arXiv subjects

Wenpin Tang

Publications and source records attributed to Wenpin Tang.

At least 19 recordsLinked to original sources

arXiv2026

Spec2Twin-Chain: Orchestrating Bi-Level Optimization with LLMs for Blockchain Digital Twin Construction

Building a blockchain digital twin largely requires translating domain knowledge and specific system descriptions into a simulator architecture, calibrating its parameters against behavioral evidence, and validating the constructed twin. These steps are commonly performed through application-specific modeling efforts that can be difficult to reuse across systems and downstream decision problems. We consider automating this process through Spec2Twin-Chain, a framework that formulates blockchain digital-twin construction as a bi-level optimization problem. At the upper level, a large language model proposes and revises structurally admissible architectures using system specifications, behavioral evidence, and feedback from evaluated designs. At the lower level, a simulation-based optimizer calibrates the architecture-conditioned parameters under explicit objectives and guardrail constraints. The two levels iterate. The evaluated candidates at lower levels are retained in a global archive and used to guide subsequent proposals at upper levels. We conduct controlled experiments involving twin calibration, feedback-driven recovery, stress analysis, downstream policy optimization, and policy updating. The results demonstrate that the framework can construct behaviorally accurate twins, improve initial designs through iterative feedback, and reuse calibrated twins to support downstream decisions.

cs.AI↗

arXiv2026

A Continuous-Time Reinforcement Learning Framework for Fine-Tuning Discrete Diffusion Models

We formulate reinforcement learning (RL) in continuous time with discrete state spaces and possibly arbitrary action spaces via a stochastic control approach, where the state dynamics are modeled as a controlled continuous-time Markov chain (CTMC). We consider policy optimization problems and derive the corresponding policy gradient methods, leading to continuous-time variants of proximal policy optimization (PPO) and group relative policy optimization (GRPO). As a primary application, we develop a complete continuous-time RL framework for fine-tuning score-based discrete diffusion models. The proposed framework enables reward-driven optimization without requiring differentiability on the reward signals. In contrast to the existing GRPO-based approaches that only rely on terminal rewards, our formulation allows intermediate reward or advantage signals to be incorporated throughout the denoising trajectory. Importantly, when specialized to masked diffusion models (MDMs), our framework encompasses a rich class of policy parameterizations over the vocabulary simplex with analytically tractable probability ratios, providing a unified perspective on exploration and policy optimization in MDMs. For masked diffusion large language models (dLLMs), we further propose trajectory subsampling techniques to efficiently estimate computationally prohibitive trajectory likelihoods, reducing the computational cost of computing per-position probability ratios. We showcase the effectiveness of our methods on both low-dimensional entropy-regularized optimization problems and RL post-training of dLLMs on mathematical reasoning and coding tasks.

cs.LG↗

arXiv2026

ART for Diffusion Sampling: Continuous-Time Control and Actor-Critic Learning

We study timestep allocation for score-based diffusion sampling, where a learned reverse-time dynamics is discretized on a finite grid. Uniform and hand-crafted schedules are standard choices, but they rely on fixed prescriptions and can therefore be suboptimal. To address this limitation, we propose Adaptive Reparameterized Time (ART), a continuous-time control formulation that learns a time change by treating the speed of the sampling clock as the control, so that a uniform grid on the learned clock induces adaptive timesteps in the original diffusion time. Based on a leading-order Euler error surrogate, ART provides a principled objective for allocating timesteps along the sampling trajectory. To solve this deterministic control problem, we introduce ART-RL, an auxiliary randomized formulation with Gaussian policies that turns schedule learning into a continuous-time reinforcement learning problem. We prove that the randomized ART-RL formulation is equivalent to ART at the optimizer level, in the sense that its optimal Gaussian policy recovers the optimal ART time-warping rate through its mean. We further establish policy evaluation and policy improvement characterizations and derive trajectory-based moment identities that yield implementable actor--critic updates for learning the schedule. Across experiments ranging from controlled low-dimensional settings to image generation, ART-RL can be plugged into existing diffusion samplers by changing only the timestep grid, consistently improving sample quality over strong baseline schedules at matched budgets while leaving the rest of the sampling pipeline unchanged. The learned schedules also exhibit broad generalization, transferring without retraining across sampling budgets, datasets, solvers, pipelines, and representation spaces.

