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This paper considers the discounted criterion of nonzero-sum decentralized stochastic games with prospect players. The state and action spaces are finite. The state transition probability is nonstationary. Each player independently controls their own Markov chain. The subjective behavior of players is described by the prospect theory (PT). Compared to the average criterion of stochastic games under PT studied firstly in 2018, we are concerned with the time value of utility, i.e., the utility should be discounted in the future. Since PT distorts the probability, the optimality equation that plays a significant role in proving the existence of equilibrium does not exist. On the other hand, the games change into Markov decision processes (MDPs) with nonstationary payoff function when fixing others' stationary Markov strategies, then the occupation measure and the linear programming of stationary MDPs are no longer suitable. Therefore, we explore a new technique by constructing the marginal distribution on the state-action pairs at any time, and establish the existence of Nash equilibrium. When the initial state is given, there exists a Markov Nash equilibrium. Furthermore, this novel technique can be extended to the finite horizon criterion. Then, we present an algorithm to find a Markov $\varepsilon$-equilibrium. Finally, the model is applied to a noncooperative stochastic game among prosumers who can produce and consume energy in the smart grid, and we give some simulation results.

With ChatGPT-like large language models (LLM) prevailing in the community, how to evaluate the ability of LLMs is an open question. Existing evaluation methods suffer from following shortcomings: (1) constrained evaluation abilities, (2) vulnerable benchmarks, (3) unobjective metrics. We suggest that task-based evaluation, where LLM agents complete tasks in a simulated environment, is a one-for-all solution to solve above problems. We present AgentSims, an easy-to-use infrastructure for researchers from all disciplines to test the specific capacities they are interested in. Researchers can build their evaluation tasks by adding agents and buildings on an interactive GUI or deploy and test new support mechanisms, i.e. memory, planning and tool-use systems, by a few lines of codes. Our demo is available at https://agentsims.com ., Comment: submit to EMNLP2023 demo track

The robustness of deep neural networks (DNNs) is crucial to the hosting system's reliability and security. Formal verification has been demonstrated to be effective in providing provable robustness guarantees. To improve its scalability, over-approximating the non-linear activation functions in DNNs by linear constraints has been widely adopted, which transforms the verification problem into an efficiently solvable linear programming problem. Many efforts have been dedicated to defining the so-called tightest approximations to reduce overestimation imposed by over-approximation. In this paper, we study existing approaches and identify a dominant factor in defining tight approximation, namely the approximation domain of the activation function. We find out that tight approximations defined on approximation domains may not be as tight as the ones on their actual domains, yet existing approaches all rely only on approximation domains. Based on this observation, we propose a novel dual-approximation approach to tighten over-approximations, leveraging an activation function's underestimated domain to define tight approximation bounds. We implement our approach with two complementary algorithms based respectively on Monte Carlo simulation and gradient descent into a tool called DualApp. We assess it on a comprehensive benchmark of DNNs with different architectures. Our experimental results show that DualApp significantly outperforms the state-of-the-art approaches with 100% - 1000% improvement on the verified robustness ratio and 10.64% on average (up to 66.53%) on the certified lower bound., Comment: 16 pages, 11 figures, 5 tables, ISSTA 2023. arXiv admin note: substantial text overlap with arXiv:2211.11186

The robustness of neural networks is fundamental to the hosting system's reliability and security. Formal verification has been proven to be effective in providing provable robustness guarantees. To improve the verification scalability, over-approximating the non-linear activation functions in neural networks by linear constraints is widely adopted, which transforms the verification problem into an efficiently solvable linear programming problem. As over-approximations inevitably introduce overestimation, many efforts have been dedicated to defining the tightest possible approximations. Recent studies have however showed that the existing so-called tightest approximations are superior to each other. In this paper we identify and report an crucial factor in defining tight approximations, namely the approximation domains of activation functions. We observe that existing approaches only rely on overestimated domains, while the corresponding tight approximation may not necessarily be tight on its actual domain. We propose a novel under-approximation-guided approach, called dual-approximation, to define tight over-approximations and two complementary under-approximation algorithms based on sampling and gradient descent. The overestimated domain guarantees the soundness while the underestimated one guides the tightness. We implement our approach into a tool called DualApp and extensively evaluate it on a comprehensive benchmark of 84 collected and trained neural networks with different architectures. The experimental results show that DualApp outperforms the state-of-the-art approximation-based approaches, with up to 71.22% improvement to the verification result., Comment: 13 pages, 9 fugures, 3 tables

