We present a method for solving service allocation problems in which a set of services must be allocated to a set of agents so as to maximize a global utility. The method is completely distributed so it can scale to any number of services without degradation. We first formalize the service allocation problem and then present a simple hill-climbing, a global hill-climbing, and a bidding-protocol algorithm for solving it. We analyze the expected performance of these algorithms as a function of various problem parameters such as the branching factor and the number of agents. Finally, we use the sensor allocation problem, an instance of a service allocation problem, to show the bidding protocol at work. The simulations also show that phase transition on the expected quality of the solution exists as the amount of communication between agents increases.
There is ongoing work in the field of complexity that attempts to study they dynamics of complex adaptive systems @cite_7 . Our approach is based on ideas borrowed from the use of NK landscapes for the analysis of co-evolving systems. As such, we are using some of the results from that field. However, complexity theory is more concerned with explaining the dynamic behavior of existing systems, while we are more concerned with the engineering of multiagent systems for distributed service allocation.
@cite_7
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Adaptive evolution, to a large extent, is a complex combinatorial optimization process. In this article we take beginning steps towards developing a general theory of adaptive “walks” via fitter variants in such optimization processes. We introduce the basic idea of a space of entities, each a 1-mutant neighbor of many other entities in the space, and the idea of a fitness ascribed to each entity. Adaptive walks proceed from an initial entity, via fitter neighbors, to locally or globally optimal entities that are fitter than their neighbors. We develop a general theory for the number of local optima, lengths of adaptive walks, and the number of alternative local optima accessible from any given initial entity, for the baseline case of an uncorrelated fitness landscape. Most fitness landscapes are correlated, however. Therefore we develop parts of a universal theory of adaptation on correlated landscapes by adaptive processes that have sufficient numbers of mutations per individual to “jump beyond” the correlation lengths in the underlying landscape. In addition, we explore the statistical character of adaptive walks in two independent complex combinatorial optimization problems, that of evolving a specific cell type in model genetic networks, and that of finding good solutions to the traveling salesman problem. Surprisingly, both show similar statistical features, encouraging the hope that a general theory for adaptive walks on correlated and uncorrelated landscapes can be found. In the final section we explore two limits to the efficacy of selection. The first is new, and surprising: for a wide class of systems, as the complexity of the entities under selection increases, the local optima that are attainable fall progressively closer to the mean properties of the underlying space of entities. This may imply that complex biological systems, such as genetic regulatory systems, are “close” to the mean properties of the ensemble of genomic regulatory systems explored by evolution. The second limit shows that with increasing complexity and a fixed mutation rate, selection often becomes unable to pull an adapting population to those local optima to which connected adaptive walks via fitter variants exist. These beginning steps in theory development are applied to maturation of the immune response, and to the problem of radiation and stasis. Despite the limitations of the adaptive landscape metaphor, we believe that further development along the lines begun here will prove useful. From the Publisher: Genetic algorithms are playing an increasingly important role in studies of complex adaptive systems, ranging from adaptive agents in economic theory to the use of machine learning techniques in the design of complex devices such as aircraft turbines and integrated circuits. Adaptation in Natural and Artificial Systems is the book that initiated this field of study, presenting the theoretical foundations and exploring applications. In its most familiar form, adaptation is a biological process, whereby organisms evolve by rearranging genetic material to survive in environments confronting them. In this now classic work, Holland presents a mathematical model that allows for the nonlinearity of such complex interactions. He demonstrates the model's universality by applying it to economics, physiological psychology, game theory, and artificial intelligence and then outlines the way in which this approach modifies the traditional views of mathematical genetics. Initially applying his concepts to simply defined artificial systems with limited numbers of parameters, Holland goes on to explore their use in the study of a wide range of complex, naturally occuring processes, concentrating on systems having multiple factors that interact in nonlinear ways. Along the way he accounts for major effects of coadaptation and coevolution: the emergence of building blocks, or schemata, that are recombined and passed on to succeeding generations to provide, innovations and improvements. John H. Holland is Professor of Psychology and Professor of Electrical Engineering and Computer Science at the University of Michigan. He is also Maxwell Professor at the Santa Fe Institute and isDirector of the University of Michigan Santa Fe Institute Advanced Research Program. The increased complexity of performance-sensitive software systems leads to increased use of automated adaptation policies in lieu of manual performance tuning. Composition of adaptive components into larger adaptive systems, however, presents