54,348 research outputs found
Nonzero-sum Stochastic Games
No full textThis paper treats of stochastic games. We focus on nonzero-sum games and provide a detailed survey of selected recent results. In Section 1, we consider stochastic Markov games. A correlation of strategies of the players, involving ``public signals'', is described, and a correlated equilibrium theorem proved recently by Nowak and Raghavan for discounted stochastic games with general state space is presented. We also report an extension of this result to a class of undiscounted stochastic games, satisfying some uniform ergodicity condition. Stopping games are related to stochastic Markov games. In Section 2, we describe a version of Dynkin's game related to observation of a Markov process with random assignment mechanism of states to the players. Some recent contributions of the second author in this area are reported. The paper also contains a brief overview of the theory of nonzero-sum stochastic games and stopping games which is very far from being complete.average payoff stochastic games, correlated stationary equilibria, nonzero-sum games, stopping time, stopping games
Bounded Approximate Decentralised Coordination via the Max-Sum Algorithm
No full textIn this paper we propose a novel approach to decentralised coordination, that is able to efficiently compute solutions with a guaranteed approximation ratio. Our approach is based on a factor graph representation of the constraint network. It builds a tree structure by eliminating dependencies between the functions and variables within the factor graph that have the least impact on solution quality. It then uses the max-sum algorithm to optimally solve the resulting tree structured constraint network, and provides a bounded approximation specific to the particular problem instance. In addition, we present two generic pruning techniques to reduce the amount of computation that agents must perform when using the max-sum algorithm. When this is combined with the above mentioned approximation algorithm, the agents are able to solve decentralised coordination problems that have very large action spaces with a low computation and communication overhead. We empirically evaluate our approach in a mobile sensor domain, where mobile agents are used to monitor and predict the state of spatial phenomena (e.g., temperature or gas concentration). Such sensors need to coordinate their movements with their direct neighbours to maximise the collective information gain, while predicting measurements at unobserved locations. When applied in this domain, our approach is able to provide solutions which are guaranteed to be within 2% of the optimal solution. Moreover, the two pruning techniques are extremely effective in decreasing the computational effort of each agent by reducing the size of the search space by up to 92%
A methodology for deploying the max-sum algorithm and a case study on unmanned aerial vehicles
No full textWe present a methodology for the deployment of the max-sum algorithm, a well known decentralised algorithm for coordinating autonomous agents, for problems related to situational awareness. In these settings, unmanned autonomous vehicles are deployed to collect information about an unknown environment. Our methodology then helps identify the choices that need to be made to apply the algorithm to these problems. Next, we present a case study where the methodology is used to develop a system for disaster management in which a team of unmanned aerial vehicles coordinate to provide the first responders of the area of a disaster with live aerial imagery. To evaluate this system, we deploy it on two unmanned hexacopters in a variety of scenarios. Our tests show that the system performs well when confronted with the dynamism and the heterogeneity of the real world
Self-organising Sensors for Wide Area Surveillance Using the Max-sum Algorithm
No full textIn this paper, we consider the self-organisation of sensors within a network deployed for wide area surveillance. We present a decentralised coordination algorithm based upon the max-sum algorithm and demonstrate how self-organisation can be achieved within a setting where sensors are deployed with no a priori information regarding their local environment. These energy-constrained sensors first learn how their actions interact with those of neighbouring sensors, and then use the max-sum algorithm to coordinate their sense/sleep schedules in order to maximise the effectiveness of the sensor network as a whole. In a simulation we show that this approach yields a 30% reduction in the number of vehicles that the sensor network fails to detect (compared to an uncoordinated network), and this performance is close to that achieved by a benchmark centralised optimisation algorithm (simulated annealing)
Beyond sum-free sets in the natural numbers
No full textFor an interval [1,N]⊆N, sets S⊆[1,N] with the property that |{(x,y)∈S2:x+y∈S}|=0, known as sum-free sets, have attracted considerable attention. In this paper, we generalize this notion by considering r(S)=|{(x,y)∈S2:x+y∈S}|, and analyze its behaviour as S ranges over the subsets of [1,N]. We obtain a comprehensive description of the spectrum of attainable r-values, constructive existence results and structural characterizations for sets attaining extremal and near-extremal values.Peer reviewe
Decentralised Coordination of Unmanned Aerial Vehicles for Target Search using the Max-Sum Algorithm
