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Estimating the total treatment effect (TTE) of a new feature in social platforms is crucial for understanding its impact on user behavior. However, the presence of network interference, which arises from user interactions, often complicates this estimation process. Experimenters typically face challenges in fully capturing the intricate structure of this interference, leading to less reliable estimates. To address this issue, we propose a novel approach that leverages surrogate networks and the pseudo inverse estimator. Our contributions can be summarized as follows: (1) We introduce the surrogate network framework, which simulates the practical situation where experimenters build an approximation of the true interference network using observable data. (2) We investigate the performance of the pseudo inverse estimator within this framework, revealing a bias-variance trade-off introduced by the surrogate network. We demonstrate a tighter asymptotic variance bound compared to previous studies and propose an enhanced variance estimator outperforming the original estimator. (3) We apply the pseudo inverse estimator to a real experiment involving over 50 million users, demonstrating its effectiveness in detecting network interference when combined with the difference-in-means estimator. Our research aims to bridge the gap between theoretical literature and practical implementation, providing a solution for estimating TTE in the presence of network interference and unknown interference structures.

This paper concerns the Cauchy problems for the nonlinear Rayleigh-Stokes equation and the corresponding system with time-fractional derivative of order $\alpha\in(0,1)$, which can be used to simulate the anomalous diffusion in viscoelastic fluids. It is shown that there exists the critical Fujita exponent which separates systematic blow-up of the solutions from possible global existence, and the critical exponent is independent of the parameter $\alpha$. Different from the general scaling argument for parabolic problems, the main ingredients of our proof are suitable decay estimates of the solution operator and the construction of the test function.

In this paper, we introduce the third party to achieve the Stackelberg equilibrium with the time inconsistency in three different Stackelberg games, which are the discrete-time games, the dynamic games, and the mean field games. Here all followers are experiencing learning-by-doing. The role of a third party is similar to industry associations, they supervise the leader's implementation and impose penalties for the defection with the discount factor. Then we obtain different forms of discount factors in different models and effective conditions to prevent defection.These results are consistent and the third party intervention is effective and maneuverable in practice.

Distributed estimation in a blockchain-aided Internet of Things (BIoT) is considered, where the integrated blockchain secures data exchanges across the BIoT and the storage of data at BIoT agents. This paper focuses on developing a performance guarantee for the distributed estimation in a BIoT in the presence of malicious attacks which jointly exploits vulnerabilities present in both IoT devices and the employed blockchain within the BIoT. To achieve this, we adopt the Cramer-Rao Bound (CRB) as the performance metric, and maximize the CRB for estimating the parameter of interest over the attack domain. However, the maximization problem is inherently non-convex, making it infeasible to obtain the globally optimal solution in general. To address this issue, we develop a relaxation method capable of transforming the original non-convex optimization problem into a convex optimization problem. Moreover, we derive the analytical expression for the optimal solution to the relaxed optimization problem. The optimal value of the relaxed optimization problem can be used to provide a valid estimation performance guarantee for the BIoT in the presence of attacks., Comment: 11 pages, 4 figures

We study the wellposedness of the master equation for a second-order mean field games with the Grushin type diffusion. In order to do this, we obtain the properties of its solution by investigating a degenerate mean field games system for which there exists an equivalent characterization with the master equation. The crucial points of this paper are to explore some regularities of solutions to two types of linear degenerate partial differential equations and a kind of degenerate linear coupled system so as to derive the existence of solutions to the master equation.

