Yuhua Zhu

Shi Jin, Yuhua Zhu

We study the Vlasov-Poisson-Fokker-Planck system with uncertainty and multiple scales. Here the uncertainty, modeled by random variables, enters the solution through initial data, while the multiple scales lead the system to its high-field or parabolic regimes. With the help of proper Lyapunov-type inequalities, under some mild conditions on the initial data, the regularity of the solution in the random space, as well as exponential decay of the solution to the global Maxwellian, are established under Sobolev norms, which are ${\it uniform}$ in terms of the scaling parameters. These are the first hypocoercivity results for a nonlinear kinetic system with random input, which are important for the understanding of the sensitivity of the system under random perturbations, and for the establishment of spectral convergence of popular numerical methods for uncertainty quantification based on (spectrally accurate) polynomial chaos expansions.

Yuhua Zhu, Zachary Izzo, Lexing Ying

This paper revisits the bandit problem in the Bayesian setting. The Bayesian approach formulates the bandit problem as an optimization problem, and the goal is to find the optimal policy which minimizes the Bayesian regret. One of the main challenges facing the Bayesian approach is that computation of the optimal policy is often intractable, especially when the length of the problem horizon or the number of arms is large. In this paper, we first show that under a suitable rescaling, the Bayesian bandit problem converges toward a continuous Hamilton-Jacobi-Bellman (HJB) equation. The optimal policy for the limiting HJB equation can be explicitly obtained for several common bandit problems, and we give numerical methods to solve the HJB equation when an explicit solution is not available. Based on these results, we propose an approximate Bayes-optimal policy for solving Bayesian bandit problems with large horizons. Our method has the added benefit that its computational cost does not increase as the horizon increases.

Hongzhan Chen, Tao Yang, Yuhua Zhu et al.

While reinforcement learning (RL) has been central to the recent success of large language models (LLMs), RL optimization is notoriously unstable, especially when compared to supervised fine-tuning (SFT). In this work, we investigate the stability gap between SFT and RL from a gradient-based perspective, and show that the convexity of the SFT loss with respect to model logits plays a key role in enabling stable training. Our theoretical analysis demonstrates that this property induces favorable gradient directionality during optimization. In contrast, Proximal Policy Optimization (PPO), a widely adopted policy gradient algorithm utilizing a clipped surrogate objective, lacks this stabilizing property. Motivated by this observation, we propose Logits Convex Optimization (LCO), a simple yet effective policy optimization framework that aligns the learned policy with an optimal target derived from the original RL objective, thereby emulating the stabilizing effects of logits-level convexity. Extensive experiments across multiple model families show that our LCO framework consistently improves training stability and outperforms conventional RL methods on a broad range of benchmarks.

José A. Carrillo, Shi Jin, Haoyu Zhang et al.

This paper presents a particle-based optimization method designed for addressing minimization problems with equality constraints, particularly in cases where the loss function exhibits non-differentiability or non-convexity. The proposed method combines components from consensus-based optimization algorithm with a newly introduced forcing term directed at the constraint set. A rigorous mean-field limit of the particle system is derived, and the convergence of the mean-field limit to the constrained minimizer is established. Additionally, we introduce a stable discretized algorithm and conduct various numerical experiments to demonstrate the performance of the proposed method.

Canbin Huang, Tianyuan Shi, Yuhua Zhu et al.

Large language model (LLM) routers improve the efficiency of multi-model systems by directing each query to the most appropriate model while leveraging the diverse strengths of heterogeneous LLMs. Most existing approaches frame routing as a classification problem based solely on the input query. While this reduces overhead by avoiding inference across all models, it overlooks valuable information that could be gleaned from potential outputs and fails to capture implicit intent or contextual nuances that often emerge only during response generation. These limitations can result in suboptimal routing decisions, particularly for complex or ambiguous queries that require deeper semantic understanding. To address this challenge, we propose Lookahead, a routing framework that "foresees" potential model outputs by predicting their latent representations and uses these predictions to guide model selection, thus enabling more informed routing without full inference. Within this framework, we implement two approaches based on causal and masked language models. Empirical evaluations across seven public benchmarks - spanning instruction following, mathematical reasoning, and code generation - show that Lookahead consistently outperforms existing routing baselines, achieving an average performance gain of 7.7% over the state-of-the-art. Our code is available at https://github.com/huangcb01/lookahead-routing.

