arXiv subjects

Xiaoli Wei

Publications and source records attributed to Xiaoli Wei.

At least 19 recordsLinked to original sources

arXiv2026

Continuous-time q-learning for mean-field control with common noise, part-I: Theoretical foundations

This paper investigates the continuous-time counterpart of the Q-function for entropy-regularized mean-field control (MFC) with controlled common noise, coined as q-function by Jia and Zhou (2023) in the single agent's model. We first show that, under discretely sampled actions, the value function in the exploratory formulation converges to the one in the relaxed control formulation as the time grid refines. Leveraging the relaxed control formulation, we derive the exploratory Hamilton-Jacobi-Bellman (HJB) equation, in which the controlled common noise gives rise to an additional nonlinear functional of policy, rendering the policy iteration intricate. Under certain concavity condition, we establish the existence and uniqueness of the optimal one-step policy iteration via a first-order condition using the partial linear functional derivative with respect to policy. The policy improvement at each iteration is verified by relating to an entropy-regularized optimization problem over the space of policies. In the mean-field setting, we introduce the integrated q-function (Iq-function) defined on the state distribution and the policy, and it is shown that an optimal policy is identified as a two-layer fixed point to the argmax operator of the Iq-function. Finally, we provide the explicit characterization of an optimal policy as a Gaussian distribution in the general linear-quadratic (LQ) setting.

math.OC↗

arXiv2026

Continuous-time q-learning for mean-field control with common noise, part-II: q-learning algorithms

This paper is a continuation work of Ren et al. (2026) aiming to further devise q-learning algorithms for mean-field control (MFC) with controlled common noise. Based on the relaxed control formulation, we first establish the martingale condition of the value function and the Iq-function by evaluating along the conditional state distributions generated by all test policies. As the data in the relaxed control formulation are not observable in practice, we quantify the error incurred when they are replaced by the observable ones in the exploratory formulation under discretely sampled actions. This, together with a two-layer fixed point characterization of an optimal policy in Ren et al. (2026), allows us to propose several algorithms including the Actor-Critic q-learning algorithm, in which the policy is updated in the Actor-step based on the iteration rule induced by the improved Iq-function, and the value function and Iq-function are updated in the Critic-step based on the martingale orthogonality condition using the data from the exploratory formulation. We also establish the convergence of the inner iterations in the Actor-step in an infinite-horizon linear quadratic (LQ) framework. In two examples, within and beyond LQ framework, our q-learning algorithms are implemented with satisfactory performance.

math.OC↗

arXiv2025

Efficient Seismic Data Interpolation via Sparse Attention Transformer and Diffusion Model

Seismic data interpolation is a critical pre-processing step for improving seismic imaging quality and remains a focus of academic innovation. To address the computational inefficiencies caused by extensive iterative resampling in current plug-and-play diffusion interpolation methods, we propose the diffusion-enhanced sparse attention transformer (Diff-spaformer), a novel deep learning framework. Our model integrates transformer architectures and diffusion models via a Seismic Prior Extraction Network (SPEN), which serves as a bridge module. Full-layer sparse multi-head attention and feed-forward propagation capture global information distributions, while the diffusion model provides robust prior guidance. To mitigate the computational burden of high-dimensional representations, self-attention is computed along the channel rather than the spatial dimension. We show that using negative squared Euclidean distance to compute sparse affinity matrices better suits seismic data modeling, enabling broader contribution from amplitude feature nodes. An adaptive ReLU function further discards low or irrelevant self-attention values. We conduct training within a single-stage optimization framework, requiring only a few reverse diffusion sampling steps during inference. Extensive experiments demonstrate improved interpolation fidelity and computational efficiency for both random and continuous missing data, offering a new paradigm for high-efficiency seismic data reconstruction under complex geological conditions.

physics.geo-ph↗

arXiv2025

Mean Field Control with Poissonian Common Noise: A Pathwise Compactification Approach

