Search arXiv⌕ Search

arXiv subjects

Shengbo Wang

Publications and source records attributed to Shengbo Wang.

At least 19 recordsLinked to original sources
arXiv2026

Dynamic Programming-Compatible Uncertainty Sets in Robust Markov Decision Processes

In this paper, we investigate the compatibility of robust Markov Decision Processes (RMDPs) with dynamic programming under various assumptions on the uncertainty set, i.e., we investigate when one can solve an RMDP by solving a fixed point equation. We show that in all generality, s-rectangular and sa-rectangular uncertainty sets are the only models of uncertainty that are compatible with dynamic programming. Our analysis shows that existing non-rectangular models, including r-rectangularity, are only weakly compatible with dynamic programming, as they require the assumption that rewards do not depend on the next state. In this case, our results imply that one can always construct a rectangular uncertainty set that is equivalent, for both policy evaluation and optimization, to the dynamic programming-compatible non-rectangular model. This highlights a key limitation: dynamic-programming-compatible non-rectangular uncertainty sets, although practically relevant for uncertainty quantification, do not provide a genuinely distinct assessment of policy performance. Interestingly, our proof techniques rely on identifying a novel simultaneous solvability property, which we show is central to several important properties of RMDPs, including the existence of stationary optimal policies and dynamic programming-based formulations. The simultaneous solvability property enables a unified approach to studying all existing models of uncertainty, rectangular and non-rectangular alike.

math.OC↗
arXiv2026

Optimal Sample Complexity of Stable Discounted Markov Decision Processes

We study the optimal sample complexity of tabular reinforcement learning for infinite-horizon discounted Markov decision processes. The unrestricted minimax sample complexity is known to scale as $\widetildeΘ((1-γ)^{-3}ε^{-2})$, where $γ$ denotes the discount factor and $ε$ is the solution-error tolerance. However, this worst-case rate does not account for stability structures that commonly arise in operational environments. Using the variance-reduced Q-learning framework, we show that, without imposing any additional stability assumptions, both sup-norm Q-function estimation and policy learning have leading sample-complexity dependence $\widetildeΘ(H(1-γ)^{-2}ε^{-2})$, where $H=|v^*|_{\mathrm{span}}$ is the span of the optimal value function. Moreover, assuming a uniform mixing time upper bound $t_{\mathrm{mix}}$ over all policies, the optimal Q-function can be estimated up to a constant shift with sample complexity $\widetildeΘ\left(t_{\mathrm{mix}}^3ε^{-2}\right)$, independent of $(1-γ)^{-1}$. Matching lower bounds establish the sharpness of these leading dependencies and reveal a separation between estimation and control: although the Q-function can be learned up to an additive constant at a horizon-free rate, policy learning generally retains its $(1-γ)^{-2}$ dependence.

cs.LG↗
arXiv2026

Q-Learning with Stable Infinite-Dimensional Linear Function Approximation

Q-learning with linear function approximation can be unstable because an arbitrary approximation architecture need not preserve the Bellman contraction. We develop a stable infinite-dimensional linear function approximation framework for Q-learning from a single Markovian behavior-policy trajectory. The learning variable is a coefficient field $θ\in C(\mathbb L)$ on a compact latent metric space $(\mathbb L,ρ)$. The framework uses a reconstruction operator that maps $θ$ to a continuous Q-function and a compression operator that maps Bellman updates back to latent coordinates. Nonexpansiveness of both operators induces a contractive latent Bellman map on $C(\mathbb L)$, with a unique fixed point $θ^*$ whose reconstruction approximates the optimal Q-function up to representation error. We propose two stochastic approximation (SA) algorithms and establish their sup-norm convergence bounds with a leading term of order $\widetilde O(n^{-1/2})$. The infinite-dimensional formulation provides a powerful abstraction for identifying the structures that govern statistical difficulty. Smoothness of the compression map in $ρ$ is inherited by $θ^*$ and the SA iterates, allowing uniform estimation errors to be controlled through covering numbers of $(\mathbb L,ρ)$ rather than the dimension of $C(\mathbb L)$. Remarkably, the SA algorithms we propose are agnostic to the choice of $ρ$, and thus can automatically adapt to both the smoothness and the geometry. We further illustrate the framework through Q-measure-learning with linear density approximation and output-layer neural weight training under a frozen pretrained network.

cs.LG↗
arXiv2026

FE-MCFormer: a novel time-frequency interpretable architecture for machinery fault diagnosis under strong noise environments