challenges that arise from potential incompatibilities among the respective adaptation policies. Consequently, unstable or poorly-tuned feedback loops may result that cause performance deterioration. This paper (i) presents a mechanism, called adaptation graph analysis, for identifying potential incompatibilities between composed adaptation policies and (ii) illustrates a general design methodology for co-adaptation that resolves such incompatibilities. Our results are demonstrated by a case study on energy minimization in multi-tier Web server farms subject to soft real-time constraints. Two independently efficient energy saving policies (an on off policy that switches machines off when not needed and a dynamic voltage scaling policy) are shown to conflict leading to increased energy consumption when combined. Our adaptation graph analysis predicts the problem, and our co-adaptation design methodology finds a solution that improves performance. Experimental results from a 17-server farm running the industry standard TPC-W e-commerce benchmark show that co-adaptation renders a cut-down in energy consumption by more than 50 , when workload is not high, while maintaining latency within acceptable bounds. The paper serves as a proof of concept of the proposed conflict-identification and resolution methodology and an invitation to further investigate a science for composing adaptive systems. Our researches on adaptive systems are inspired by their ability of building by themselves a representation of their surrounding world. Using cooperation as a local criterion of self-organization, we study in a network of neuro-agents the evolution of the system and in the same way, the emergence of a functioning coherent with the environmental feed-back. In this paper we expose the abilities of the neuro-agents that give them the autonomy required to build an ab nihilo topology. And finally we want to emphasize the dynamic of the network organization that is basically its best property of adaptation to a changing environment. The work presented here concerns our approach to self-organization in a dynamic neural network. We present some experiments of emergent learning based on our knowledge of complex systems through multi-agent systems technology and cellular biology. In fact we are most interested in the mechanisms involved in the construction of a network able to stabilize its structure in a given environment, than in the efficiency of the learning supported by this structure. Obviously those two ontogenetic processes are strongly coupled and appear simultaneously as mutual consequences. Under those conditions, we conceive artificial systems presenting an inherent complexity close to biological systems as they are open and as their structure evolves from nothing (at least an empty shell) up to an organized, stable and functional network of neuro-agents. Our working hypothesis tells minimal entities of such a system can be built and given with sufficient behavioral potentialities in order to organize themselves to satisfy the whole system activity. In this study, we want to show that a coherent and useful system can emerge without any global model for its functioning, solely from activity and organizational rules of its sub-parts; only agents are designed, not the topology of the network they will belong to. Our thought process supposes four distinct steps that description will be formerly extended. Firstly the neuro-agent unit has to be designed, their properties, their abilities (calculus, communication) and their knowledge. Secondly, initial system is constituted of a minimal number of unlinked neuro-agents. Those pre-built neuro-agents are only receptors (inputs) and actuators (outputs) of the network. Thirdly the global system has to be plunged in a dynamic and open environment in which it will have to adapt to; regarding neuromimetic systems, this phase suppose This study derives geometric, variational discretization of continuum theories arising in fluid dynamics, magnetohydrodynamics (MHD), and the dynamics of complex fluids. A central role in these discretizations is played by the geometric formulation of fluid dynamics, which views solutions to the governing equations for perfect fluid flow as geodesics on the group of volume-preserving diffeomorphisms of the fluid domain. Inspired by this framework, we construct a finite-dimensional approximation to the diffeomorphism group and its Lie algebra, thereby permitting a variational temporal discretization of geodesics on the spatially discretized diffeomorphism group. The extension to MHD and complex fluid flow is then made through an appeal to the theory of Euler–Poincare systems with advection, which provides a generalization of the variational formulation of ideal fluid flow to fluids with one or more advected parameters. Upon deriving a family of structured integrators for these systems, we test their performance via a numerical implementation of the update schemes on a cartesian grid. Among the hallmarks of these new numerical methods are exact preservation of momenta arising from symmetries, automatic satisfaction of solenoidal constraints on vector fields, good long-term energy behavior, robustness with respect to the spatial and temporal resolution of the discretization, and applicability to irregular meshes. Time varying problems usually have complex underlying structures represented as dynamic networks where entities and relationships appear and disappear over time. The problem of efficiently performing dynamic link inference is extremely challenging due to the dynamic nature in massive evolving networks especially when there exist sparse connectivities and nonlinear transitional patterns. In this paper, we propose a novel deep learning framework, i.e., Conditional Temporal Restricted Boltzmann Machine (ctRBM), which predicts links based on individual transition variance as well as influence introduced