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Baoxiang Wang

Baoxiang Wang appears in the imported research catalog. Authorship, coauthor and topic links are available while profile ownership is still unclaimed.

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math.APmath.FAMachine LearningArtificial Intelligencemath.OAMultiagent SystemsData Structures and Algorithmsmath-phmath.MPmath.SPnucl-exSocial and Information Networks

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Published work

26 published item(s)

preprint2026arXiv

The Reciprocity Gradient

Communication is fundamental to sustaining reciprocity and cooperation in strategic interactions. We identify and formulate the influence attribution problem as the central optimization difficulty inherent in such dynamics for a learning agent: any action or signal the agent emits reshapes the reputations of many third parties along combinatorially branching paths before feeding back into its own future rewards, forcing the agent to account for all of these indirect channels at once when choosing every action. To address this, we introduce the reciprocity gradient, which explicitly backpropagates reward gradients through private estimators of opponents' policies trained from public observations. The gradient flows through the reputation chain itself analytically, rather than being estimated from sampled returns. It jointly optimizes actions and evaluative signals without intrinsic rewards or reward shaping. Empirically, the method recovers near-optimal context-sensitive policies, while sample-based baselines collapse into constant-output policies.

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preprint2022arXiv

CGIBNet: Bandwidth-constrained Communication with Graph Information Bottleneck in Multi-Agent Reinforcement Learning

Communication is one of the core components for cooperative multi-agent reinforcement learning (MARL). The communication bandwidth, in many real applications, is always subject to certain constraints. To improve communication efficiency, in this article, we propose to simultaneously optimize whom to communicate with and what to communicate for each agent in MARL. By initiating the communication between agents with a directed complete graph, we propose a novel communication model, named Communicative Graph Information Bottleneck Network (CGIBNet), to simultaneously compress the graph structure and the node information with the graph information bottleneck principle. The graph structure compression is designed to cut the redundant edges for determining whom to communicate with. The node information compression aims to address the problem of what to communicate via learning compact node representations. Moreover, CGIBNet is the first universal module for bandwidth-constrained communication, which can be applied to various training frameworks (i.e., policy-based and value-based MARL frameworks) and communication modes (i.e., single-round and multi-round communication). Extensive experiments are conducted in Traffic Control and StarCraft II environments. The results indicate that our method can achieve better performance in bandwidth-constrained settings compared with state-of-the-art algorithms.

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preprint2022arXiv

Complex valued semi-linear heat equations in super-critical spaces $E^s_σ$

We consider the Cauchy problem for the complex valued semi-linear heat equation $$ \partial_t u - Δu - u^m =0, \ \ u (0,x) = u_0(x), $$ where $m\geq 2$ is an integer and the initial data belong to super-critical spaces $E^s_σ$ for which the norms are defined by $$ \|f\|_{E^s_σ} = \|\langle ξ\rangle^σ2^{s|ξ|}\hat{f}(ξ)\|_{L^2}, \ \ σ\in \mathbb{R}, \ s<0. $$ If $s<0$, then any Sobolev space $H^{r}$ is a subspace of $E^s_σ$, i.e., $\cup_{r \in \mathbb{R}} H^r \subset E^s_σ$. We obtain the global existence and uniqueness of the solutions if the initial data belong to $E^s_σ$ ($s<0, \ σ\geq d/2-2/(m-1)$) and their Fourier transforms are supported in the first octant, the smallness conditions on the initial data in $E^s_σ$ are not required for the global solutions. Moreover, we show that the error between the solution $u$ and the iteration solution $u^{(j)}$ is $C^j/(j\,!)^2$. Similar results also hold if the nonlinearity $u^m$ is replaced by an exponential function $e^u-1$.