Wenlong Mou, Yuhua Zhu

We study the problem of computing the value function from a discretely-observed trajectory of a continuous-time diffusion process. We develop a new class of algorithms based on easily implementable numerical schemes that are compatible with discrete-time reinforcement learning (RL) with function approximation. We establish high-order numerical accuracy as well as the approximation error guarantees for the proposed approach. In contrast to discrete-time RL problems where the approximation factor depends on the effective horizon, we obtain a bounded approximation factor using the underlying elliptic structures, even if the effective horizon diverges to infinity.

Pan Liao, Feng Yang, Di Wu et al.

Multi-Object Tracking (MOT) is evolving from geometric localization to Semantic MOT (SMOT) to answer complex relational queries, yet progress is hindered by semantic data scarcity and a structural disconnect between tracking architectures and Multi-modal Large Language Models (MLLMs). To address this, we introduce Grand-SMOT, a large-scale, open-world benchmark providing high-density, dual-stream narratives that comprehensively decouple individual behaviors from environmental contexts. Furthermore, we propose LLMTrack, the first framework to seamlessly integrate MLLMs into the SMOT task. LLMTrack establishes a Macro-Understanding-First paradigm, utilizing a novel Spatio-Temporal Fusion Module to align discrete geometric trajectories with continuous semantic features, effectively suppressing temporal hallucinations during online processing. Extensive experiments demonstrate that LLMTrack achieves state-of-the-art geometric tracking performance while delivering a qualitative leap in dynamic semantic reasoning. Notably, our analysis reveals that high-quality semantic narratives empower the language model to deduce complex social interactions naturally, demonstrating that direct cognitive reasoning is more effective than cumbersome explicit visual modeling. Ultimately, our contributions bridge the gap between perceptual tracking and cognitive reasoning, establishing a robust new foundation for comprehensive video understanding and intelligent narrative generation.

Hui Wu, Yi Gan, Feng Yuan et al.

Transformer based Large Language Models (LLMs) have been widely used in many fields, and the efficiency of LLM inference becomes hot topic in real applications. However, LLMs are usually complicatedly designed in model structure with massive operations and perform inference in the auto-regressive mode, making it a challenging task to design a system with high efficiency. In this paper, we propose an efficient LLM inference solution with low latency and high throughput. Firstly, we simplify the LLM decoder layer by fusing data movement and element-wise operations to reduce the memory access frequency and lower system latency. We also propose a segment KV cache policy to keep key/value of the request and response tokens in separate physical memory for effective device memory management, helping enlarge the runtime batch size and improve system throughput. A customized Scaled-Dot-Product-Attention kernel is designed to match our fusion policy based on the segment KV cache solution. We implement our LLM inference solution on Intel GPU and publish it publicly. Compared with the standard HuggingFace implementation, the proposed solution achieves up to 7x lower token latency and 27x higher throughput for some popular LLMs on Intel GPU.

Tao Yang, Yuhua Zhu, Xiaojun Quan et al.

The current research on Role-Playing Conversational Agents (RPCAs) with Large Language Models (LLMs) primarily focuses on imitating specific speaking styles and utilizing character backgrounds, neglecting the depiction of deeper personality traits.~In this study, we introduce personality-infused role-playing for LLM agents, which encourages agents to accurately portray their designated personality traits during dialogues. We then propose PsyPlay, a dialogue generation framework that facilitates the expression of rich personalities among multiple LLM agents. Specifically, PsyPlay enables agents to assume roles with distinct personality traits and engage in discussions centered around specific topics, consistently exhibiting their designated personality traits throughout the interactions. Validation on generated dialogue data demonstrates that PsyPlay can accurately portray the intended personality traits, achieving an overall success rate of 80.31% on GPT-3.5. Notably, we observe that LLMs aligned with positive values are more successful in portraying positive personality roles compared to negative ones. Moreover, we construct a dialogue corpus for personality-infused role-playing, called PsyPlay-Bench. The corpus, which consists of 4745 instances of correctly portrayed dialogues using PsyPlay, aims to further facilitate research in personalized role-playing and dialogue personality detection.

