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Jianhui Huang

Publications and source records attributed to Jianhui Huang.

At least 19 recordsLinked to original sources

Compiler-Grounded Hierarchical Diagnosis for LLM-Based Triton Kernel Optimization

Recent advances in large language models (LLMs) have enabled automated kernel generation and optimization, but most existing approaches rely on surface signals such as compilation feedback and profiling metrics. These signals reveal that a kernel is slow, but not why the backend compiler fails to realize a profitable optimization, especially on emerging accelerators such as NPUs. We therefore formulate kernel optimization as a progressive cross-layer diagnosis problem that links runtime symptoms to IR structure and compiler behavior before rewriting source. Based on this insight, we present our system, a compiler-grounded and hierarchical optimization framework for Triton kernels. the system escalates from lightweight pattern triage and profiling diagnosis to IR attribution and compiler-grounded analysis only when deeper evidence is needed, then proposes evidence-backed source-level rewrites. We implement the system on Triton for Ascend NPUs and evaluate it on 37 successfully converted entries from a standardized NPUKernelBench-derived Ascend 950 benchmark. Across these entries, the system attains a geometric-mean speedup of 4.35$\times$ and a median speedup of 2.73$\times$ from the initial to optimized Triton kernel; 22/37 exceed 2$\times$ and 13/37 exceed 5$\times$. The complete distribution ranges from near-baseline entries to large wins, motivating transparent reporting of the current system's scope and limitations.

cs.AI

Nonlinear Open-Loop Mean field Stackelberg Stochastic Differential Game

This paper studies a nonlinear open-loop mean field Stackelberg stochastic differential game by using the probabilistic method through the FBSDE system and the idea of taking control as the fixed point. We successively construct the decentralized optimal control problems for the followers and the leader, among which the leader's decentralized optimal control problem is a partial information optimal control problem with the fully coupled conditional mean-field forward-backward stochastic differential equation (FBSDE, in short) as the state equation. We successively derive the maximum principles for the corresponding decentralized optimal control problems of the followers and the leader. To obtain the existence, uniqueness and estimations of solutions of the state equation, the variational equation and the adjoint equation for the leader's decentralized optimal control problem, we study the well-posedness of a new form of conditional mean-field FBSDE. And the decentralized optimal controls of the leader and followers are proved to be the approximate Stackelberg equilibrium of the nonlinear mean field Stackelberg game. Finally, we apply the theoretical results developed in this paper to solve a nonlinear mean field Stackelberg game problem between a robot control center and unicycle-type swarm robots.

math.OC

Mean field games of major-minor agents with recursive functionals

This paper investigates a novel class of mean field games involving a major agent and numerous minor agents, where the agents' functionals are recursive with nonlinear backward stochastic differential equation (BSDE) representations. We term these games "recursive major-minor" (RMM) problems. Our RMM modeling is quite general, as it employs empirical (state, control) averages to define the weak couplings in both the functionals and dynamics of all agents, regardless of their status as major or minor. We construct an auxiliary limiting problem of the RMM by a novel unified structural scheme combining a bilateral perturbation with a mixed hierarchical recomposition. This scheme has its own merits as it can be applied to analyze more complex coupling structures than those in the current RMM. Subsequently, we derive the corresponding consistency condition and explore asymptotic RMM equilibria. Additionally, we examine the RMM problem in specific linear-quadratic settings for illustrative purposes.

math.OC

Backward stochastic differential equations with conditional reflection and related recursive optimal control problems

We introduce a new type of reflected backward stochastic differential equations (BSDEs) for which the reflection constraint is imposed on its main solution component, denoted as $Y$ by convention, but in terms of its conditional expectation $\mathbb{E}[Y_t|\mathcal{G}_{t}]$ on a general sub-filtration $\{\mathcal{G}_{t}\}.$ We thus term such equation as conditionally reflected BSDE (for short, conditional RBSDE). Conditional RBSDE subsumes classical RBSDE with a pointwise reflection barrier, and the recent developed BSDE with a mean reflection constraint, as its two special and extreme cases: they exactly correspond to $\{\mathcal{G}_{t}\}$ being the full filtration to represent complete information, and the degenerated filtration to deterministic scenario, respectively. For conditional RBSDE, we obtain its existence and uniqueness under mild conditions by combining the Snell envelope method with Skorokhod lemma. We also discuss its connection, in the case of linear driver, to a class of optimal stopping problems in presence of partial information. As a by-product, a new version of comparison theorem is obtained. With the help of this connection, we study weak formulations of a class of optimal control problems with reflected recursive functionals by characterizing the related optimal solution and value. Moreover, in the special case of recursive functionals being RBSDE with pointwise reflections, we study the strong formulations of related stochastic backward recursive control and zero-sum games, both in non-Markovian framework, that are of their own interests and have not been fully explored by existing literatures yet.