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preprint2022arXiv

Differentially Private Temporal Difference Learning with Stochastic Nonconvex-Strongly-Concave Optimization

Temporal difference (TD) learning is a widely used method to evaluate policies in reinforcement learning. While many TD learning methods have been developed in recent years, little attention has been paid to preserving privacy and most of the existing approaches might face the concerns of data privacy from users. To enable complex representative abilities of policies, in this paper, we consider preserving privacy in TD learning with nonlinear value function approximation. This is challenging because such a nonlinear problem is usually studied in the formulation of stochastic nonconvex-strongly-concave optimization to gain finite-sample analysis, which would require simultaneously preserving the privacy on primal and dual sides. To this end, we employ a momentum-based stochastic gradient descent ascent to achieve a single-timescale algorithm, and achieve a good trade-off between meaningful privacy and utility guarantees of both the primal and dual sides by perturbing the gradients on both sides using well-calibrated Gaussian noises. As a result, our DPTD algorithm could provide $(ε,δ)$-differential privacy (DP) guarantee for the sensitive information encoded in transitions and retain the original power of TD learning, with the utility upper bounded by $\widetilde{\mathcal{O}}(\frac{(d\log(1/δ))^{1/8}}{(nε)^{1/4}})$ (The tilde in this paper hides the log factor.), where $n$ is the trajectory length and $d$ is the dimension. Extensive experiments conducted in OpenAI Gym show the advantages of our proposed algorithm.

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preprint2022arXiv

Edge Rewiring Goes Neural: Boosting Network Resilience without Rich Features

Improving the resilience of a network is a fundamental problem in network science, which protects the underlying system from natural disasters and malicious attacks. This is traditionally achieved via successive degree-preserving edge rewiring operations, with the major limitation of being transductive. Inductively solving graph-related tasks with sequential actions is accomplished by adopting graph neural networks (GNNs) coupled with reinforcement learning under the scenario with rich graph features. However, such frameworks cannot be directly applied to resilience tasks where only pure topological structure is available. In this case, GNNs can barely learn useful information, resulting in prohibitive difficulty in making actions for successively rewiring edges under a reinforcement learning context. In this paper, we study in depth the reasons why typical GNNs cause such failure. Based on this investigation, we propose ResiNet, the first end-to-end trainable inductive framework to discover resilient network topologies while balancing network utility. To this end, we reformulate resilience optimization as an MDP equipped with edge rewiring action space, and propose a pure topology-oriented variant of GNN called filtration enhanced graph neural network (FireGNN), which can learn from graphs without rich features. Extensive experiments demonstrate that ResiNet achieves a near-optimal resilience gain on various graphs while balancing the utility, and outperforms existing approaches by a large margin.

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preprint2022arXiv

Global Cauchy problems for the nonlocal (derivative) NLS in $E^s_σ$

We consider the Cauchy problem for the (derivative) nonlocal NLS in super-critical function spaces $E^s_σ$ for which the norms are defined by $$ \|f\|_{E^s_σ} = \|\langleξ\rangle^σ2^{s|ξ|}\hat{f}(ξ)\|_{L^2}, \ s<0, \ σ\in \mathbb{R}. $$ Any Sobolev space $H^{r}$ is a subspace of $E^s_σ$, i.e., $H^r \subset E^s_σ$ for any $ r,σ\in \mathbb{R}$ and $s<0$. Let $s<0$ and $σ>-1/2$ ($σ>0$) for the nonlocal NLS (for the nonlocal derivative NLS). We show the global existence and uniqueness of the solutions if the initial data belong to $E^s_σ$ and their Fourier transforms are supported in $(0, \infty)$, the smallness conditions on the initial data in $E^s_σ$ are not required for the global solutions.

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preprint2022arXiv

Provably Efficient Convergence of Primal-Dual Actor-Critic with Nonlinear Function Approximation

We study the convergence of the actor-critic algorithm with nonlinear function approximation under a nonconvex-nonconcave primal-dual formulation. Stochastic gradient descent ascent is applied with an adaptive proximal term for robust learning rates. We show the first efficient convergence result with primal-dual actor-critic with a convergence rate of $\mathcal{O}\left(\sqrt{\frac{\ln \left(N d G^2 \right)}{N}}\right)$ under Markovian sampling, where $G$ is the element-wise maximum of the gradient, $N$ is the number of iterations, and $d$ is the dimension of the gradient. Our result is presented with only the Polyak-Łojasiewicz condition for the dual variables, which is easy to verify and applicable to a wide range of reinforcement learning (RL) scenarios. The algorithm and analysis are general enough to be applied to other RL settings, like multi-agent RL. Empirical results on OpenAI Gym continuous control tasks corroborate our theoretical findings.

