arXiv subjects

Donghwan Lee

Publications and source records attributed to Donghwan Lee.

At least 37 records · Page 2Linked to original sources

arXiv2026

Tree-based methods for length-biased survival data

Left-truncated survival data commonly arise in prevalent cohort studies, where only individuals who have experienced disease onset and survived until enrollment in the study. When the onset process follows a stationary Poisson process, the resulting data are length-biased. This sampling mechanism induces a selection bias towards longer survival individuals, and statistical methods for traditional survival data are not directly applicable. While tree-based methods developed for left-truncated data can be applied, they may be inefficient for length-biased data, as they do not account for the distribution of truncation times. To address this, we propose new survival trees and forests for length-biased right-censored data within the conditional inference framework. Our approach uses a score function derived from the full likelihood to construct permutation test statistics for variable splitting. For survival prediction, we consider two estimators of the unbiased survival function, differing in statistical efficiency and computational complexity. These elements enhance efficiency in tree construction and improve accuracy of survival prediction in ensemble settings. Simulation studies demonstrate efficiency gains in both tree recovery and survival prediction, often exceeding the gains from ensembling alone. We further illustrate the utility of the proposed methods using lung cancer data from the Cancer Public Library Database, a nationwide cancer registry in South Korea.

stat.ME↗

arXiv2026

Geometrically Averaged Hard Target Updates for Linear Q-Learning

Periodic hard target updates are among the most common stabilization devices in modern deep Q-learning. Recent studies suggest that target updates can improve stability in Q-learning with function approximation, including linear function approximation. We introduce and analyze the so-called $λ$-target update, obtained by averaging the $m$-periodic target update maps with $λ$-geometric weights $(1-λ)λ^{m-1}$, $λ\in [0,1]$. The endpoint $λ=0$ recovers the one-period target update, while the continuous endpoint $λ\uparrow1$ recovers projected Q-value iteration. We study this mechanism for Q-learning with linear function approximation, namely linear Q-learning, using a switching-system model and related tools. For clarity, the paper treats a deterministic version; the formulation extends to stochastic reinforcement-learning settings.

cs.LG↗

arXiv2026

Bellman Residual Minimization for Control: Geometry, Stationarity, and Convergence

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.

cs.LG↗

arXiv2026

Target Updates May Stabilize Linear Q-Learning: Periodic and Soft Dynamics

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.

stat.ML↗

arXiv2026

Switching-Geometry Analysis of Deflated Q-Value Iteration

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.

math.OC↗

arXiv2026

R-GTD: A Geometric Analysis of Gradient Temporal-Difference Learning in Singular Regimes

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. While some prior works have applied regularization to relax the nonsingularity assumption, their theoretical guarantees inevitably rely on other restrictive conditions. In this paper, we propose a regularized optimization objective by reformulating the mean-square projected Bellman error 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 conduct a geometric analysis to establish theoretical convergence guarantees and explicit error bounds for the proposed method, and validate its effectiveness through empirical experiments.

cs.LG↗

arXiv2026

Soft Deterministic Policy Gradient with Gaussian Smoothing

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.

cs.LG↗

arXiv2026

Beyond the Bellman Fixed Point: Geometry and Fast Policy Identification in Value Iteration

Q-value iteration (Q-VI) is usually analyzed through the $γ$-contraction of the Bellman operator. This argument proves convergence to $Q^*$, but it gives only a coarse account of when the induced greedy policy becomes optimal. We study discounted Q-VI as a switching system and focus on the practically optimal solution set (POSS), the set of $Q$-functions whose tie-broken greedy policies are optimal. The main result shows that Q-VI reaches the optimal action class in finite time by entering an invariant tube around $\mathcal X_1=Q^*+\operatorname{span}(\mathbf 1)$, which is contained in the POSS. For every $\varepsilon>0$, the distance to $\mathcal X_1$ satisfies an exponential bound with rate $(\barρ+\varepsilon)^k$, where $\barρ$ is the joint spectral radius of the projected switching family restricted to directions transverse to $\mathcal X_1$. When $\barρ<γ$, this transverse convergence is faster than the classical contraction rate. The analysis separates fast policy identification from the subsequent convergence to $Q^*$, which may still be governed by the all-ones mode. We also give spectral and graph-theoretic conditions under which the strict inequality $\barρ<γ$ holds or fails.

math.OC↗

arXiv2026

Safe-Support Q-Learning: Learning without Unsafe Exploration

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.

cs.LG↗

arXiv2026

Contraction-Aligned Analysis of Soft Bellman Residual Minimization with Weighted Lp-Norm for Markov Decision Problem

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.

cs.LG↗

arXiv2026

Finite-Time Analysis of Q-Value Iteration for General-Sum Stackelberg Games

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.

cs.LG↗

arXiv2026

Learning the Model While Learning Q: Finite-Time Sample Complexity of Online SyncMBQ

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 investigate the sample complexity of $Q$-learning when integrated with a model-based approach. The proposed algorihtms learns both the model and Q-value in an online manner. We demonstrate a near-optimal sample complexity result within a broad range of step sizes.

cs.LG↗

arXiv2026

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

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.

cs.LG↗

arXiv2026

Analysis of approximate linear programming solution to Markov decision problem with log barrier function

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.

cs.AI↗

arXiv2026

(Im)possibility of Incentive Design for Challenge-based Blockchain Protocols

Blockchains offer a decentralized and secure execution environment strong enough to host cryptocurrencies, but the state-replication model makes on-chain computation expensive. To avoid heavy on-chain workloads, systems like Truebit and optimistic rollups use challenge-based protocols, performing computations off-chain and invoking the chain only when challenged. This keeps normal-case costs low and, if at least one honest challenger exists, can catch fraud. What has been less clear is whether honest challengers are actually incentivized and a dishonest proposer is properly damaged under the worst case environment. We build a model with a colluding minority, heterogeneous costs, and three ordering modes. We then ask whether two goals can be met together: honest non-loss and fraud deterrence. Our results are clear: in single-winner designs, the incentive design is impossible or limited in scale. By contrast, in multi-winner designs, we obtain simple, explicit conditions under which both goals hold.

cs.GT↗

arXiv2026

Periodic Regularized Q-Learning

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.

cs.LG↗

arXiv2026

Finite-Time Accuracy of Temporal-Difference Learning Under Schur-Stable Recursions

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.

cs.LG↗

arXiv2026

Finite-Time Analysis of Simultaneous Double Q-learning

$Q$-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.

cs.LG↗