This paper contributes to the compactification approach to study mean-field control problems with Poissonian common noise. To overcome the lack of compactness and continuity issues caused by common noise, we exploit the point process representation of the Poisson random measure with finite intensity and propose a pathwise formulation in a two-step procedure by freezing a sample path of the common noise. In the first step, we establish the existence of optimal relaxed controls in the pathwise formulation as if common noise is absent, but with finite deterministic jumping times. The second step plays the key role in our approach, which is to aggregate the optimal solutions in the pathwise formulation over all sample paths of common noise and show that it yields an optimal solution in the original model. To this end, with the help of concatenation techniques, we first develop a pathwise superposition principle in the model with deterministic jumping times, drawing a relationship between the pathwise relaxed control problem and the pathwise measure-valued control problem. We then further bridge the equivalence among different problem formulations and verify that the constructed solution under aggregation is indeed optimal in the original problem.

math.OC↗

arXiv2024

Extended mean-field control problems with Poissonian common noise: Stochastic maximum principle and Hamiltonian-Jacobi-Bellman equation

This paper studies mean-field control problems with state-control joint law dependence and Poissonian common noise. We develop the stochastic maximum principle (SMP) and establish its connection to the Hamiltonian-Jacobi-Bellman (HJB) equation on the Wasserstein space. The presence of the conditional joint law and its discontinuity under Poissonian common noise bring new technical challenges. To develop the SMP when the control domain is not necessarily convex, we first consider a strong relaxed control formulation that allows us to perform the first-order variation. We propose the technique of extension transformation to overcome the compatibility issues arising from the joint law in the relaxed control formulation. By further establishing the equivalence between the relaxed control and the strict control formulations, we obtain the SMP for the original problem with strict controls. In the part to investigate the HJB equation, we formulate an equivalent controlled Fokker-Planck problem subjecting to a controlled measure-valued dynamics with Poisson jumps, which allows us to derive the HJB equation of the original problem under open-loop strict controls. We also establish the connection between the SMP and the HJB equation.

math.OC↗

arXiv2024

Unified continuous-time q-learning for mean-field game and mean-field control problems

This paper studies the continuous-time q-learning in mean-field jump-diffusion models in a setting where the environment simulator does not provide direct access to the population distribution. We propose the integrated q-function in decoupled form (decoupled Iq-function) and establish its martingale characterization, which provides a unified policy evaluation rule for both mean-field game (MFG) and mean-field control (MFC) problems. Moreover, we consider the learning procedure where population distribution is updated based on the representative agent's state values. Depending on the task to solve the MFG or MFC problem, we can employ the decoupled Iq-function differently to characterize the mean-field equilibrium policy or the mean-field optimal policy respectively. Based on these theoretical findings, we devise a unified parametric q-learning algorithm for both MFG and MFC problems by utilizing test policies and the averaged martingale orthogonality condition. In two applications within and beyond LQ framework, we illustrate the effectiveness and efficiency of our unified parametric q-learning algorithm for both MFG and MFC learning tasks.

math.OC↗

arXiv2024

Training-Free Robust Interactive Video Object Segmentation

Interactive video object segmentation is a crucial video task, having various applications from video editing to data annotating. However, current approaches struggle to accurately segment objects across diverse domains. Recently, Segment Anything Model (SAM) introduces interactive visual prompts and demonstrates impressive performance across different domains. In this paper, we propose a training-free prompt tracking framework for interactive video object segmentation (I-PT), leveraging the powerful generalization of SAM. Although point tracking efficiently captures the pixel-wise information of objects in a video, points tend to be unstable when tracked over a long period, resulting in incorrect segmentation. Towards fast and robust interaction, we jointly adopt sparse points and boxes tracking, filtering out unstable points and capturing object-wise information. To better integrate reference information from multiple interactions, we introduce a cross-round space-time module (CRSTM), which adaptively aggregates mask features from previous rounds and frames, enhancing the segmentation stability. Our framework has demonstrated robust zero-shot video segmentation results on popular VOS datasets with interaction types, including DAVIS 2017, YouTube-VOS 2018, and MOSE 2023, maintaining a good tradeoff between performance and interaction time.

