Better Approximation for Distributed Weighted Vertex Cover via Game-Theoretic Learning

Test-cost-sensitive rough set based approach for minimum weight vertex cover problem

An efficient local search framework for the minimum weighted vertex cover problem

Game theoretic learning in multiagent systems is a rapidly developing area of research. It gained popularity since the wide range of optimization problems in multiagent systems can be reformulated in terms of potential games, where the set of potential function maximizers represents the set of optimal states. The crucial point of such approach is the design of local decision rules that leads the system to a potential function maximizer. In this paper, we consider the independent log-linear learning procedure applicable to continuous action potential games. We provide the analysis of the stochastic stability of potential function maximizers in case of continuous action games. To analyze the behavior of the underlying Markov chain, we develop a new method for approximating the initial chain with continuous states by chains whose long run properties can be established. After that, we study the finite time behavior of the algorithm with a definite time-dependent parameter and obtain settings that guarantee an efficient implementation of the learning procedure under consideration.

Minimum weighted vertex cover (MWVC) problem of weighted networks is one of the most important combinatorial optimization problems in network optimization. This paper models the MWVC problem as an asymmetric game on weighted networks. Then, an asynchronous game-based algorithm (AGB) is proposed to solve the MWVC problem, which can guarantee to obtain a vertex cover (VC). Numerical illustrations verify the performance of the proposed game solution on the representative weighted networks.

The choice of monetary instrument in two interdependent economies under uncertainty

The generalized vertex cover problem and some variations

The Weighted Constraint Satisfaction Problem (WCSP) is a very expressive framework for optimization problems. The Constraint Composite Graph (CCG) is a graphical representation of a given (Boolean) WCSP that facilitates its reduction to a Minimum Weighted Vertex Cover (MWVC) problem by introducing intelligently chosen auxiliary variables. It also enables kernelization: a maxflow procedure used to fix the optimal values of a subset of the variables before initiating search. In this paper, we present some CCG-based WCSP solvers and compare their performance against toulbar2, a state-of-the-art WCSP solver, on a variety of benchmark instances. We also study the effectiveness of kernelization.

The minimum weight vertex cover problem (MWVCP) is one of the classic combinatorial optimisation problems. In this paper, we have proposed a modified jumping particle swarm optimisation approach, n...

Coordination is one of the essential problems in multi-agent systems. Typically multi-agent reinforcement learning (MARL) methods treat agents equally and the goal is to solve the Markov game to an arbitrary Nash equilibrium (NE) when multiple equilibra exist, thus lacking a solution for NE selection. In this paper, we treat agents unequally and consider Stackelberg equilibrium as a potentially better convergence point than Nash equilibrium in terms of Pareto superiority, especially in cooperative environments. Under Markov games, we formally define the bi-level reinforcement learning problem in finding Stackelberg equilibrium. We propose a novel bi-level actor-critic learning method that allows agents to have different knowledge base (thus intelligent), while their actions still can be executed simultaneously and distributedly. The convergence proof is given, while the resulting learning algorithm is tested against the state of the arts. We found that the proposed bi-level actor-critic algorithm successfully converged to the Stackelberg equilibria in matrix games and find a asymmetric solution in a highway merge environment.

Game theoretical learning in multi-agent systems is a rapidly developing area of research. It gained popularity since the wide range of optimization problems in multi-agent systems can be reformulated in terms of potential games, where the set of potential function maximizers represents the set of optimal system states. The crucial point of such approach is the design of a distributed algorithm that is guaranteed to converge to the set of potential function maximizers. Various learning algorithms, whose features depend on system properties, have been proposed so far. However, there is currently no learning algorithm that can be efficiently executed in a multi-agent system in which uncoupled agents update their actions synchronously and do not take into account the past history of actions. In this paper, we fill this gap by introducing a new learning algorithm for potential games with uncoupled dynamics and memoryless players who act synchronously. We prove the probabilistic convergence of this algorithm to potential function maximizers, which correspond to the optimal system states under appropriate game settings.

Consensus conditions for heterogeneous multi-agent sampled-data control systems with nonlinearities and inter-agent communication delay.

We consider several basic consensus problems in multi-agents systems with switching interconnection graphs, where the connections between any two agents are assumed bidirectional for notation simplicity. When the switching interconnection graphs are always connected, it has been shown in the literature that the Laplacian based algorithm always achieves the average consensus. We first extend the discussion to the case where disconnected interconnection graphs are involved, by showing that the average consensus is still achieved if the dwell time ratio between connected graphs and disconnected ones satisfies a specified condition. Next, we consider the case where there is no connected graph but the combination of a set of graphs is connected, and propose two switching strategies for achieving the average consensus. Several numerical examples are provided to show the algorithms.

A fundamental problem in multi agent systems is conflict resolution. A conflict occurs in general when the agents have to deal with inconsistent goals, such as a demand for shared resources. We investigate some theoretical game approaches as efficient methods to examine a class of conflicts in multi agent systems.

As a new area of research, consensus problems for multi-agent systems have been studied extensively in the literature. It is usually assumed that all agents share a common one-dimensional state space. The authors of this study concentrate on the consensus problems of multi-agent systems in the framework of high-dimensional state space. As a basis for the analysis, a general model is first introduced by presenting two typical examples along with some necessary and sufficient conditions for the system to solve a consensus problem. Then the structures of consensus functions are investigated and some algebraic characterisations are given. Finally, a class of switched multi-agent systems are discussed and some sufficient conditions for the possession of the consensus property are provided. Several examples to illustrate the effectiveness of theoretical results are given.

We investigate the fixed-time containment control (FCC) problem of multi-agent systems (MASs) under discontinuous communication. A saturation function is used in the controller to achieve the containment control in MASs. One difference from using a symbolic function is that it avoids the differential calculation process for discontinuous functions, which further ensures the continuity of the control input. Considering the discontinuous communication, a dynamic variable is constructed, which is always non-negative between any two communications of the agent. Based on the designed variable, the dynamic event-triggered algorithm is proposed to achieve FCC, which can effectively reduce controller updating. In addition, we further design a new event-triggered algorithm to achieve FCC, called the team-trigger mechanism, which combines the self-triggering technique with the proposed dynamic event trigger mechanism. It has faster convergence than the proposed dynamic event triggering technique and achieves the tradeoff between communication cost, convergence time and number of triggers in MASs. Finally, Zeno behavior is excluded and the validity of the proposed theory is confirmed by simulation.