cs.LG↗

arXiv2026

From Pitman's local times representation to the Gorin-Shkolnikov identity and beyond

We give a novel proof of the Gorin-Shkolnikov identity based on Pitman's SDE representation of Brownian excursion local times. More generally, we derive a family of Gaussian identities for nonlinear functionals of excursion local times, which includes Hariya's identity. These results extend naturally to reflected Brownian bridges conditioned on their local times and to Brownian meanders.

math.PR↗

arXiv2026

Proof of Stake economy under centralized exchanges--a mean field model

We consider the interaction between centralized trading and decentralized Proof of Stake (PoS) blockchain ecosystems. Motivated by the increasing dominance of centralized exchanges and the institutionalization of crypto markets, we study how trading activities on centralized exchanges affect staking behavior, token allocation, and decentralization within a PoS blockchain. We formulate a continuous-time mean field model, where the miners simultaneously act as validators in the PoS protocol and traders in a centralized market with price impact. Under suitable assumptions, we establish the local well-posedness of the mean field system, and derive a semi-explicit characterization of the equilibrium trading strategy. Numerical results suggest that centralized trading activities may enhance staking participation, and promote decentralization of the staking distribution through market incentives. We also study the effects of transaction costs and token supply mechanisms on the equilibrium staking ratio and concentration profile. These results illustrate how market microstructure and centralized liquidity provision can exert significant influence on decentralized blockchain protocols.

q-fin.MF↗

arXiv2026

OPD+: Rethinking the Advantage Design for On-Policy Distillation

On-policy distillation (OPD) is a widely used technique to transfer capabilities from capable teacher language models to the base student models, and can be formulated in a reinforcement learning style objective using student generated rollouts. Yet, despite the divergence reward being dependent on student model likelihood, existing works usually adopt a stop gradient design primarily for stability, which makes the resulting advantage estimation questionable. In this work, we provide a generic optimization framework based on f-divergence between the student and teacher, and mathematically revisit whether such design space is valid. We prove that general stop-gradient operation would lead to biased estimates of the reward objective and corresponding gradient for general divergence functions. We propose OPD+, the corrected version of OPD that demonstrates improved performance over the baseline KL approach and also supports the choice of various f-divergence. We validate our findings on mathematical reasoning and tool-use benchmarks.

cs.LG↗

arXiv2026

Tweedie's Formulae and Diffusion Generative Models Beyond Gaussian

Diffusion models have achieved remarkable success in generating samples from unknown data distributions. Most popular stochastic differential equation-based diffusion models perturb the target distribution by adding Gaussian noise, transforming it into a simple prior, and then use denoising score matching, a consequence of Tweedie's formula, to learn the score function and generate clean samples from noise. However, non-Gaussian diffusion models with state-dependent diffusion coefficient have been largely underexplored, as have the corresponding Tweedie's formulae. In this work, we extend Tweedie's formula to important non-Gaussian processes, including geometric Brownian motion (GBM), squared Bessel (BESQ) processes, and Cox-Ingersoll-Ross (CIR) processes, thereby yielding the corresponding denoising score-matching objectives. We then apply the derived formulae to image and financial time series generation using GBM- and CIR-based diffusion models, and to empirical Bayes estimation under the BESQ setting. The reported experimental results demonstrate the potential of non-Gaussian models.