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preprint2022arXiv

Shapley Counterfactual Credits for Multi-Agent Reinforcement Learning

Centralized Training with Decentralized Execution (CTDE) has been a popular paradigm in cooperative Multi-Agent Reinforcement Learning (MARL) settings and is widely used in many real applications. One of the major challenges in the training process is credit assignment, which aims to deduce the contributions of each agent according to the global rewards. Existing credit assignment methods focus on either decomposing the joint value function into individual value functions or measuring the impact of local observations and actions on the global value function. These approaches lack a thorough consideration of the complicated interactions among multiple agents, leading to an unsuitable assignment of credit and subsequently mediocre results on MARL. We propose Shapley Counterfactual Credit Assignment, a novel method for explicit credit assignment which accounts for the coalition of agents. Specifically, Shapley Value and its desired properties are leveraged in deep MARL to credit any combinations of agents, which grants us the capability to estimate the individual credit for each agent. Despite this capability, the main technical difficulty lies in the computational complexity of Shapley Value who grows factorially as the number of agents. We instead utilize an approximation method via Monte Carlo sampling, which reduces the sample complexity while maintaining its effectiveness. We evaluate our method on StarCraft II benchmarks across different scenarios. Our method outperforms existing cooperative MARL algorithms significantly and achieves the state-of-the-art, with especially large margins on tasks with more severe difficulties.

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preprint2020arXiv

Learning and Testing Variable Partitions

$ $Let $F$ be a multivariate function from a product set $Σ^n$ to an Abelian group $G$. A $k$-partition of $F$ with cost $δ$ is a partition of the set of variables $\mathbf{V}$ into $k$ non-empty subsets $(\mathbf{X}_1, \dots, \mathbf{X}_k)$ such that $F(\mathbf{V})$ is $δ$-close to $F_1(\mathbf{X}_1)+\dots+F_k(\mathbf{X}_k)$ for some $F_1, \dots, F_k$ with respect to a given error metric. We study algorithms for agnostically learning $k$ partitions and testing $k$-partitionability over various groups and error metrics given query access to $F$. In particular we show that $1.$ Given a function that has a $k$-partition of cost $δ$, a partition of cost $\mathcal{O}(k n^2)(δ+ ε)$ can be learned in time $\tilde{\mathcal{O}}(n^2 \mathrm{poly} (1/ε))$ for any $ε> 0$. In contrast, for $k = 2$ and $n = 3$ learning a partition of cost $δ+ ε$ is NP-hard. $2.$ When $F$ is real-valued and the error metric is the 2-norm, a 2-partition of cost $\sqrt{δ^2 + ε}$ can be learned in time $\tilde{\mathcal{O}}(n^5/ε^2)$. $3.$ When $F$ is $\mathbb{Z}_q$-valued and the error metric is Hamming weight, $k$-partitionability is testable with one-sided error and $\mathcal{O}(kn^3/ε)$ non-adaptive queries. We also show that even two-sided testers require $Ω(n)$ queries when $k = 2$. This work was motivated by reinforcement learning control tasks in which the set of control variables can be partitioned. The partitioning reduces the task into multiple lower-dimensional ones that are relatively easier to learn. Our second algorithm empirically increases the scores attained over previous heuristic partitioning methods applied in this context.