Nicolás García Trillos, Aditya Kumar Akash, Sixu Li et al. · oxford

Adversarial attacks pose significant challenges in many machine learning applications, particularly in the setting of distributed training and federated learning, where malicious agents seek to corrupt the training process with the goal of jeopardizing and compromising the performance and reliability of the final models. In this paper, we address the problem of robust federated learning in the presence of such attacks by formulating the training task as a bi-level optimization problem. We conduct a theoretical analysis of the resilience of consensus-based bi-level optimization (CB$^2$O), an interacting multi-particle metaheuristic optimization method, in adversarial settings. Specifically, we provide a global convergence analysis of CB$^2$O in mean-field law in the presence of malicious agents, demonstrating the robustness of CB$^2$O against a diverse range of attacks. Thereby, we offer insights into how specific hyperparameter choices enable to mitigate adversarial effects. On the practical side, we extend CB$^2$O to the clustered federated learning setting by proposing FedCB$^2$O, a novel interacting multi-particle system, and design a practical algorithm that addresses the demands of real-world applications. Extensive experiments demonstrate the robustness of the FedCB$^2$O algorithm against label-flipping attacks in decentralized clustered federated learning scenarios, showcasing its effectiveness in practical contexts.

Qihao Ye, Xiaochuan Tian, Yuhua Zhu

This paper develops a model-based framework for continuous-time policy evaluation (CTPE) in reinforcement learning, incorporating both Brownian and Lévy noise to model stochastic dynamics influenced by rare and extreme events. Our approach formulates the policy evaluation problem as solving a partial integro-differential equation (PIDE) for the value function with unknown coefficients. A key challenge in this setting is accurately recovering the unknown coefficients in the stochastic dynamics, particularly when driven by Lévy processes with heavy tail effects. To address this, we propose a robust numerical approach that effectively handles both unbiased and censored trajectory datasets. This method combines maximum likelihood estimation with an iterative tail correction mechanism, improving the stability and accuracy of coefficient recovery. Additionally, we establish a theoretical bound for the policy evaluation error based on coefficient recovery error. Through numerical experiments, we demonstrate the effectiveness and robustness of our method in recovering heavy-tailed Lévy dynamics and verify the theoretical error analysis in policy evaluation.

Jiale Han, Xiaowu Dai, Yuhua Zhu

Experience replay is a foundational technique in reinforcement learning that enhances learning stability by storing past experiences in a replay buffer and reusing them during training. Despite its practical success, its theoretical properties remain underexplored. In this paper, we present a theoretical framework that models experience replay using resampled $U$- and $V$-statistics, providing rigorous variance reduction guarantees. We apply this framework to policy evaluation tasks using the Least-Squares Temporal Difference (LSTD) algorithm and a Partial Differential Equation (PDE)-based model-free algorithm, demonstrating significant improvements in stability and efficiency, particularly in data-scarce scenarios. Beyond policy evaluation, we extend the framework to kernel ridge regression, showing that the experience replay-based method reduces the computational cost from the traditional $O(n^3)$ in time to as low as $O(n^2)$ in time while simultaneously reducing variance. Extensive numerical experiments validate our theoretical findings, demonstrating the broad applicability and effectiveness of experience replay in diverse machine learning tasks.

Jose A. Carrillo, Nicolas Garcia Trillos, Sixu Li et al.

Federated learning is an important framework in modern machine learning that seeks to integrate the training of learning models from multiple users, each user having their own local data set, in a way that is sensitive to data privacy and to communication loss constraints. In clustered federated learning, one assumes an additional unknown group structure among users, and the goal is to train models that are useful for each group, rather than simply training a single global model for all users. In this paper, we propose a novel solution to the problem of clustered federated learning that is inspired by ideas in consensus-based optimization (CBO). Our new CBO-type method is based on a system of interacting particles that is oblivious to group memberships. Our model is motivated by rigorous mathematical reasoning, including a mean field analysis describing the large number of particles limit of our particle system, as well as convergence guarantees for the simultaneous global optimization of general non-convex objective functions (corresponding to the loss functions of each cluster of users) in the mean-field regime. Experimental results demonstrate the efficacy of our FedCBO algorithm compared to other state-of-the-art methods and help validate our methodological and theoretical work.