stat.ML↗

arXiv2026

Sample Complexity of Transfer Learning: An Optimal Transport Approach

Transfer learning is an essential technique for many machine learning/AI models of complex structures such as large language models and generative AI. The essence of transfer learning is to leverage knowledge from resolved source tasks for a new target task, especially when the sample size $m$ of the training data for the latter is low. In this work, we rigorously analyze the potential benefit of transfer learning in terms of sample efficiency. Specifically, taking an optimal transport viewpoint of transfer learning, we find that when the data dimension $d$ is higher than $3$, the sample complexity for transfer learning is $O(m^{-(\alpha+1)/d})$, with $\alpha$ indicating the smoothness of the data distribution, as opposed to the $O(m^{-p/d})$ sample complexity for direct learning with $p$ indicating the smoothness of the optimal target model. Our finding theoretically supports a better sample efficiency for transfer learning, when the target task is optimizing over a family of not-so-smooth models (i.e., highly complex networks with the possible use of non-smooth activation functions). Using image classification as an example, we numerically demonstrate the sample efficiency for transfer learning, that is, in the data hungry regime, the model performance can be significantly improved by transfer learning.

stat.ML↗

arXiv2026

Improved techniques for fine-tuning flow models via adjoint matching: a deterministic control pipeline

We propose a deterministic adjoint matching framework that formulates human preference alignment for flow-based generative models as an optimal control problem over velocity fields. One can directly regress the control toward a value-gradient-induced target under the current policy, leading to a simple and stable training objective. Building on this perspective, we introduce a truncated adjoint scheme that focuses computation on the terminal portion of the trajectory, where reward-relevant signals concentrate, which yields substantial computational savings while preserving alignment quality. We further generalize the framework beyond standard KL-based regularization, allowing more flexible trade-offs between alignment strength and distributional preservation. Experiments on SiT-XL/2 and FLUX.2-Klein-4B demonstrate consistent gains across multiple alignment metrics, along with substantially improved diversity and mode preservation.

cs.AI↗

arXiv2026

Optimal resource allocation for maintaining system solvency

We study two optimal allocation problems for a system of independent Brownian agents whose states evolve under a limited shared control. At each time, a unit of resource can be divided and allocated across components to increase their drifts, with the objective of maximizing either (i) the probability that all components avoid ruin, or (ii) the expected number of components that avoid ruin. We identify drift thresholds separating trivial and nontrivial regimes, and derive the associated Hamilton-Jacobi-Bellman equations on the positive orthant with mixed boundary conditions at the absorbing boundary and at infinity. We also establish the existence, uniqueness, and regularity of a bounded classical solution and a verification theorem linking the PDE to the stochastic control value function. Finally, we prove a conjecture on the optimality of a socialistic allocation rule : the push-the-laggard strategy. It is optimal for the all-survive value function, while it is suboptimal for the count-survivors criterion.

math.OC↗

arXiv2026

Conditional Diffusion Guidance under Hard Constraint: A Stochastic Analysis Approach

We study conditional generation in diffusion models under hard constraints, where generated samples must satisfy prescribed events with probability one. Such constraints arise naturally in safety-critical applications and in rare-event simulation, where soft or reward-based guidance methods offer no guarantee of constraint satisfaction. Building on a probabilistic interpretation of diffusion models, we develop a principled conditional diffusion guidance framework based on Doob's h-transform, martingale representation and quadratic variation process. Specifically, the resulting guided dynamics augment a pretrained diffusion with an explicit drift correction involving the logarithmic gradient of a conditioning function, without modifying the pretrained score network. Leveraging martingale and quadratic-variation identities, we propose two novel off-policy learning algorithms based on a martingale loss and a martingale-covariation loss to estimate h and its gradient using only trajectories from the pretrained model. We provide non-asymptotic guarantees for the resulting conditional sampler in both total variation and Wasserstein distances, explicitly characterizing the impact of score approximation and guidance estimation errors. Numerical experiments demonstrate the effectiveness of the proposed methods in enforcing hard constraints and generating rare-event samples. The code of the numerical experiments can be found at https://github.com/ZhengyiGuo2002/CDG_Finance.

cs.AI↗

arXiv2026

ART for Diffusion Sampling: A Reinforcement Learning Approach to Timestep Schedule

