this paper, we delve into the sample complexity of $Q$-learning when integrated with a model-based approach. Through theoretical analyses and empirical evaluations, we seek to elucidate the conditions under which model-based $Q$-learning excels in terms of sample efficiency compared to its model-free counterpart.

Han-Dong Lim, Donghwan Lee

Q-learning is widely used algorithm in reinforcement learning community. Under the lookup table setting, its convergence is well established. However, its behavior is known to be unstable with the linear function approximation case. This paper develops a new Q-learning algorithm that converges when linear function approximation is used. We prove that simply adding an appropriate regularization term ensures convergence of the algorithm. We prove its stability using a recent analysis tool based on switching system models. Moreover, we experimentally show that it converges in environments where Q-learning with linear function approximation has known to diverge. We also provide an error bound on the solution where the algorithm converges.

Donghwan Lee, Do Wan Kim

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.