math.PR

A Class of Mean-Field Games with Optimal Stopping and its Inverse Problem

This paper revisits the well-studied \emph{optimal stopping} problem but within the \emph{large-population} framework. In particular, two classes of optimal stopping problems are formulated by taking into account the \emph{relative performance criteria}. It is remarkable the relative performance criteria, also understood by the \emph{Joneses preference}, \emph{habit formation utility}, or \emph{relative wealth concern} in economics and finance, plays an important role in explaining various decision behaviors such as price bubbles. By introducing such criteria in large-population setting, a given agent can compare his individual stopping rule with the average behaviors of its cohort. The associated mean-field games are formulated in order to derive the decentralized stopping rules. The related consistency conditions are characterized via some coupled equation system and the asymptotic Nash equilibrium properties are also verified. In addition, some \emph{inverse} mean-field optimal stopping problem is also introduced and discussed.

math.OC

Mixed Social Optima and Nash equilibrium in Linear-Quadratic-Gaussian Mean-field System

This paper investigates a class of mixed stochastic linear-quadratic-Gaussian (LQG) social optimization and Nash game in the context of a large scale system. Two types of interactive agents are involved: a major agent and a large number of weakly-coupled minor agents. All minor agents are cooperative to minimize the social cost as the sum of their individual costs, whereas such social cost are conflictive to that of major agent. Thus, major agent and all minor agents are further competitive to reach some non-zero Nash equilibrium. The control processes enter both diffusion and drift terms of all major and minors' states. This extends the standard setup in which control only enters the drift terms, and such extension brings more modeling difference and technical difficulties, in particular, when dealing with the feedback decentralized strategy via Riccati equation and mean-field consistency condition (CC) representation. Applying the mean-field approximations and person-by-person optimality, we obtain auxiliary control problems for major agent and minor agents, respectively. The decentralized social strategy is derived by a class of new CC system, which is mean-field forward-backward stochastic differential equations. The well-posedness of the CC system is obtained by the discounting method. The related asymptotic social optimality for minor agents, and Nash equilibrium for major-minor agents are also verified.

math.OC

A unified approach to mean-field team: homogeneity, heterogeneity and quasi-exchangeability

This paper aims to systematically solve stochastic team optimization of large-scale system, in a rather general framework. Concretely, the underlying large-scale system involves considerable weakly-coupled cooperative agents for which the individual admissible controls: (\textbf{i}) enter the diffusion terms, (\textbf{ii}) are constrained in some closed-convex subsets, and (\textbf{iii}) subject to a general \emph{partial decentralized information} structure. A more important but serious feature: (\textbf{iv}) all agents are heterogenous with \emph{continuum} instead \emph{finite} diversity. Combination of (\textbf{i})-(\textbf{iv}) yields a quite general modeling of stochastic team-optimization, but on the other hand, also fails current existing techniques of team analysis. In particular, classical team consistency with continuum heterogeneity collapses because of (\textbf{i}). As the resolution, a novel \emph{unified approach} is proposed under which the intractable \emph{continuum} \emph{heterogeneity} can be converted to a more tractable \emph{homogeneity}. As a trade-off, the underlying randomness is augmented, and all agents become (quasi) weakly-exchangeable. Such approach essentially involves a subtle balance between homogeneity v.s. heterogeneity, and left (prior-sampling)- v.s. right (posterior-sampling) information filtration. Subsequently, the consistency condition (CC) system takes a new type of forward-backward stochastic system with \emph{double-projections} (due to (\textbf{ii}), (\textbf{iii})), along with \emph{spatial mean} on continuum heterogenous index (due to (\textbf{iv})). Such system is new in team literature and its well-posedness is also challenging. We address this issue under mild conditions. Related asymptotic optimality is also established.