Xiaowu Dai, Yuhua Zhu

We study the statistical properties of the dynamic trajectory of stochastic gradient descent (SGD). We approximate the mini-batch SGD and the momentum SGD as stochastic differential equations (SDEs). We exploit the continuous formulation of SDE and the theory of Fokker-Planck equations to develop new results on the escaping phenomenon and the relationship with large batch and sharp minima. In particular, we find that the stochastic process solution tends to converge to flatter minima regardless of the batch size in the asymptotic regime. However, the convergence rate is rigorously proven to depend on the batch size. These results are validated empirically with various datasets and models.

Xun Tang, Lexing Ying, Yuhua Zhu

In model-based reinforcement learning, the transition matrix and reward vector are often estimated from random samples subject to noise. Even if the estimated model is an unbiased estimate of the true underlying model, the value function computed from the estimated model is biased. We introduce an operator shifting method for reducing the error introduced by the estimated model. When the error is in the residual norm, we prove that the shifting factor is always positive and upper bounded by $1+O\left(1/n\right)$, where $n$ is the number of samples used in learning each row of the transition matrix. We also propose a practical numerical algorithm for implementing the operator shifting.

Yuhua Zhu, Lexing Ying

We introduce a class of variational actor-critic algorithms based on a variational formulation over both the value function and the policy. The objective function of the variational formulation consists of two parts: one for maximizing the value function and the other for minimizing the Bellman residual. Besides the vanilla gradient descent with both the value function and the policy updates, we propose two variants, the clipping method and the flipping method, in order to speed up the convergence. We also prove that, when the prefactor of the Bellman residual is sufficiently large, the fixed point of the algorithm is close to the optimal policy.

Jing An, Lexing Ying, Yuhua Zhu

A data set sampled from a certain population is biased if the subgroups of the population are sampled at proportions that are significantly different from their underlying proportions. Training machine learning models on biased data sets requires correction techniques to compensate for the bias. We consider two commonly-used techniques, resampling and reweighting, that rebalance the proportions of the subgroups to maintain the desired objective function. Though statistically equivalent, it has been observed that resampling outperforms reweighting when combined with stochastic gradient algorithms. By analyzing illustrative examples, we explain the reason behind this phenomenon using tools from dynamical stability and stochastic asymptotics. We also present experiments from regression, classification, and off-policy prediction to demonstrate that this is a general phenomenon. We argue that it is imperative to consider the objective function design and the optimization algorithm together while addressing the sampling bias.

Yuhua Zhu, Zach Izzo, Lexing Ying

In model-free reinforcement learning, the temporal difference method and its variants become unstable when combined with nonlinear function approximations. Bellman residual minimization with stochastic gradient descent (SGD) is more stable, but it suffers from the double sampling problem: given the current state, two independent samples for the next state are required, but often only one sample is available. Recently, the authors of [Zhu et al, 2020] introduced the borrowing from the future (BFF) algorithm to address this issue for the prediction problem. The main idea is to borrow extra randomness from the future to approximately re-sample the next state when the underlying dynamics of the problem are sufficiently smooth. This paper extends the BFF algorithm to action-value function based model-free control. We prove that BFF is close to unbiased SGD when the underlying dynamics vary slowly with respect to actions. We confirm our theoretical findings with numerical simulations.

Xiaowu Dai, Yuhua Zhu

Stochastic gradient descent (SGD) is almost ubiquitously used for training non-convex optimization tasks. Recently, a hypothesis proposed by Keskar et al. [2017] that large batch methods tend to converge to sharp minimizers has received increasing attention. We theoretically justify this hypothesis by providing new properties of SGD in both finite-time and asymptotic regimes. In particular, we give an explicit escaping time of SGD from a local minimum in the finite-time regime and prove that SGD tends to converge to flatter minima in the asymptotic regime (although may take exponential time to converge) regardless of the batch size. We also find that SGD with a larger ratio of learning rate to batch size tends to converge to a flat minimum faster, however, its generalization performance could be worse than the SGD with a smaller ratio of learning rate to batch size. We include numerical experiments to corroborate these theoretical findings.