arXiv subjects

Yuhua Zhu

Publications and source records attributed to Yuhua Zhu.

At least 19 recordsLinked to original sources

arXiv2026

Mean-Field PhiBE: Continuous-Time Mean-Field Reinforcement Learning from Discrete-Time Data

This paper develops a model-free framework for continuous-time mean-field control when the population evolves according to unknown controlled McKean--Vlasov dynamics and only discrete-time transition data are available. Model-based mean-field control requires the continuous-time drift and diffusion coefficients, which are not directly observed from fixed-step transitions, while a direct reduction to a discrete-time Bellman equation loses the continuous-time generator structure. To bridge these two viewpoints, we introduce a Mean-Field-PhiBE (MF-PhiBE), which incorporates discrete-time transition information into a continuous-time PDE on the Wasserstein space. The MF-PhiBE replaces the unknown infinitesimal drift and covariance in the policy-evaluation equation by one-step estimators computed from data, while preserving the generator structure of the McKean-Vlasov HJB equation. We also derive a policy-gradient theorem for entropy-regularized randomized feedback policies, expressing the actor direction through an action-wise infinitesimal advantage and the score of the policy. Combining these two ingredients yields a model-free actor-critic method. We prove a first-order consistency estimate showing that the value induced by an optimal MF-PhiBE policy approximates the optimal continuous-time value as the observation time step vanishes. For entropy-regularized LQR, we establish first-order policy convergence and second-order value convergence; under suitable conditions, the population-averaged feedback means coincide exactly. Numerical experiments on an LQR benchmark and a crowd-aversion problem illustrate the proposed framework.

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arXiv2026

A Robust Model-Based Approach for Continuous-Time Policy Evaluation with Unknown Lévy Process Dynamics

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, including a real-data BTC price experiment, we demonstrate the effectiveness and robustness of our method in recovering heavy-tailed Lévy dynamics and verify the theoretical error analysis in policy evaluation.

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arXiv2026

PhiBE-Q-Learning: Bridging Off-Policy Reinforcement Learning and Continuous-Time Control

In this paper, we develop an off-policy method for continuous-time reinforcement learning (CTRL), where the system dynamics are governed by an unknown stochastic differential equation (SDE) and only discrete-time trajectory data are available. A central challenge is that the classical state-action value function $Q(s,a)$, which enables off-policy learning in discrete-time RL, does not exist in CTRL (Baird, 1994; Jia and Zhou, 2023; Tallec et al., 2019). On the other hand, continuous-time control provides local notions such as the instantaneous advantage function $q(s,a)$, but these typically rely on state value function $V(s)$. To address this, we introduce a new definition of the state-action value function in CTRL and derive its governing equation. Building on the PhiBE approximation (Zhu, 2024; Zhu et al., 2025), we propose iterative algorithms to approximate the optimal $Q$-function in both model-based and model-free settings using only discrete-time off-policy data. Under linear function approximation, we establish convergence guarantees and derive explicit convergence rates for the proposed method.

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arXiv2026

Stabilizing Policy Optimization via Logits Convexity

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.

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arXiv2026

Policy Gradient for Continuous-Time Mean-Field Control

This paper develops a policy gradient method for entropy-regularized mean-field control in the discounted infinite-horizon setting. We consider randomized feedback policies and a coupled representative-particle/population system, in which the representative state evolves jointly with a population law governed by a McKean--Vlasov equation. The resulting value function is therefore defined on the product space $\mathbb R^d \times \mathcal P_2(\mathbb R^d)$. A key distinction from existing policy gradient methods for mean-field control is that, after computing the value function under a fixed policy, our approach does not require solving an additional equation to obtain the policy gradient. Instead, we derive an explicit policy gradient formula directly in terms of the value function. The formulation is based on an instantaneous advantage function, which quantifies the gain of taking a given action relative to the current randomized policy. We establish a Gâteaux policy-gradient formula, which gives the first-order variation of the objective along arbitrary policy perturbations, and then derive the corresponding ascent direction under finite-dimensional policy parametrization. The resulting formula leads to a model-based actor--critic scheme. The critic is obtained by solving the associated linear stationary Hamilton--Jacobi--Bellman equation for the value function, using cylindrical functions to represent dependence on the population law. The actor is then updated according to the derived policy-gradient formula. We further analyze the well-posedness of the PDE in a polynomial-growth function class. Finally, we illustrate the proposed method through numerical experiments on an LQR model and a crowd-motion problem.

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arXiv2026

Discretization error from regularized Reinforcement Learning to continuous-time stochastic control

This paper establishes a rigorous connection between regularized discrete-time reinforcement learning (RL) and continuous-time stochastic optimal control. Specifically, classical RL algorithms are typically solving a regularized discrete-time Bellman equation. We study the discretization error, namely, the gap between the optimal policy induced by the regularized discrete-time Bellman equation and the true optimal feedback control of the underlying continuous-time stochastic control problem. By deriving quantitative convergence rates for this gap, we provide a rigorous foundation for understanding the stability and implementation of exploratory RL policies in stochastic continuous-time environments.

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arXiv2026

An interacting particle consensus method for constrained global optimization

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.