Interpretable fault diagnosis (FD) plays a critical role in industrial manufacturing, as it improves human-machine understanding and operational efficiency. However, harsh operating environments often introduce strong background interference or noise, which weakens the discriminative capability and interpretability of existing FD methods. To address this issue, this paper proposes FE-MCFormer, a time-frequency fusion framework for robust and time-frequency interpretable fault diagnosis under strong noise conditions. A frequency adaptive learning layer (FALL) is developed to perform learnable spectral reconstruction, which explicitly suppresses noise-dominated frequency responses while preserving fault-sensitive harmonic structures. Furthermore, a multiscale time-frequency fusion (MSTFF) architecture is designed to jointly capture localized impulsive characteristics and structured global spectral interactions. Extensive experiments on a rolling bearing dataset and a real-world centrifugal compressor dataset demonstrate that the proposed method achieves stable and interpretable diagnostic performance under severe noise environments down to -10 dB SNR. The results indicate that FE-MCFormer provides an effective framework for turbomachinery fault diagnosis in complex noisy environments.

eess.SP↗
arXiv2026

A neuromorphic vision system for open-world visual intelligence

Time-efficient and robust visual intelligence remains a critical challenge in unstructured open-world environments, yet current approaches often rely on computationally intensive neural architectures or task-specific sensors with limited versatility. Inspired by biological vision and information bottleneck theory, we report a neuromorphic vision system that performs task-oriented visual intelligence through an information distillation strategy (named as task traction mechanism) implemented on hardware. The system integrates a polarization-sensitive imager with a resistive random-access memory (RRAM) array to progressively distill task-relevant information via light field selection, region of interest extraction, and target anticipation. The neuromorphic vision system conducts visual tasks within an execution time of 193 μs. Evaluation across eight challenging open-world scenarios shows accuracy improvements of 25.54%, 37.73%, and 36.10% for object tracking, object segmentation, and trajectory prediction, respectively, together with an average 30.6-fold reduction in latency relative to state-of-the-art solutions.

eess.IV↗
arXiv2026

His2Trans: A Knowledge-Guided Agentic Framework for Project-Level C-to-Rust Migration

C remains a major implementation language for operating systems, embedded platforms, and infrastructure software, but manual memory management continues to create security and maintenance costs. Rust is a practical migration target because it retains low-level control while enforcing stronger memory-safety checks. At project scale, especially under gradual C/Rust coexistence, migration is not a sequence of syntax-preserving function rewrites. A translator must preserve project interfaces, observable behavior, system interaction protocols, and low-level interoperability boundaries while staying consistent with migration choices already made in the codebase. We introduce His2Trans, a knowledge-guided agentic framework for project-level C-to-Rust migration. His2Trans reuses interface-level and fragment-level knowledge mined from historical C/Rust migrations to guide new translations toward Rust interfaces, wrapper choices, and local idioms already accepted in the evolving project. It then refines the assembled crate with project-level agentic feedback. On ten OpenHarmony modules, His2Trans reaches a 100.00\% incremental compilation pass rate, a 94.92\% Test Pass Rate, and a 16.35\% Unsafe Ratio. On eight open-source C projects, it reaches 100.00\% for both incremental compilation and Test Pass Rate, reducing Unsafe Ratio from 42.88\% under C2Rust to 8.59\%. These results support knowledge-guided migration and project-level agentic refinement as practical mechanisms for preserving observable behavior while reducing the unsafe burden of rule-based transpilation.

cs.SE↗
arXiv2026

Lipschitz Regularity in Wasserstein Robust Stochastic Optimal Control

Robust Markov decision processes provide a principled framework for protecting sequential decision-making against transition-law misspecification and have attracted substantial recent research interest. As in non-robust stochastic optimal control, an important question is whether the robust value function is sufficiently regular for approximation and learning. This paper studies Lipschitz regularity of optimal value functions for Wasserstein robust stochastic optimal control on possibly unbounded Polish state spaces under an infinite-horizon discounted reward criterion. We consider two robustness formulations: a kernel-robust model, in which the adversary perturbs the next-state distribution within a Wasserstein ball around a nominal transition kernel, and a noise-robust model, in which the adversary perturbs the driving noise of the state transition dynamics. In the non-robust setting, Lipschitz rewards and Lipschitz transition dynamics do not, in general, imply a Lipschitz value function. In contrast, we show that in these Wasserstein robust formulations, Lipschitz assumptions on the model primitives yield Lipschitz robust value functions. Thus, Wasserstein robustness not only protects against misspecification but also regularizes the Bellman fixed point, providing stability relevant to discretization, value-function approximation, estimation, and learning.