math.OC

Backward Stackelberg Differential Game with Constraints: a Mixed Terminal-Perturbation and Linear-Quadratic Approach

We discuss an open-loop backward Stackelberg differential game involving single leader and single follower. Unlike most Stackelberg game literature, the state to be controlled is characterized by a backward stochastic differential equation (BSDE) for which the terminal- instead initial-condition is specified as a priori; the decisions of leader consist of a static terminal-perturbation and a dynamic linear-quadratic control. In addition, the terminal control is subject to (convex-closed) pointwise and (affine) expectation constraints. Both constraints are arising from real applications such as mathematical finance. For information pattern: the leader announces both terminal and open-loop dynamic decisions at the initial time while takes account the best response of follower. Then, two interrelated optimization problems are sequentially solved by the follower (a backward linear-quadratic (BLQ) problem) and the leader (a mixed terminal-perturbation and backward-forward LQ (BFLQ) problem). Our open-loop Stackelberg equilibrium is represented by some coupled backward-forward stochastic differential equations (BFSDEs) with mixed initial-terminal conditions. Our BFSDEs also involve nonlinear projection operator (due to pointwise constraint) combining with a Karush-Kuhn-Tucker (KKT) system (due to expectation constraint) via Lagrange multiplier. The global solvability of such BFSDEs is also discussed in some nontrivial cases. Our results are applied to one financial example.

math.OC

Analytical phase optical transfer function for Gaussian illumination and the optimized profiles

The imaging performance of tomographic deconvolution phase microscopy can be described in terms of the phase optical transfer function (POTF) which, in turn, depends on the illumination profile. To facilitate the optimization of the illumination profile, an analytical calculation method based on polynomial fitting is developed to describe the POTF for general non-uniform axially-symmetric illumination. This is then applied to Gaussian and related profiles. Compared to numerical integration methods that integrate over a series of annuli, the present analytical method is much faster and is equally accurate. Further, a balanced distribution criterion for the POTF and a least-squares minimization are presented to optimize the uniformity of the POTF. An optimum general profile is found analytically by relaxed optimal search and an optimum Gaussian profile is found through a tree search. Numerical simulations confirm the performance of these optimum profiles and support the balanced distribution criterion introduced.

physics.optics

Non-interferometric accurate phase imaging via a linear-convergence iterative optimization

This paper reported a general noninterferometric high-accuracy quantitative phase imaging (QPI) method for arbitrary complex valued objects. Given by a typical 4f optical configuration as the imaging system, three frames of small-window phase modulation are applied on the object Fourier spectrum so that redistributed intensity patterns are produced on the image plane, in which the object phase emerges at different degree. Then, an algebraic relationship that connects the object phase with the output intensity is established to provide us with an approximate closed form phase recovery. Further, an efficient iterative optimization strategy is developed to turn that approximate solution into an accurate one. Due to the linear convergence property of the iteration, a high accuracy phase recovery is achieved without requiring heavy iterations. The feasibility and accuracy of the proposed method are verified by both numerical simulations and experiments on diverse phase objects.

eess.IV

Social Optima in Leader-Follower Mean Field Linear Quadratic Control

This paper investigates a linear quadratic mean field leader-follower team problem, where the model involves one leader and a large number of weakly-coupled interactive followers. The leader and the followers cooperate to optimize the social cost. Specifically, for any strategy provided first by the leader, the followers would like to choose a strategy to minimize social cost functional. Using variational analysis and person-by-person optimality, we construct two auxiliary control problems. By solving sequentially the auxiliary control problems with consistent mean field approximations, we can obtain a set of decentralized social optimality strategy with help of a class of forward-backward consistency systems. The relevant Stackelberg equilibrium is further proved under some proper conditions.