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arXiv2026

PhiBE: A PDE-based Bellman Equation for Continuous Time Policy Evaluation

In this paper, we study policy evaluation in continuous-time reinforcement learning (RL), where the state follows an unknown stochastic differential equation (SDE), but only discrete-time data are available. We first highlight that the discrete-time Bellman equation (BE) is not always a reliable approximation to the true value function because it ignores the underlying continuous-time structure. We then introduce a new Bellman equation, PhiBE, which integrates the discrete-time information into a continuous-time PDE formulation. By leveraging the smooth structure of the underlying dynamics, PhiBE provides a provably more accurate approximation to the true value function, especially in scenarios where the underlying dynamics change slowly or the reward oscillates. Moreover, we extend PhiBE to higher orders, providing increasingly accurate approximations. We further develop a model-free algorithm for PhiBE under linear function approximation and establish its convergence under model misspecification, together with finite-sample guarantees. In contrast to existing continuous-time RL analyses, where the model misspecification error diverges as the sampling interval $Δt\to 0$ and the sample complexity typically scales as $O(Δt^{-4})$, our misspecification error is independent of $Δt$ and the resulting sample complexity improves to $O(Δt^{-1})$ by exploiting the smoothness of the underlying dynamics. Moreover, we identify a fundamental trade-off between discretization error and sample error that is intrinsic to continuous-time policy evaluation: finer time discretization reduces bias but amplifies variance, so excessively frequent sampling does not necessarily improve performance. This is an insight that does not arise in classical discrete-time RL analyses. Numerical experiments are provided to validate the theoretical guarantees we propose.

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arXiv2025

Variance Reduction via Resampling and Experience Replay

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.

stat.ML↗

arXiv2025

Lookahead Routing for Large Language Models

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.

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arXiv2025

Optimal-PhiBE: A PDE-based Model-free framework for Continuous-time Reinforcement Learning

This paper addresses continuous-time reinforcement learning (CTRL) where the system dynamics are governed by an unknown stochastic differential equation, and only discrete-time observations are available. Existing approaches face limitations: model-based PDE methods suffer from non-identifiability, while model-free methods based on the discrete-time optimal Bellman equation (Optimal-BE) suffer from large discretization errors that are highly sensitive to both the system dynamics and the reward structure. To overcome these challenges, we introduce Optimal-PhiBE, a formulation that integrates discrete-time information into a continuous-time PDE, combining the strength of both existing frameworks while mitigating their limitations. Optimal-PhiBE exhibits smaller discretization errors when the uncontrolled system evolves slowly, and demonstrates reduced sensitivity to oscillatory reward structures, and enables model-free algorithms that bypass explicit dynamics estimation. In the linear-quadratic regulator (LQR) setting, sharp error bounds are established for both Optimal-PhiBE and Optimal-BE. The results show that Optimal-PhiBE exactly recovers the optimal policy in the undiscounted case and substantially outperforms Optimal-BE when the problem is weakly discounted or control-dominant. Furthermore, we extend Optimal-PhiBE to higher orders, providing increasingly accurate approximations. A model-free policy iteration algorithm is proposed to solve the Optimal-PhiBE directly from trajectory data. Numerical experiments are conducted to verify the theoretical findings.

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arXiv2025

Defending Against Diverse Attacks in Federated Learning Through Consensus-Based Bi-Level Optimization

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.

cs.LG↗

arXiv2025

CB$^2$O: Consensus-Based Bi-Level Optimization

Bi-level optimization problems, where one wishes to find the global minimizer of an upper-level objective function over the globally optimal solution set of a lower-level objective, arise in a variety of scenarios throughout science and engineering, machine learning, and artificial intelligence. In this paper, we propose and investigate, analytically and experimentally, consensus-based bi-level optimization (CB$^2$O), a multi-particle metaheuristic derivative-free optimization method designed to solve bi-level optimization problems when both objectives may be nonconvex. Our method leverages within the computation of the consensus point a carefully designed particle selection principle implemented through a suitable choice of a quantile on the level of the lower-level objective, together with a Laplace principle-type approximation w.r.t. the upper-level objective function, to ensure that the bi-level optimization problem is solved in an intrinsic manner. We give an existence proof of solutions to a corresponding mean-field dynamics, for which we first establish the stability of our consensus point w.r.t. a combination of Wasserstein and $L^2$ perturbations, and consecutively resort to PDE considerations extending the classical Picard iteration to construct a solution. For such solution, we provide a global convergence analysis in mean-field law showing that the solution of the associated nonlinear nonlocal Fokker-Planck equation converges exponentially fast to the unique solution of the bi-level optimization problem provided suitable choices of the hyperparameters. The practicability and efficiency of our CB$^2$O algorithm is demonstrated through extensive numerical experiments in the settings of constrained global optimization, sparse representation learning, and robust (clustered) federated learning.

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arXiv2025

PsyPlay: Personality-Infused Role-Playing Conversational Agents

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.

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arXiv2024

On Bellman equations for continuous-time policy evaluation I: discretization and approximation

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.

cs.LG↗

arXiv2024

Efficient LLM inference solution on Intel GPU

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.

cs.AR↗

arXiv2023

Continuous-in-time Limit for Bayesian Bandits

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.

math.OC↗

arXiv2023

FedCBO: Reaching Group Consensus in Clustered Federated Learning through Consensus-based Optimization

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.

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