We consider time discretization for score-based diffusion models to generate samples from a learned reverse-time dynamic on a finite grid. Uniform and hand-crafted grids can be suboptimal given a budget on the number of time steps. We introduce Adaptive Reparameterized Time (ART), which controls the clock speed of a reparameterized time variable to redistribute computation along the sampling trajectory while preserving the terminal time, with the objective of minimizing the aggregate Euler discretization error. We derive a randomized companion ART-RL that recasts ART as a continuous-time reinforcement learning problem with Gaussian policies, and prove a two-directional bridge between the two: the deterministic ART optimum lifts to an optimal Gaussian policy, and conversely any optimal Gaussian policy must recover the ART control through its mean. This bridge turns continuous-time actor--critic learning into a principled, rather than heuristic, route to the deterministic timestep optimum. Within the official EDM pipeline, ART-RL improves FID on CIFAR--10 across a wide range of budgets; after one-time offline training, the distilled deterministic schedule transfers without retraining to AFHQv2, FFHQ, and ImageNet at no extra inference cost.

cs.LG↗

arXiv2025

SOCRATES: Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations

The field of simulation optimization (SO) encompasses various methods developed to optimize complex, expensive-to-sample stochastic systems. Established methods include, but are not limited to, ranking-and-selection for finite alternatives and surrogate-based methods for continuous domains, with broad applications in engineering and operations management. The recent advent of large language models (LLMs) offers a new paradigm for exploiting system structure and automating the strategic selection and composition of these established SO methods into a tailored optimization procedure. This work introduces SOCRATES (Simulation Optimization with Correlated Replicas and Adaptive Trajectory Evaluations), a novel two-stage procedure that leverages LLMs to automate the design of tailored SO algorithms. The first stage constructs an ensemble of digital replicas of the real system. An LLM is employed to implement causal discovery from a textual description of the system, generating a structural `skeleton' that guides the sample-efficient learning of the replicas. In the second stage, this replica ensemble is used as an inexpensive testbed to evaluate a set of baseline SO algorithms. An LLM then acts as a meta-optimizer, analyzing the performance trajectories of these algorithms to iteratively revise and compose a final, hybrid optimization schedule. This schedule is designed to be adaptive, with the ability to be updated during the final execution on the real system when the optimization performance deviates from expectations. By integrating LLM-driven reasoning with LLM-assisted trajectory-aware meta-optimization, SOCRATES creates an effective and sample-efficient solution for complex SO optimization problems.

stat.ML↗

arXiv2025

Understanding Sampler Stochasticity in Training Diffusion Models for RLHF

Reinforcement Learning from Human Feedback (RLHF) is increasingly used to fine-tune diffusion models, but a key challenge arises from the mismatch between stochastic samplers used during training and deterministic samplers used during inference. In practice, models are fine-tuned using stochastic SDE samplers to encourage exploration, while inference typically relies on deterministic ODE samplers for efficiency and stability. This discrepancy induces a reward gap, raising concerns about whether high-quality outputs can be expected during inference. In this paper, we theoretically characterize this reward gap and provide non-vacuous bounds for general diffusion models, along with sharper convergence rates for Variance Exploding (VE) and Variance Preserving (VP) Gaussian models. Methodologically, we adopt the generalized denoising diffusion implicit models (gDDIM) framework to support arbitrarily high levels of stochasticity, preserving data marginals throughout. Empirically, our findings through large-scale experiments on text-to-image models using denoising diffusion policy optimization (DDPO) and mixed group relative policy optimization (MixGRPO) validate that reward gaps consistently narrow over training, and ODE sampling quality improves when models are updated using higher-stochasticity SDE training.

cs.LG↗

arXiv2025

DiFFPO: Training Diffusion LLMs to Reason Fast and Furious via Reinforcement Learning