cs.CV↗

arXiv2024

Seismic First Break Picking in a Higher Dimension Using Deep Graph Learning

Contemporary automatic first break (FB) picking methods typically analyze 1D signals, 2D source gathers, or 3D source-receiver gathers. Utilizing higher-dimensional data, such as 2D or 3D, incorporates global features, improving the stability of local picking. Despite the benefits, high-dimensional data requires structured input and increases computational demands. Addressing this, we propose a novel approach using deep graph learning called DGL-FB, constructing a large graph to efficiently extract information. In this graph, each seismic trace is represented as a node, connected by edges that reflect similarities. To manage the size of the graph, we develop a subgraph sampling technique to streamline model training and inference. Our proposed framework, DGL-FB, leverages deep graph learning for FB picking. It encodes subgraphs into global features using a deep graph encoder. Subsequently, the encoded global features are combined with local node signals and fed into a ResUNet-based 1D segmentation network for FB detection. Field survey evaluations of DGL-FB show superior accuracy and stability compared to a 2D U-Net-based benchmark method.

cs.LG↗

arXiv2023

From Bandits Model to Deep Deterministic Policy Gradient, Reinforcement Learning with Contextual Information

The problem of how to take the right actions to make profits in sequential process continues to be difficult due to the quick dynamics and a significant amount of uncertainty in many application scenarios. In such complicated environments, reinforcement learning (RL), a reward-oriented strategy for optimum control, has emerged as a potential technique to address this strategic decision-making issue. However, reinforcement learning also has some shortcomings that make it unsuitable for solving many financial problems, excessive resource consumption, and inability to quickly obtain optimal solutions, making it unsuitable for quantitative trading markets. In this study, we use two methods to overcome the issue with contextual information: contextual Thompson sampling and reinforcement learning under supervision which can accelerate the iterations in search of the best answer. In order to investigate strategic trading in quantitative markets, we merged the earlier financial trading strategy known as constant proportion portfolio insurance (CPPI) into deep deterministic policy gradient (DDPG). The experimental results show that both methods can accelerate the progress of reinforcement learning to obtain the optimal solution.

cs.LG↗

arXiv2023

Seismic Data Interpolation via Denoising Diffusion Implicit Models with Coherence-corrected Resampling

Accurate interpolation of seismic data is crucial for improving the quality of imaging and interpretation. In recent years, deep learning models such as U-Net and generative adversarial networks have been widely applied to seismic data interpolation. However, they often underperform when the training and test missing patterns do not match. To alleviate this issue, here we propose a novel framework that is built upon the multi-modal adaptable diffusion models. In the training phase, following the common wisdom, we use the denoising diffusion probabilistic model with a cosine noise schedule. This cosine global noise configuration improves the use of seismic data by reducing the involvement of excessive noise stages. In the inference phase, we introduce the denoising diffusion implicit model to reduce the number of sampling steps. Different from the conventional unconditional generation, we incorporate the known trace information into each reverse sampling step for achieving conditional interpolation. To enhance the coherence and continuity between the revealed traces and the missing traces, we further propose two strategies, including successive coherence correction and resampling. Coherence correction penalizes the mismatches in the revealed traces, while resampling conducts cyclic interpolation between adjacent reverse steps. Extensive experiments on synthetic and field seismic data validate our model's superiority and demonstrate its generalization capability to various missing patterns and different noise levels with just one training session. In addition, uncertainty quantification and ablation studies are also investigated.