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preprint2020arXiv

Resonant Decompositions and Global Well-posedness for 2D Zakharov-Kuznetsov Equation in Sobolev spaces of Negative Indices

The Cauchy problem for Zakharov-Kuznetsov equation on $\mathbb{R}^2$ is shown to be global well-posed for the initial date in $H^{s}$ provided $s>-\frac{1}{13}$. As conservation laws are invalid in Sobolev spaces below $L^2$, we construct an almost conserved quantity using multilinear correction term following the $I$-method introduced by Colliander, Keel, Staffilani, Takaoka and Tao. In contrast to KdV equation, the main difficulty is to handle the resonant interactions which are significant due to the multidimensional and multilinear setting of the problem. The proof relies upon the bilinear Strichartz estimate and the nonlinear Loomis-Whitney inequality.

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preprint2020arXiv

Scaling limit of Modulation Spaces and Their Applications

Modulation spaces $M^s_{p,q}$ were introduced by Feichtinger \cite{Fei83} in 1983. By resorting to the wavelet basis, Bényi and Oh \cite{BeOh20} defined a modified version to Feichtinger's modulation spaces for which the symmetry scalings are emphasized for its possible applications in PDE. By carefully investigating the scaling properties of modulation spaces and their connections with the wavelet basis, we will introduce a class of generalized modulation spaces, which contain both Feichtinger's and Bényi and Oh's modulation spaces. As their applications, we will give a local well-posedness and a (small data) global well-posedness results for NLS in some rougher generalized modulation spaces, which generalize the well posedness results of \cite{BeOk09} and \cite{WaHud07}, and certain super-critical initial data in $H^s$ or in $L^p$ are involved in these spaces.

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preprint2020arXiv

The Gambler's Problem and Beyond

We analyze the Gambler's problem, a simple reinforcement learning problem where the gambler has the chance to double or lose the bets until the target is reached. This is an early example introduced in the reinforcement learning textbook by Sutton and Barto (2018), where they mention an interesting pattern of the optimal value function with high-frequency components and repeating non-smooth points. It is however without further investigation. We provide the exact formula for the optimal value function for both the discrete and the continuous cases. Though simple as it might seem, the value function is pathological: fractal, self-similar, derivative taking either zero or infinity, and not written as elementary functions. It is in fact one of the generalized Cantor functions, where it holds a complexity that has been uncharted thus far. Our analyses could provide insights into improving value function approximation, gradient-based algorithms, and Q-learning, in real applications and implementations.

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preprint2016arXiv

Approximation property and nuclearity on mixed-norm $L^p$, modulation and Wiener amalgam spaces

In this paper we first prove the metric approximation property for weighted mixed-norm $L_w^{(p_1,\dots ,p_n)}$ spaces. Using Gabor frame representation this implies that the same property holds in weighted modulation and Wiener amalgam spaces. As a consequence, Grothendieck's theory becomes applicable, and we give criteria for nuclearity and $r$-nuclearity for operators acting on these space as well as derive the corresponding trace formulae. Finally, we apply the notion of nuclearity to functions of the harmonic oscillator on modulation spaces.

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preprint2016arXiv

Dynamical Behavior for the Solutions of the Navier-Stokes Equation

We study the Cauchy problem for the incompressible Navier-Stokes equations (NS) in three and higher spatial dimensions: \begin{align} u_t -Δu+u\cdot \nabla u +\nabla p=0, \ \ {\rm div} u=0, \ \ u(0,x)= u_0(x). \label{NSa} \end{align} Leray and Giga obtained that for the weak and mild solutions $u$ of NS in $L^p(\mathbb{R}^d)$ which blow up at finite time $T>0$, respectively, one has that for $d <p \leq \infty$, $$ \|u(t)\|_p \gtrsim ( T-t )^{-(1-d/p)/2}, \ \ 0< t<T. $$ We will obtain the blowup profile and the concentration phenomena in $L^p(\mathbb{R}^d)$ with $d\leq p\leq \infty$ for the blowup mild solution. On the other hand, if the Fourier support has the form ${\rm supp} \ \widehat{u_0} \subset \{ξ\in \mathbb{R}^n: ξ_1\geq L \}$ and $\|u_0\|_{\infty} \ll L$ for some $L >0$, then \eqref{NSa} has a unique global solution $u\in C(\mathbb{R}_+, L^\infty)$. Finally, if the blowup rate is of type I: $$ \|u(t)\|_p \sim ( T-t )^{-(1-d/p)/2}, \ for \ 0< t<T<\infty, \ d<p<\infty $$ in 3 dimensional case, then we can obtain a minimal blowup solution $Φ$ for which $$ \inf \{\limsup_{t \to T}(T-t)^{(1-3/p)/2}\|u(t)\|_{L^p_x}: \ u\in C([0,T); L^p) \mbox{\ solves \eqref{NSa}}\} $$ is attainable at some $Φ\in L^\infty (0,T; \ \dot B^{-1+6/p}_{p/2,\infty})$.