math.OC↗
arXiv2026

Bio-plausible Neuromorphic Disturbance Observer Based on Emulation Theory: Extended Version

Biological neural systems achieve remarkable robustness and adaptability in uncertain environments through sparse, event-driven spike-based information processing and adaptive regulation. Inspired by this paradigm, this paper develops a neuromorhpic disturbance observer (NDO) and control framework that replaces conventional continuous-time signal representations with spike-timing encoding. Both disturbance estimates and control inputs are constructed via integrate-and-fire (IF) neuron dynamics from discrete spike events, yielding intrinsically event-driven updates. An adaptive-threshold triggering mechanism is inspired by spike-frequency adaptation (SFA), enabling history-dependent regulation of spike generation. Simulation results demonstrate that the proposed framework achieves neurally inspired robustness and adaptability, while the adaptive-threshold spiking scheme reduces spike events to 42.6% of the fixed-threshold case under noisy conditions.

q-bio.NC↗
arXiv2026

Fast Convergence of Policy Regret in Learning Stochastic Optimal Control

Policy learning in modern operations environments faces a fundamental tension between limited operational data and the large, often continuous, state and action spaces over which good decisions must be identified and deployed. We study value-based policy learning in stochastic optimal control: a greedy policy induced by an estimate of the optimal action-value function $Q^*$ is deployed, and its performance is measured by regret. The empirical success of this approach calls for statistical insight into the structures that enable fast regret convergence. We show that, in continuous action spaces, fast policy learning is induced by three geometric structures: a growth exponent $p$, which quantifies how quickly $Q^*$ separates suboptimal actions from its maximizers; a margin-mass exponent $m$, which controls how much deployment mass lies on states with weak growth; and an action-wise regularity exponent $q$, which measures the smoothness of the $Q^*$-estimation error across actions. Given a $n^{-1/2}$-accurate estimator of $Q^*$, we show that the minimax-optimal policy regret convergence rate is \[ \widetildeΘ\left( n^{-\min\left\{\frac{p}{2(p-q)},\frac{m+1}{2m}\right\}} \right), \] up to a logarithmic factor at the boundary between the two regimes. The exponent $q$ is crucial: $q>0$ yields faster-than-$n^{-1/2}$ regret. This regime is natural in operations applications. In particular, we verify $q>0$ under mild regularity conditions in dynamic inventory control and service allocation examples, while the mechanism underlying this fast rate regime extends beyond these settings.

math.OC↗
arXiv2026

Central Limit Theorem for Two-Time-Scale Approximate Distributionally Robust RL

Designing model-free algorithms for distributionally robust reinforcement learning (DRRL) poses fundamental challenges. The robust Bellman operator is nonlinear in the transition kernel, which makes one-sample Bellman updates biased, while the adversarial optimization underlying robustness makes robust evaluation computationally demanding. To address these difficulties, we consider the natural small-ambiguity regime under Kullback--Leibler ambiguity sets and propose an approximate DRRL framework based on a first-order expansion of the relevant robust functional. This yields an approximate robust Bellman equation that removes the adversarial optimization while remaining first-order accurate in the ambiguity radius. To learn the fixed point of this approximate equation, we propose Mean-Variance Stochastic Approximation (MVSA), a model-free algorithm that uses only one-sample updates. This is achieved via a lifted stochastic approximation dynamics and a two-time-scale design. We then prove convergence and a central limit theorem for MVSA: its main iterate satisfies a central limit theorem at the canonical $n^{-1/2}$ scale, with explicitly characterized asymptotic covariances. Finally, we validate our theoretical findings with a numerical experiment.

cs.LG↗
arXiv2026

Near-Optimal Sample Complexities of Divergence-based S-rectangular Distributionally Robust Reinforcement Learning