physics.geo-ph↗

arXiv2023

Continuous-time q-learning for mean-field control problems

This paper studies the q-learning, recently coined as the continuous time counterpart of Q-learning by Jia and Zhou (2023), for continuous time Mckean-Vlasov control problems in the setting of entropy-regularized reinforcement learning. In contrast to the single agent's control problem in Jia and Zhou (2023), the mean-field interaction of agents renders the definition of the q-function more subtle, for which we reveal that two distinct q-functions naturally arise: (i) the integrated q-function (denoted by $q$) as the first-order approximation of the integrated Q-function introduced in Gu, Guo, Wei and Xu (2023), which can be learnt by a weak martingale condition involving test policies; and (ii) the essential q-function (denoted by $q_e$) that is employed in the policy improvement iterations. We show that two q-functions are related via an integral representation under all test policies. Based on the weak martingale condition and our proposed searching method of test policies, some model-free learning algorithms are devised. In two examples, one in LQ control framework and one beyond LQ control framework, we can obtain the exact parameterization of the optimal value function and q-functions and illustrate our algorithms with simulation experiments.

cs.LG↗

arXiv2023

UPNet: Uncertainty-based Picking Deep Learning Network for Robust First Break Picking

In seismic exploration, first break (FB) picking is a crucial aspect in the determination of subsurface velocity models, significantly influencing the placement of wells. Many deep neural networks (DNNs)-based automatic picking methods have been proposed to accelerate this processing. Significantly, the segmentation-based DNN methods provide a segmentation map and then estimate FB from the map using a picking threshold. However, the uncertainty of the results picked by DNNs still needs to be analyzed. Thus, the automatic picking methods applied in field datasets can not ensure robustness, especially in the case of a low signal-to-noise ratio (SNR). In this paper, we introduce uncertainty quantification into the FB picking task and propose a novel uncertainty-based picking deep learning network called UPNet. UPNet not only estimates the uncertainty of network output but also can filter the pickings with low confidence. Many experiments evaluate that UPNet exhibits higher accuracy and robustness than the deterministic DNN-based model, achieving State-of-the-Art (SOTA) performance in field surveys. In addition, we verify that the measurement uncertainty is meaningful, which can provide a reference for human decision-making.

cs.CV↗

arXiv2022

Itô's formula for flows of measures on semimartingales

We establish Itô's formula along flows of probability measures associated with general semimartingales; this generalizes existing results for flows of measures on Itô processes. Our approach is to first establish Itô's formula for cylindrical functions and then extend it to the general case via function approximation and localization techniques. This general form of Itô's formula enables the derivation of dynamic programming equations and verification theorems for McKean--Vlasov controls with jump diffusions and for McKean--Vlasov mixed regular-singular control problems. It also allows for generalizing the classical relationship between the maximum principle and the dynamic programming principle to the McKean--Vlasov singular control setting, where the adjoint process is expressed in terms of the derivative of the value function with respect to the probability measures.

math.PR↗

arXiv2022

Graphon Mean-Field Control for Cooperative Multi-Agent Reinforcement Learning

The marriage between mean-field theory and reinforcement learning has shown a great capacity to solve large-scale control problems with homogeneous agents. To break the homogeneity restriction of mean-field theory, a recent interest is to introduce graphon theory to the mean-field paradigm. In this paper, we propose a graphon mean-field control (GMFC) framework to approximate cooperative multi-agent reinforcement learning (MARL) with nonuniform interactions and show that the approximate order is of $\mathcal{O}(\frac{1}{\sqrt{N}})$, with $N$ the number of agents. By discretizing the graphon index of GMFC, we further introduce a smaller class of GMFC called block GMFC, which is shown to well approximate cooperative MARL. Our empirical studies on several examples demonstrate that our GMFC approach is comparable with the state-of-art MARL algorithms while enjoying better scalability.

cs.MA↗

arXiv2022

MSSPN: Automatic First Arrival Picking using Multi-Stage Segmentation Picking Network