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preprint2016arXiv

Grothendieck-Lidskii trace formula for mixed-norm and variable Lebesgue spaces

In this note we present the metric approximation property for weighted mixed-norm $L_w^{(p_1,\dots ,p_n)}$ and variable exponent Lebesgue type spaces. As a consequence, this also implies the same property for modulation and Wiener-Amalgam spaces. We then characterise nuclear operators on such spaces and state the corresponding Grothendieck-Lidskii trace formulae. We apply the obtained results to derive criteria for nuclearity and trace formulae for periodic operators on $\mathbb R^n$ and functions of the harmonic oscillator in terms of the global symbol.

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preprint2016arXiv

Local Well-Posedness for the Derivative Nonlinear Schrödinger Equations with $L^2$ Subcritical Data

We will show its local well-posedness in modulation spaces $M^{1/2}_{2,q}({\Real})$ $(2\leq q<\infty) $. It is well-known that $H^{1/2}$ is a critical Sobolev space of DNLS so that it is locally well-posedness in $H^s$ for $s\geq 1/2$ and ill-posed in $H^{s'}$ with $s'<1/2.$ Noticing that that $M^{1/2}_{2,q} \subset B^{1/q}_{2,q}$ is a sharp embedding and $L^2 \subset B^0_{2,\infty}$, our result contains all of the subcritical data in $M^{1/2}_{2,q}$, which contains a class of functions in $L^2\setminus H^{1/2}$.

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preprint2013arXiv

Analyticity for the (generalized) Navier-Stokes equations with rough initial data

We study the Cauchy problem for the (generalized) incompressible Navier-Stokes equations \begin{align} u_t+(-Δ)^αu+u\cdot \nabla u +\nabla p=0, \ \ {\rm div} u=0, \ \ u(0,x)= u_0. \nonumber \end{align} We show the analyticity of the local solutions of the Navier-Stokes equation ($α=1$) with any initial data in critical Besov spaces $\dot{B}^{n/p-1}_{p,q}(\mathbb{R}^n)$ with $1< p<\infty, \ 1\le q\le \infty $ and the solution is global if $u_0$ is sufficiently small in $\dot{B}^{n/p-1}_{p,q}(\mathbb{R}^n)$. In the case $p=\infty$, the analyticity for the local solutions of the Navier-Stokes equation ($α=1$) with any initial data in modulation space $M^{-1}_{\infty,1}(\mathbb{R}^n)$ is obtained. We prove the global well-posedness for a fractional Navier-stokes equation ($α=1/2$) with small data in critical Besov spaces $\dot{B}^{n/p}_{p,1}(\mathbb{R}^n) \ (1\leq p\leq\infty)$ and show the analyticity of solutions with small initial data either in $\dot{B}^{n/p}_{p,1}(\mathbb{R}^n) \ (1\leq p<\infty)$ or in $\dot{B}^0_{\infty,1} (\mathbb{R}^n)\cap {M}^0_{\infty,1}(\mathbb{R}^n)$. Similar results also hold for all $α\in (1/2,1)$.

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preprint2012arXiv

$α$-Modulation Spaces (I)

First, we consider some fundamental properties including dual spaces, complex interpolations of $α$-modulation spaces $M^{s,α}_{p,q}$ with $0<p,q \le \infty$. Next, necessary and sufficient conditions for the scaling property and the inclusions between $α_1$-modulation and $α_2$-modulation spaces are obtained. Finally, we give some criteria for $α$-modulation spaces constituting multiplication algebra. As a by-product, we show that there exists an $α$-modulation space which is not an interpolation space between modulation and Besov spaces.