by local neighbors. The proposed model is robust to noise and have the exponential capability to capture nonlinear variance. We tackle the computational challenges by developing an efficient algorithm for learning and inference of the proposed model. To improve the efficiency of the approach, we give a faster approximated implementation based on a proposed Neighbor Influence Clustering algorithm. Extensive experiments on simulated as well as real-world dynamic networks show that the proposed method outperforms existing algorithms in link inference on dynamic networks. Abstract We investigate the effect of predictions upon a model of coevolutionary systems which was originally inspired by computational ecosystems. The model incorporates many of the features of distributed resource allocation in systems comprised of many individual agents, including asynchrony, resource contention, and decision-making based upon incomplete knowledge and delayed information. Previous analyses of a similar model of non-predictive agents have demonstrated that periodic or chaotic oscillations in resource allocation can occur under certain conditions, and that these oscillations can affect the performance of the system adversely. In this work, we show that the system performance can be improved if the agents do an adequate job of predicting the current state of the system. We explore two plausible methods for prediction - technical analysis and system analysis. Technical analysts are responsive to the behavior of the system, but suffer from an inability to take their own behavior into account. System analysts perform extremely well when they have very accurate information about the other agents in the system, but can perform very poorly when their information is even slightly inaccurate. By combining the strengths of both methods, we obtain a successful hybrid of the two prediction methods which adapts its model of other agents in response to the observed behavior of the system. Recent years have seen an increasing interest in the study of continuous-time computational models. However, not so much has been done with respect to setting up a complexity theoretic framework for such models. The present paper intends to go a step into this direction. We consider problems over the real numbers which we try to relate to Lyapunov theory for dynamical systems: The global minimizers of particular energy functions are supposed to give solutions of the problem. The structure of such energy functions leads to the introduction of problem classes U and NU; for the systems we are considering they parallel the classical complexity classes P and NP. We then introduce a notion of reducibility among problems and show existence of complete problems for NU and for PU, a polynomial hierarchy of continuous-time problems. For previous work on the computational capabilities of continuous-time systems see the surveys by Cris Moore [9] and by Pekka Orponen [10]. Our paper presents a step into the direction of creating a general framework for a complexity theory of continuous-time systems as outlined in [10]. It is closely related to work done by A. Ben-Hur, H. Siegelmann, and S. Fishman [12, 11]. Concepts used in the scientific study of complex systems have become so widespread that their use and abuse has led to ambiguity and confusion in their meaning. In this article, we use information theory to provide abstract and concise measures of complexity, emergence, self-organization, and homeostasis. The purpose is to clarify the meaning of these concepts with the aid of the proposed formal measures. In a simplified version of the measures (focusing on the information produced by a system), emergence becomes the opposite of self-organization, while complexity represents their balance. Homeostasis can be seen as a measure of the stability of the system. We use computational experiments on random Boolean networks and elementary cellular automata to illustrate our measures at multiple scales. © 2012 Wiley Periodicals, Inc. Complexity, 2012 © 2012 Wiley Periodicals, Inc. Complexity is now one of the major challenges for the IT industry [1]. Systems might become too complex to be managed by humans and, thus, will have to be self-managed: Self-configure themselves for operation, self-protect from attacks, self-heal from errors and self-tune for optimal performance [2]. (Self-)Adaptive systems evaluate their own behavior and change it when the evaluation indicates that it is not accomplishing the software's purpose or when better functionality and performance are possible [3]. To that end, we need to monitor the behavior of the running system and compare it to an explicit formulation of requirements and domain assumptions [4]. Feedback loops (e.g., the MAPE loop [2]) constitute an architectural solution for this and, as proposed by past research [5], should be a first class citizen in the design of such systems. We advocate that adaptive systems should be designed this way from as early as Requirements Engineering and that reasoning over requirements is fundamental for run-time adaptation. We therefore propose an approach for the design of adaptive systems based on requirements and inspired in control theory [6]. Our proposal is goal-oriented and targets softwareintensive socio-technical systems [7], in an attempt to integrate control-loop approaches with decentralized agents inspired approaches [8]. Our final objective is a set of extensions to state-of-the-art goal-oriented modeling languages that allow practitioners to clearly specify the requirements of adaptive systems and a run-time framework that helps developers implement such requirements. In this 2-page abstract paper, we summarize this approach. Several researchers have demonstrated how complex action sequences can be learned through neuroevolution (i.e., evolving neural networks with genetic algorithms). However, complex general behavior such as evading predators