Distributionally robust reinforcement learning (DR-RL) has recently gained significant attention as a principled approach that addresses discrepancies between training and testing environments. To balance robustness, conservatism, and computational traceability, the literature has introduced DR-RL models with SA-rectangular and S-rectangular adversaries. While most existing statistical analyses focus on SA-rectangular models, owing to their algorithmic simplicity and the optimality of deterministic policies, S-rectangular models more accurately capture distributional discrepancies in many real-world applications and often yield more effective robust randomized policies. In this paper, we study the empirical value iteration algorithm for divergence-based S-rectangular DR-RL and establish near-optimal sample complexity bounds of $\widetilde{O}(|\mathcal{S}||\mathcal{A}|(1-γ)^{-4}\varepsilon^{-2})$, where $\varepsilon$ is the target accuracy, $|\mathcal{S}|$ and $|\mathcal{A}|$ denote the cardinalities of the state and action spaces, and $γ$ is the discount factor. To the best of our knowledge, these are the first sample complexity results for divergence-based S-rectangular models that achieve optimal dependence on $|\mathcal{S}|$, $|\mathcal{A}|$, and $\varepsilon$ simultaneously. We further validate this theoretical dependence through numerical experiments on a robust inventory control problem and a theoretical worst-case example, demonstrating the fast learning performance of our proposed algorithm.

cs.LG↗
arXiv2026

Non-Rectangular Average-Reward Robust MDPs: Optimal Policies and Their Transient Values

We study non-rectangular robust Markov decision processes under the average-reward criterion, where the ambiguity set couples transition probabilities across states and the adversary commits to a stationary kernel for the entire horizon. We show that any history-dependent policy achieving sublinear expected regret uniformly over the ambiguity set is robust-optimal, and that the robust value admits a minimax representation as the infimum over the ambiguity set of the classical optimal gains, without requiring any form of rectangularity or robust dynamic programming principle. Under the weak communication assumption, we establish the existence of such policies by converting high-probability regret bounds from the average-reward reinforcement learning literature into the expected-regret criterion. We then introduce a transient-value framework to evaluate finite-time performance of robust optimal policies, proving that average-reward optimality alone can mask arbitrarily poor transients and deriving regret-based lower bounds on transient values. Finally, we construct an epoch-based policy that combines an optimal stationary policy for the worst-case model with an anytime-valid sequential test and an online learning fallback, achieving a constant-order transient value.

math.OC↗
arXiv2026

Q-Measure-Learning for Continuous State RL: Efficient Implementation and Convergence

We study reinforcement learning in infinite-horizon discounted Markov decision processes with continuous state spaces, where data are generated online from a single trajectory under a Markovian behavior policy. To avoid maintaining an infinite-dimensional, function-valued estimate, we propose the novel Q-Measure-Learning, which learns a signed empirical measure supported on visited state-action pairs and reconstructs an action-value estimate via kernel integration. The method jointly estimates the stationary distribution of the behavior chain and the Q-measure through coupled stochastic approximation, leading to an efficient weight-based implementation with $O(n)$ memory and $O(n)$ computation cost per iteration. Under uniform ergodicity of the behavior chain, we prove almost sure sup-norm convergence of the induced Q-function to the fixed point of a kernel-smoothed Bellman operator. We also bound the approximation error between this limit and the optimal $Q^*$ as a function of the kernel bandwidth. To assess the performance of our proposed algorithm, we conduct RL experiments in a two-item inventory control setting.

cs.LG↗
arXiv2026

Sample Complexity of Distributionally Robust Average-Reward Reinforcement Learning

Motivated by practical applications where stable long-term performance is critical-such as robotics, operations research, and healthcare-we study the problem of distributionally robust (DR) average-reward reinforcement learning. We propose two algorithms that achieve near-optimal sample complexity. The first reduces the problem to a DR discounted Markov decision process (MDP), while the second, Anchored DR Average-Reward MDP, introduces an anchoring state to stabilize the controlled transition kernels within the uncertainty set. Assuming the nominal MDP is uniformly ergodic, we prove that both algorithms attain a sample complexity of $\widetilde{O}\left(|\mathbf{S}||\mathbf{A}| t_{\mathrm{mix}}^2\varepsilon^{-2}\right)$ for estimating the optimal policy as well as the robust average reward under KL and $f_k$-divergence-based uncertainty sets, provided the uncertainty radius is sufficiently small. Here, $\varepsilon$ is the target accuracy, $|\mathbf{S}|$ and $|\mathbf{A}|$ denote the sizes of the state and action spaces, and $t_{\mathrm{mix}}$ is the mixing time of the nominal MDP. This represents the first finite-sample convergence guarantee for DR average-reward reinforcement learning. We further validate the convergence rates of our algorithms through numerical experiments.

cs.LG↗
arXiv2026

Achieving $\varepsilon^{-2}$ Dependence for Average-Reward Q-Learning with a New Contraction Principle