No full textThis paper considers the coordination of a team of Unmanned Aerial Vehicles (UAVs) that are deployed to search for a moving target within a continuous space. We present an online and decentralised coordination mechanism, based on the max-sum algorithm, to address this problem. In doing so, we introduce a novel coordination technique to the field of robotic search, and we extend the max-sum algorithm beyond the much simpler coordination problems to which it has been applied to date. Within a simulation environment, we benchmarked our max-sum algorithm against three other existing approaches for coordinating UAVs. The results showed that coordination with the max sum algorithm out-performed a best response algorithm, which represents the state of the art in the coordination of UAVs for search, by up to 26%. The results further showed that the max-sum algorithm out-performed an implicitly coordinated approach, where the coordination arises from the agents making decisions based on a common belief, by up to 34% and finally a non-coordinated approach by up to 68%
Weighted Sum of Correlated Lognormals: Convolution Integral Solution
No full textProbability density function (pdf) for sum of n
correlated lognormal variables is deducted as a special
convolution integral. Pdf for weighted sums (where weights can
be any real numbers) is also presented. The result for four
dimensions was checked by Monte Carlo simulation
A Hybrid Continuous Max-Sum Algorithm for Decentralised Coordination
No full textRecent advances in decentralised coordination of multiple agents have led to the proposal of the max-sum algorithm for solving distributed constraint optimisation problems (DCOPs). The max-sum algorithm is fully decentralised, converges to optimality for problems with acyclic constraint graphs and otherwise performs well in empirical studies. However, it requires agents to have discrete state spaces, which are of practical size to conduct repeated searches over. In contrast, there are decentralised non-linear optimisation methods that are capable of accurately finding local optima over multi-dimensional continuous state spaces, however these methods are not designed to navigate complex interactions between local constraints in order to find globally optimal solutions. Given this background, in this paper we tackle the problem of coordinating multiple decentralised agents with continuous state variables. Specifically we propose a hybrid approach, which combines the max-sum algorithm with continuous non-linear optimisation methods. We show that, for problems with acyclic factor graph representations, for suitable parameter choices, our proposed algorithm converges to a state with utility close to the global optimum. We empirically evaluate our approach for cyclic constraint graphs in a multi-sensor target classification problem, and compare its performance to the discrete max-sum algorithm, as well as a non-coordinated approach and the distributed stochastic algorithm (DSA). We show that our hybrid max-sum algorithm outperforms the non-coordinated algorithm, DSA and discrete max-sum considerably. Furthermore, the improvements in outcome over discrete max-sum come without significant increases in running time nor communication cost
Mean Value of r-gcd-sum and r-lcm-Sum Functions
No full textIn this paper we perform a further investigation for r-gcd-sum and r-lcm-sum functions. By making use of the properties of generalization of Euler’s φ-function, Abel’s identity and elementary arguments, we derive asymptotic formulas for the average of the r-gcd-sum function, r-lcm-sum function and their generalizations. Moreover, we also study the sums of reciprocals of r-gcd and r-lcm
Agent-based decentralised coordination for sensor networks using the max-sum algorithm
No full textIn this paper, we consider the generic problem of how a network of physically distributed, computationally constrained devices can make coordinated decisions to maximise the effectiveness of the whole sensor network. In particular, we propose a new agent-based representation of the problem, based on the factor graph, and use state-of-the-art DCOP heuristics (i.e., DSA and the max-sum algorithm) to generate sub-optimal solutions. In more detail, we formally model a specific real-world problem where energy-harvesting sensors are deployed within an urban environment to detect vehicle movements. The sensors coordinate their sense/sleep schedules, maintaining energy neutral operation while maximising vehicle detection probability. We theoretically analyse the performance of the sensor network for various coordination strategies and show that by appropriately coordinating their schedules the sensors can achieve significantly improved system-wide performance, detecting up to 50% of the events that a randomly coordinated network fails to detect. Finally, we deploy our coordination approach in a realistic simulation of our wide area surveillance problem, comparing its performance to a number of benchmarking coordination strategies. In this setting, our approach achieves up to a 57% reduction in the number of missed vehicles (compared to an uncoordinated network). This performance is close to that achieved by a benchmark centralised algorithm (simulated annealing) and to a continuously powered network (which is an unreachable upper bound for any coordination approach)
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