math.OC

Linear Quadratic Gaussian Mean-Field Controls of Social Optima

This paper investigates a class of unified stochastic linear quadratic Gaussian (LQG) social optima problems involving a large number of weakly-coupled interactive agents under a {generalized} setting. For each individual agent, the control and state process enters both diffusion and drift terms in its linear dynamics, and the control weight might be \emph{indefinite} in cost functional. This setup is {innovative and has great theoretical and realistic significance} as its applications in mathematical finance {(e.g., portfolio selection in mean-variation model)}. Using some \emph{fully-coupled} variational analysis under person-by-person optimality principle, and mean-field approximation method, the decentralized social control is derived by a class of new type consistency condition (CC) system for typical representative agent. Such CC system is some mean-field forward-backward stochastic differential equation (MF-FBSDE) combined with \emph{embedding representation}. The well-posedness of such forward-backward stochastic differential equation (FBSDE) system is carefully examined. The related social asymptotic optimality is related to the convergence of the average of a series of weakly-coupled backward stochastic differential equation (BSDE). They are verified through some Lyapunov equations.

math.OC

Social Optima in Mean Field Linear-Quadratic-Gaussian Control with Volatility Uncertainty

This paper examines mean field linear-quadratic-Gaussian (LQG) social optimum control with volatility-uncertain common noise. The diffusion terms in the dynamics of agents contain an unknown volatility process driven by a common noise. We apply a robust optimization approach in which all agents view volatility uncertainty as an adversarial player. Based on the principle of person-by-person optimality and a two-step-duality technique for stochastic variational analysis, we construct an auxiliary optimal control problem for a representative agent. Through solving this problem combined with a consistent mean field approximation, we design a set of decentralized strategies, which are further shown to be asymptotically social optimal by perturbation analysis.

math.OC

Social Optima in Robust Mean Field LQG Control: From Finite to Infinite Horizon

This paper studies social optimal control of mean field LQG (linear-quadratic-Gaussian) models with uncertainty. Specially, the uncertainty is represented by a uncertain drift which is common for all agents. A robust optimization approach is applied by assuming all agents treat the uncertain drift as an adversarial player. In our model, both dynamics and costs of agents are coupled by mean field terms, and both finite- and infinite-time horizon cases are considered. By examining social functional variation and exploiting person-by-person optimality principle, we construct an auxiliary control problem for the generic agent via a class of forward-backward stochastic differential equation system. By solving the auxiliary problem and constructing consistent mean field approximation, a set of decentralized control strategies is designed and shown to be asymptotically optimal.

math.OC

Linear-Quadratic-Gaussian Mixed Mean-field Games with Heterogeneous Input Constraints

We consider a class of linear-quadratic-Gaussian mean-field games with a major agent and considerable heterogeneous minor agents in the presence of mean-field interactions. The individual admissible controls are constrained in closed convex subsets $Γ_{k}$ of $\mathbb{R}^{m}.$ The decentralized strategies for individual agents and consistency condition system are represented in an unified manner through a class of mean-field forward-backward stochastic differential equations involving projection operators on $Γ_{k}$. The well-posedness of consistency system is established in both the local and global cases by the contraction mapping and discounting method respectively. Related $\varepsilon-$Nash equilibrium property is also verified.

math.OC

Equilibrium for Time-Inconsistent Stochastic Linear--Quadratic Control under Constraint

In this paper, we study a class of stochastic time-inconsistent linear-quadratic (LQ) control problems with control input constraints. These problems are investigated within the more general framework associated with random coefficients. This paper aims to further develop a new methodology, which fundamentally differs from those in the standard control (without constraints) theory in the literature, to cope with the mathematical difficulties raised due to the presence of input constraints. We first prove that the existence of an equilibrium solution is equivalent to the existence of a solution to some forward-backward stochastic differential equations with constraints. Under convex cone constraint, an explicit solution to equilibrium for mean-variance portfolio selection can be obtained and proved to be unique. Finally, some examples are discussed to shed light on the comparison between our established results and standard control theory.

math.OC

Robust Mean Field Linear-Quadratic-Gaussian Games with Unknown $L^2$-Disturbance

This paper considers a class of mean field linear-quadratic-Gaussian (LQG) games with model uncertainty. The drift term in the dynamics of the agents contains a common unknown function. We take a robust optimization approach where a representative agent in the limiting model views the drift uncertainty as an adversarial player. By including the mean field dynamics in an augmented state space, we solve two optimal control problems sequentially, which combined with consistent mean field approximations provides a solution to the robust game. A set of decentralized control strategies is derived by use of forward-backward stochastic differential equations (FBSDE) and shown to be a robust epsilon-Nash equilibrium.

math.OC