We present the convergence rates of synchronous and asynchronous Q-learning for average-reward Markov decision processes, where the absence of contraction poses a fundamental challenge. Existing non-asymptotic results overcome this challenge by either imposing strong assumptions to enforce seminorm contraction or relying on discounted or episodic Markov decision processes as successive approximations, which either require unknown parameters or result in suboptimal sample complexity. In this work, under a reachability assumption, we establish optimal $\widetilde{O}(\varepsilon^{-2})$ sample complexity guarantees (up to logarithmic factors) for a simple variant of synchronous and asynchronous Q-learning that samples from the lazified dynamics, where the system remains in the current state with some fixed probability. At the core of our analysis is the construction of an instance-dependent seminorm and showing that, after a lazy transformation of the Markov decision process, the Bellman operator becomes one-step contractive under this seminorm.

cs.LG↗
arXiv2025

Bellman Optimality of Average-Reward Robust Markov Decision Processes with a Constant Gain

Learning and optimal control under robust Markov decision processes (MDPs) have received increasing attention, yet most existing theory, algorithms, and applications focus on finite-horizon or discounted models. Long-run average-reward formulations, while natural in many operations research and management contexts, remain underexplored. This is primarily because the dynamic programming foundations are technically challenging and only partially understood, with several fundamental questions remaining open. This paper steps toward a general framework for average-reward robust MDPs by analyzing the constant-gain setting. We study the average-reward robust control problem with possible information asymmetries between the controller and an S-rectangular adversary. Our analysis centers on the constant-gain robust Bellman equation, examining both the existence of solutions and their relationship to the optimal average reward. Specifically, we identify when solutions to the robust Bellman equation characterize the optimal average reward and stationary policies, and we provide one-sided weak communication conditions ensuring solutions' existence. These findings expand the dynamic programming theory for average-reward robust MDPs and lay a foundation for robust dynamic decision making under long-run average criteria in operational environments.

math.OC↗
arXiv2025

Evolving Triple Knowledge-Augmented LLMs for Code Translation in Repository Context

Large language models (LLMs) have behaved well in function-level code translation without repository-level context. However, the performance of LLMs in repository-level context code translation remains suboptimal due to complex dependencies and context, hindering their adoption in industrial settings. In this work, we propose a novel LLM-based code translation technique K-Trans, which leverages triple knowledge augmentation to enhance LLM's translation quality under repository context in real-world software development. First, K-Trans constructs a evolving translation knowledge base by extracting relevant information from target-language codebases, the repository being translated, and prior translation results. Second, for each function to be translated, K-Trans retrieves relevant triple knowledge, including target-language code samples, dependency usage examples, and successful translation function pairs, serving as references to enhance LLM for translation. Third, K-Trans constructs a knowledge-augmented translation prompt using the retrieved triple knowledge and employs LLMs to generate the translated code while preserving repository context. It further leverages LLMs for self-debugging, enhancing translation correctness. Lastly, K-Trans continuously evolves the translation knowledge base. The experiments show that K-Trans substantially outperforms the baseline adapted from previous work by 19.4%/40.2% relative improvement in pass@1 and 0.138 in CodeBLEU. It is important to note that the results also demonstrate that each knowledge significantly contributes to K-Trans's effectiveness in handling repository-level context code translation, with dependency usage examples making the most notable contribution. Moreover, as the self-evolution process progresses, the knowledge base continuously enhances the LLM's performance across various aspects of the repository-level code translation.

cs.SE↗
arXiv2025

Learning Optimal Distributionally Robust Stochastic Control in Continuous State Spaces

We study data-driven learning of robust stochastic control for infinite-horizon systems with potentially continuous state and action spaces. In many managerial settings--supply chains, finance, manufacturing, services, and dynamic games--the state-transition mechanism is determined by system design, while available data capture the distributional properties of the stochastic inputs from the environment. For modeling and computational tractability, a decision maker often adopts a Markov control model with i.i.d. environment inputs, which can render learned policies fragile to internal dependence or external perturbations. We introduce a distributionally robust stochastic control paradigm that promotes policy reliability by introducing adaptive adversarial perturbations to the environment input, while preserving the modeling, statistical, and computational tractability of the Markovian formulation. From a modeling perspective, we examine two adversary models--current-action-aware and current-action-unaware--leading to distinct dynamic behaviors and robust optimal policies. From a statistical learning perspective, we characterize optimal finite-sample minimax rates for uniform learning of the robust value function across a continuum of states under ambiguity sets defined by the $f_k$-divergence and Wasserstein distance. To efficiently compute the optimal robust policies, we further propose algorithms inspired by deep reinforcement learning methodologies. Finally, we demonstrate the applicability of the framework to real managerial problems.

stat.ML↗