Numerous blockchain applications are designed with tasks that naturally have finite durations, and hence, a double-spending attack (DSA) on such blockchain applications leans towards being conducted within a finite timeframe, specifically before the completion of their tasks. Furthermore, existing research suggests that practical attackers typically favor executing a DSA within a finite timeframe due to their limited computational resources. These observations serve as the impetus for this paper to investigate a time-restricted DSA (TR-DSA) model on Proof-of-Work based blockchains. In this TR-DSA model, an attacker only mines its branch within a finite timeframe, and the TR-DSA is considered unsuccessful if the attacker's branch fails to surpass the honest miners' branch when the honest miners' branch has grown by a specific number of blocks. First, we developed a general closed-form expression for the success probability of a TR-DSA. This developed probability not only can assist in evaluating the risk of a DSA on blockchain applications with timely tasks, but also can enable practical attackers with limited computational resources to assess the feasibility and expected reward of launching a TR-DSA. In addition, we provide rigorous proof that the success probability of a TR-DSA is no greater than that of a time-unrestricted DSA where the attacker indefinitely mines its branch. This result implies that blockchain applications with timely tasks are less vulnerable to DSAs than blockchain applications that provide attackers with an unlimited timeframe for their attacks. Furthermore, we show that the success probability of a TR-DSA is always smaller than one even though the attacker controls more than half of the hash rate in the network. This result alerts attackers that there is still a risk of failure in launching a TR-DSA even if they amass a majority of the hash rate in the network., Comment: 13 pages, 8 figures. arXiv admin note: text overlap with arXiv:2304.09965

In this paper, we consider a class of infinitely degenerate partial differential systems to obtain the Nash equilibria in the mean field games. The degeneracy in the diffusion and the Hamiltonian may be different. This feature brings difficulties to the uniform boundness of the solutions, which is central to the existence and regularity results. First, from the perspective of the value function in the stochastic optimal control problems, we prove the Lipschitz continuity and the semiconcavity for the solutions of the Hamilton-Jacobi equations (HJE). Then the existence of the weak solutions for the degenerate systems is obtained via a vanishing viscosity method. Furthermore, by constructing an auxiliary function, we conclude the regularity of the viscosity solution for the HJE in the almost everywhere sense.

In randomized experiments, the classic stable unit treatment value assumption (SUTVA) states that the outcome for one experimental unit does not depend on the treatment assigned to other units. However, the SUTVA assumption is often violated in applications such as online marketplaces and social networks where units interfere with each other. We consider the estimation of the average treatment effect in a network interference model using a mixed randomization design that combines two commonly used experimental methods: Bernoulli randomized design, where treatment is independently assigned for each individual unit, and cluster-based design, where treatment is assigned at an aggregate level. Essentially, a mixed randomization experiment runs these two designs simultaneously, allowing it to better measure the effect of network interference. We propose an unbiased estimator for the average treatment effect under the mixed design and show the variance of the estimator is bounded by $O({d^2}n^{-1}p^{-1})$ where $d$ is the maximum degree of the network, $n$ is the network size, and $p$ is the probability of treatment. We also establish a lower bound of $\Omega(d^{1.5}n^{-1}p^{-1})$ for the variance of any mixed design. For a family of sparse networks characterized by a growth constant $\kappa \leq d$, we improve the upper bound to $O({\kappa^7 d}n^{-1}p^{-1})$. Furthermore, when interference weights on the edges of the network are unknown, we propose a weight-invariant design that achieves a variance bound of $O({d^3}n^{-1}p^{-1})$.

In this paper, we study a class of degenerate mean field game systems arising from the mean field games with H\"ormander diffusion, where the generic player may have a ``forbidden'' direction at some point. Here we prove the existence and uniqueness of the classical solutions in weighted H\"older spaces for the PDE systems, which describe the Nash equilibria in the games. The degeneracy causes the lack of commutation of vector fields and the fundamental solution which are the main difficulties in the proof of the global Schauder estimate and the weak maximum principle. Based on the idea of the localizing technique and the local homogeneity of degenerate operators, we extend the maximum regularity result and obtain the global Schauder estimates. For the weak maximum principle, we construct a subsolution instead of the fundamental solution of the degenerate operators., Comment: We deeply appreciate your consideration of the manuscript. Thank you very much