We propose DiFFPO, Diffusion Fast and Furious Policy Optimization, a unified framework for training masked diffusion large language models (dLLMs) to reason not only better (furious), but also faster via reinforcement learning (RL). We first unify the existing baseline approach such as d1 by proposing to train surrogate policies via off-policy RL, whose likelihood is much more tractable as an approximation to the true dLLM policy. This naturally motivates a more accurate and informative two-stage likelihood approximation combined with importance sampling correction, which leads to generalized RL algorithms with better sample efficiency and superior task performance. Second, we propose a new direction of joint training efficient samplers/controllers of dLLMs policy. Via RL, we incentivize dLLMs' natural multi-token prediction capabilities by letting the model learn to adaptively allocate an inference threshold for each prompt. By jointly training the sampler, we yield better accuracies with lower number of function evaluations (NFEs) compared to training the model only, obtaining the best performance in improving the Pareto frontier of the inference-time compute of dLLMs. We showcase the effectiveness of our pipeline by training open source large diffusion language models over benchmark math and planning tasks.

cs.LG↗

arXiv2025

Diffusion Generative Models Meet Compressed Sensing, with Applications to Imaging and Finance

In this study we develop dimension-reduction techniques to accelerate diffusion model inference in the context of synthetic data generation. The idea is to integrate compressed sensing into diffusion models (hence, CSDM): First, compress the dataset into a latent space (from an ambient space), and train a diffusion model in the latent space; next, apply a compressed sensing algorithm to the samples generated in the latent space for decoding back to the original space; and the goal is to facilitate the efficiency of both model training and inference. Under certain sparsity assumptions on data, our proposed approach achieves provably faster convergence, via combining diffusion model inference with sparse recovery. It also sheds light on the best choice of the latent space dimension. To illustrate the effectiveness of this approach, we run numerical experiments on a range of datasets, including handwritten digits, medical and climate images, and financial time series for stress testing.

stat.ML↗

arXiv2025

Optimal Decisions for Liquid Staking: Allocation and Exit Timing

In this paper, we study an investor's optimal entry and exit decisions in a liquid staking protocol (LSP) and an automated market maker (AMM), primarily from the standpoint of the investor. Our analysis focuses on two key investor actions: the initial allocation decision at time $t=0$, and the optimal timing of exit. First, we derive an optimal allocation strategy that enables the investor to distribute risk across the LSP, AMM, and direct holding. Our results also offer insights for LSP and AMM designers, identifying the necessary and sufficient conditions under which the investor is incentivized to stake through an LSP, and further, to provide liquidity in addition to staking. These conditions include a lower bound on the transaction fee, for which we propose a fee mechanism that attains the bound. Second, given a fixed protocol design, we model the optimal exit timing of an individual investor using Laplace transforms and free-boundary techniques. We analyze scenarios with and without transaction fees. In the absence of fees, we decompose the investor's payoff into impermanent loss and opportunity cost, and provide theoretical results characterizing the investor's payoff and the optimal exit threshold. With transaction fees, we conduct numerical analyses to examine how fee accumulation influences exit strategies. Our results reveal that in both settings, a stop-loss strategy often maximizes the investor's expected payoff, driven by opportunity gains and the accumulation of fees where fees are present. Our analyses rely on various tools from stochastic processes and control theory, as well as convex optimization and analysis. We further support our theoretical insights with numerical experiments and explore additional properties of the investor's value function and optimal behavior.

q-fin.MF↗

arXiv2025

Beyond separability: convergence rate of vanishing viscosity approximations to mean field games via FBSDE stability

This paper studies the vanishing viscosity approximation to mean field games (MFGs) in $\mathbb{R}^d$ with a nonlocal and possibly non-separable Hamiltonian. We prove that the value function converges at a rate of $\mathcal{O}(\beta)$, where $\beta^2$ is the diffusivity constant, which matches the classical convergence rate of vanishing viscosity for Hamilton-Jacobi (HJ) equations. The same rate is also obtained for the approximation of the distribution of players as well as for the gradient of the value function. The proof is a combination of probabilistic and analytical arguments by first analyzing the forward-backward stochastic differential equation associated with the MFG, and then applying a general stability result for HJ equations. Applications of our result to $N$-player games, mean field control, and policy iteration for solving MFGs are also presented.

math.OC↗