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preprint2012arXiv

Sharp global well-posedness for non-elliptic derivative Schrödinger equations with small rough data

We show the sharp global well posedness for the Cauchy problem for the cubic (quartic) non-elliptic derivative Schrödinger equations with small rough data in modulation spaces $M^s_{2,1}(\mathbb{R}^n)$ for $n\ge 3$ ($n= 2$). In 2D cubic case, using the Gabor frame, we get some time-global dispersive estimates for the Schrödinger semi-group in anisotropic Lebesgue spaces, which include a time-global maximal function estimate in the space $L^2_{x_1}L^\infty_{x_2,t}$. By resorting to the smooth effect estimate together with the dispersive estimates in anisotropic Lebesgue spaces, we show that the cubic hyperbolic derivative NLS in 2D has a unique global solution if the initial data in Feichtinger-Segal algebra or in weighted Sobolev spaces are sufficiently small.

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preprint2011arXiv

Sufficient and Necessary Conditions for the fractional Gagliardo-Nirenberg Inequalities and applications to Navier-Stokes and generalized boson equations

Sufficient and necessary conditions for the generalized Gagliardo-Nirenberg (GN) inequality in Besov spaces and Triebel-Lizorkin spaces are obtained. Applying the GN inequality, we show that the finite-time blowup solutions have concentration phenomena in critical Lebesgue space L^3. Moreover, we consider the minimizer for a class of variational problem by applying the fractional GN inequality.

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preprint2010arXiv

Local well posedness for KdV with data in a subspace of $H^{-1}$ and applications to illposedness theory for KdV and mKdV

We prove the local well posedness for the KdV equation in the modulation space $M^{-1}_{2,1}(\mathbb{R})$. Our method is to substitute the dyadic decomposition by the uniform decomposition in the discrete Bourgain space. This wellposedness result enables us to show that the solution map is discontinuous at the origin with respect to the $H^{s} $-topology as soon as $s<-1$. Making use of the Miura transform we also deduce a discontinuity result for the $ H^s(\Real) $-topology, $s<0 $, for the solution map associated with the focussing and defocussing mKdV equations.

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preprint2010arXiv

Neutron spectroscopic factors of 7Li and astrophysical 6Li(n,g)7Li reaction rates

Angular distributions of the 7Li(6Li,6Li)7Li elastic scattering and the 7Li(6Li,7Li_{g.s.})6Li, 7Li(6Li,7Li*_{0.48})6Li transfer reactions at Ec.m. = 23.7 MeV were measured with the Q3D magnetic spectrograph. The optical potential of 6Li+7Li was obtained by fitting the elastic scattering differential cross sections. Based on the distorted wave Born approximation (DWBA) analysis, spectroscopic factors of 7Li=6Li+n were determined to be 0.73 +- 0.05 and 0.90 +- 0.09 for the ground and first exited states in 7Li, respectively. Using the spectroscopic factors, the cross sections of the 6Li(n,g)7Li direct neutron capture reactions and the astrophysical 6Li(n,g)7Li reaction rates were derived.

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preprint2008arXiv

Global well posedness and inviscid limit for the Korteweg-de Vries-Burgers equation

Considering the Cauchy problem for the Korteweg-de Vries-Burgers equation \begin{eqnarray*} u_t+u_{xxx}+ε|\partial_x|^{2α}u+(u^2)_x=0, \ u(0)=ϕ, \end{eqnarray*} where $0<ε,α\leq 1$ and $u$ is a real-valued function, we show that it is globally well-posed in $H^s\ (s>s_α)$, and uniformly globally well-posed in $H^s (s>-3/4)$ for all $ε\in (0,1)$. Moreover, we prove that for any $T>0$, its solution converges in $C([0,T]; H^s)$ to that of the KdV equation if $ε$ tends to 0.

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