Adam-type algorithms have become a preferred choice for optimisation in the deep learning setting, however, despite success, their convergence is still not well understood. To this end, we introduce a unified framework for Adam-type algorithms (called UAdam). This is equipped with a general form of the second-order moment, which makes it possible to include Adam and its variants as special cases, such as NAdam, AMSGrad, AdaBound, AdaFom, and Adan. This is supported by a rigorous convergence analysis of UAdam in the non-convex stochastic setting, showing that UAdam converges to the neighborhood of stationary points with the rate of $\mathcal{O}(1/T)$. Furthermore, the size of neighborhood decreases as $\beta$ increases. Importantly, our analysis only requires the first-order momentum factor to be close enough to 1, without any restrictions on the second-order momentum factor. Theoretical results also show that vanilla Adam can converge by selecting appropriate hyperparameters, which provides a theoretical guarantee for the analysis, applications, and further developments of the whole class of Adam-type algorithms.

Distributed detection over a blockchain-aided Internet of Things (BIoT) network in the presence of attacks is considered, where the integrated blockchain is employed to secure data exchanges over the BIoT as well as data storage at the agents of the BIoT. We consider a general adversary model where attackers jointly exploit the vulnerability of IoT devices and that of the blockchain employed in the BIoT. The optimal attacking strategy which minimizes the Kullback-Leibler divergence is pursued. It can be shown that this optimization problem is nonconvex, and hence it is generally intractable to find the globally optimal solution to such a problem. To overcome this issue, we first propose a relaxation method that can convert the original nonconvex optimization problem into a convex optimization problem, and then the analytic expression for the optimal solution to the relaxed convex optimization problem is derived. The optimal value of the relaxed convex optimization problem provides a detection performance guarantee for the BIoT in the presence of attacks. In addition, we develop a coordinate descent algorithm which is based on a capped water-filling method to solve the relaxed convex optimization problem, and moreover, we show that the convergence of the proposed coordinate descent algorithm can be guaranteed., Comment: 16 pages, 4 figures. This work has been submitted to the IEEE TIFS

Recently, blockchain has been applied in various fields to secure data exchanges and storage in decentralized systems. In a blockchain application where the task of the application which makes use of the data stored in a blockchain has to be accomplished by a time instant, the employed blockchain is essentially finitely-long. In this paper, we consider a general finitely-long blockchain model which is generalized from most existing works on finitely-long blockchain applications, and take the first step towards characterizing the vulnerability of finitely-long blockchains in securing data against double-spending attacks. For the first time, we develop a general closed-form expression for the probability of success in launching a double-spending attack on a finitely-long blockchain. This probability essentially characterizes the vulnerability of finitely-long blockchains. Then, we prove that the probability of success in launching a double-spending attack on a finitely-long blockchain is no greater than that on an infinitely-long blockchain, which implies that finitely-long blockchains are less vulnerable to double-spending attacks than infinitely-long blockchains. Moreover, we show that unlike infinitely-long blockchains which can be surely paralyzed by a 51% attack, finitely-long blockchains are more resistant to 51% attacks., Comment: 13 pages. 8 figures. This work has been submitted to the IEEE

In this work, we focus on improving the robot's dexterous capability by exploiting visual sensing and adaptive force control. TeachNet, a vision-based teleoperation learning framework, is exploited to map human hand postures to a multi-fingered robot hand. We augment TeachNet, which is originally based on an imprecise kinematic mapping and position-only servoing, with a biomimetic learning-based compliance control algorithm for dexterous manipulation tasks. This compliance controller takes the mapped robotic joint angles from TeachNet as the desired goal, computes the desired joint torques. It is derived from a computational model of the biomimetic control strategy in human motor learning, which allows adapting the control variables (impedance and feedforward force) online during the execution of the reference joint angle trajectories. The simultaneous adaptation of the impedance and feedforward profiles enables the robot to interact with the environment in a compliant manner. Our approach has been verified in multiple tasks in physics simulation, i.e., grasping, opening-a-door, turning-a-cap, and touching-a-mouse, and has shown more reliable performances than the existing position control and the fixed-gain-based force control approaches., Comment: Accepted by the 2021 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS 2021)