Picking the first arrival times of prestack gathers is called First Arrival Time (FAT) picking, which is an indispensable step in seismic data processing, and is mainly solved manually in the past. With the current increasing density of seismic data collection, the efficiency of manual picking has been unable to meet the actual needs. Therefore, automatic picking methods have been greatly developed in recent decades, especially those based on deep learning. However, few of the current supervised deep learning-based method can avoid the dependence on labeled samples. Besides, since the gather data is a set of signals which are greatly different from the natural images, it is difficult for the current method to solve the FAT picking problem in case of a low Signal to Noise Ratio (SNR). In this paper, for hard rock seismic gather data, we propose a Multi-Stage Segmentation Pickup Network (MSSPN), which solves the generalization problem across worksites and the picking problem in the case of low SNR. In MSSPN, there are four sub-models to simulate the manually picking processing, which is assumed to four stages from coarse to fine. Experiments on seven field datasets with different qualities show that our MSSPN outperforms benchmarks by a large margin.Particularly, our method can achieve more than 90\% accurate picking across worksites in the case of medium and high SNRs, and even fine-tuned model can achieve 88\% accurate picking of the dataset with low SNR.

cs.CV↗

arXiv2022

Dynamic Programming Principles for Mean-Field Controls with Learning

Dynamic programming principle (DPP) is fundamental for control and optimization, including Markov decision problems (MDPs), reinforcement learning (RL), and more recently mean-field controls (MFCs). However, in the learning framework of MFCs, DPP has not been rigorously established, despite its critical importance for algorithm designs. In this paper, we first present a simple example in MFCs with learning where DPP fails with a mis-specified Q function; and then propose the correct form of Q function in an appropriate space for MFCs with learning. This particular form of Q function is different from the classical one and is called the IQ function. In the special case when the transition probability and the reward are independent of the mean-field information, it integrates the classical Q function for single-agent RL over the state-action distribution. In other words, MFCs with learning can be viewed as lifting the classical RLs by replacing the state-action space with its probability distribution space. This identification of the IQ function enables us to establish precisely the DPP in the learning framework of MFCs. Finally, we illustrate through numerical experiments the time consistency of this IQ function.

math.OC↗

arXiv2022

Thompson Sampling on Asymmetric $α$-Stable Bandits

In algorithm optimization in reinforcement learning, how to deal with the exploration-exploitation dilemma is particularly important. Multi-armed bandit problem can optimize the proposed solutions by changing the reward distribution to realize the dynamic balance between exploration and exploitation. Thompson Sampling is a common method for solving multi-armed bandit problem and has been used to explore data that conform to various laws. In this paper, we consider the Thompson Sampling approach for multi-armed bandit problem, in which rewards conform to unknown asymmetric $α$-stable distributions and explore their applications in modelling financial and wireless data.

stat.ML↗

arXiv2022

Mean-Field Multi-Agent Reinforcement Learning: A Decentralized Network Approach

One of the challenges for multi-agent reinforcement learning (MARL) is designing efficient learning algorithms for a large system in which each agent has only limited or partial information of the entire system. While exciting progress has been made to analyze decentralized MARL with the network of agents for social networks and team video games, little is known theoretically for decentralized MARL with the network of states for modeling self-driving vehicles, ride-sharing, and data and traffic routing. This paper proposes a framework of localized training and decentralized execution to study MARL with network of states. Localized training means that agents only need to collect local information in their neighboring states during the training phase; decentralized execution implies that agents can execute afterwards the learned decentralized policies, which depend only on agents' current states. The theoretical analysis consists of three key components: the first is the reformulation of the MARL system as a networked Markov decision process with teams of agents, enabling updating the associated team Q-function in a localized fashion; the second is the Bellman equation for the value function and the appropriate Q-function on the probability measure space; and the third is the exponential decay property of the team Q-function, facilitating its approximation with efficient sample efficiency and controllable error. The theoretical analysis paves the way for a new algorithm LTDE-Neural-AC, where the actor-critic approach with over-parameterized neural networks is proposed. The convergence and sample complexity is established and shown to be scalable with respect to the sizes of both agents and states. To the best of our knowledge, this is the first neural network based MARL algorithm with network structure and provably convergence guarantee.

cs.LG↗