The robustness of deep neural networks is crucial to modern AI-enabled systems and should be formally verified. Sigmoid-like neural networks have been adopted in a wide range of applications. Due to their non-linearity, Sigmoid-like activation functions are usually over-approximated for efficient verification, which inevitably introduces imprecision. Considerable efforts have been devoted to finding the so-called tighter approximations to obtain more precise verification results. However, existing tightness definitions are heuristic and lack theoretical foundations. We conduct a thorough empirical analysis of existing neuron-wise characterizations of tightness and reveal that they are superior only on specific neural networks. We then introduce the notion of network-wise tightness as a unified tightness definition and show that computing network-wise tightness is a complex non-convex optimization problem. We bypass the complexity from different perspectives via two efficient, provably tightest approximations. The results demonstrate the promising performance achievement of our approaches over state of the art: (i) achieving up to 251.28% improvement to certified lower robustness bounds; and (ii) exhibiting notably more precise verification results on convolutional networks., Comment: Accepted at ASE 2022

Utilizing the advantage of quantum entanglement swapping, a multi-party quantum key agreement protocol with authentication is proposed. In this protocol, a semi-trusted third party is introduced, who prepares Bell states, and sends one particle to multiple participants respectively. After that the participants can share a Greenberger-Horne-Zeilinger state by entanglement swapping. Finally, these participants measure the particles in their hands and obtain an agreement key. Here, classical hash function and Hadamard operation are utilized to authenticate the identity of participants. The correlations of GHZ states ensure the security of the proposed protocol. To illustrated it detailly, the security of this protocol against common attacks is analyzed, which shows that the proposed protocol is secure in theory.

In this paper, we present a quantum secure multi-party summation protocol, which allows multiple mutually distrustful parties to securely compute the summation of their secret data. In the presented protocol, a semitrusted third party is introduced to help multiple parties to achieve this secure task. Besides, the entanglement swapping of $d$-level cat states and Bell states is employed to securely transmit message between each party and the semitrusted third party. At last, its security against some common attacks is analyzed, which shows that the presented protocol is secure in theory.

Let $G=(V,E)$ be a locally finite, connected and weighted graph. We prove that, for a graph satisfying curvature dimension condition $CDE'(n,0)$ and uniform polynomial volume growth of degree $m$, all non-negative solutions of the equation $\partial_tu=\Delta u+u^{1+\alpha}$ blow up in a finite time provided that $\alpha=\frac{2}{m}$. We also consider the blow-up problem under certain conditions for volume growth and initial value. The obtained results provide a significant complement to the work by Lin and Wu in earlier paper.

Let $G=(V,E)$ be a locally finite connected weighted graph, $\Delta$ be the usual graph Laplacian. In this paper, we study the blow-up problems for the nonlinear parabolic equation $u_t=\Delta u + f(u)$ on $G$. The blow-up phenomenons of the equation are discussed in terms of two cases: (i) an initial condition is given; (ii) a Dirichlet boundary condition is given. We prove that if $f$ satisfies appropriate conditions, then the solution of the equation blows up in a finite time., Comment: 14 pages

Let $G=(V,E)$ be a finite or locally finite connected weighted graph, $\Delta$ be the usual graph Laplacian. Using heat kernel estimate, we prove the existence and nonexistence of global solutions for the following semilinear heat equation on $G$ \begin{equation*} \left\{ \begin{array}{lc} u_t=\Delta u + u^{1+\alpha} &\, \text{in $(0,+\infty)\times V$,}\\ u(0,x)=a(x) &\, \text{in $V$.} \end{array} \right. \end{equation*} We conclude that, for a graph satisfying curvature dimension condition $CDE'(n,0)$ and $V(x,r)\simeq r^m$, if $02$, then there is a non-negative global solution $u$ provided that the initial value is small enough. In particular, these results are true on lattice $\mathbb{Z}^m$., Comment: 18 pages, 3 figures

The purpose of this paper is to establish a new continuous-time on-diagonal lower estimate of heat kernel for large time on graphs. To achieve the goal, we first give an upper bound of heat kernel in natural graph metric, and then use this bound and the volume growth condition to show the validity of the on-diagonal lower bound., Comment: 10 pages