or avoiding obstacles, which is not tied to specific environments, turns out to be very difficult to evolve. Often the system discovers mechanical strategies, such as moving back and forth, that help the agent cope but are not very effective, do not appear believable, and do not generalize to new environments. The problem is that a general strategy is too difficult for the evolution system to discover directly. This article proposes an approach wherein such complex general behavior is learned incrementally, by starting with simpler behavior and gradually making the task more challenging and general. The task transitions are implemented through successive stages of Delta coding (i.e., evolving modifications), which allows even converged populations to adapt to the new task. The method is... We study a particular multiagent resource allocation problem with indivisible, but sharable resources. In our model, the utility of an agent for using a bundle of resources is the difference between the valuation of that bundle and a congestion cost (or delay), a figure formed by adding up the individual congestion costs of each resource in the bundle. The valuation and the delay can be agent-dependent. When the agents that share a resource also share the resource's control, the current users of a resource will require some compensation when a new agent wants to use the resource. We study the existence of distributed protocols that lead to a social optimum. Depending on constraints on the valuation functions (mainly modularity), on the delay functions (e.g., convexity), and the structural complexity of the deals between agents, we prove either the existence of some sequences of deals or the convergence of all sequences of deals to a social optimum. When the agents do not have joint control over the resources (i.e., they can use any resource they want), we study the existence of pure Nash equilibria. We provide results for modular valuation functions and relate them to results from the literature on congestion games. The key challenge in multiagent learning is learning a best response to the behaviour of other agents, which may be non-stationary: if the other agents adapt their strategy as well, the learning target moves. Disparate streams of research have approached non-stationarity from several angles, which make a variety of implicit assumptions that make it hard to keep an overview of the state of the art and to validate the innovation and significance of new works. This survey presents a coherent overview of work that addresses opponent-induced non-stationarity with tools from game theory, reinforcement learning and multi-armed bandits. Further, we reflect on the principle approaches how algorithms model and cope with this non-stationarity, arriving at a new framework and five categories (in increasing order of sophistication): ignore, forget, respond to target models, learn models, and theory of mind. A wide range of state-of-the-art algorithms is classified into a taxonomy, using these categories and key characteristics of the environment (e.g., observability) and adaptation behaviour of the opponents (e.g., smooth, abrupt). To clarify even further we present illustrative variations of one domain, contrasting the strengths and limitations of each category. Finally, we discuss in which environments the different approaches yield most merit, and point to promising avenues of future research. Abstract When the initial distribution and transition rates for a continuous time Markov chain are not known precisely, robust methods are needed to study the evolution of the process in time to avoid judgements based on unwarranted precision. We follow the ideas successfully applied in the study of discrete time model to build a framework of imprecise Markov chains in continuous time. The imprecision in the distributions over the set of states is modelled with upper and lower expectation functionals, which equivalently represent sets of probability distributions. Uncertainty in transitions is modelled with sets of transition rates compatible with available information. The Kolmogorov’s backward equation is then generalised into the form of a generalised differential equation, with generalised derivatives and set valued maps. The upper and lower expectation functionals corresponding to imprecise distributions at given times are determined by the maximal and minimal solutions of these equations. The second part of the paper is devoted to numerical methods for approximating the boundary solutions. The methods are based on discretisation of the time interval. A uniform and adaptive grid discretisations are examined. The latter is computationally much more efficient than the former one, but is not applicable on every interval. Therefore, to achieve maximal efficiency a combination of the methods is used. The advent of large-scale distributed systems poses unique engineering challenges. In open systems such as the internet it is not possible to prescribe the behaviour of all of the components of the system in advance. Rather, we attempt to design infrastructure, such as network protocols, in such a way that the overall system is robust despite the fact that numerous arbitrary, non-certified, third-party components can connect to our system. Economists have long understood this issue, since it is analogous to the design of the rules governing auctions and other marketplaces, in which we attempt to achieve socially-desirable outcomes despite the impossibility of prescribing the exact behaviour of the market participants, who may attempt to subvert the market for their own personal gain. This field is known as "mechanism design": the science of designing rules of a game to achieve a specific outcome, even though each participant may be self-interested. Although it originated in economics, mechanism design has become an important foundation of multi-agent systems (MAS) research. In a traditional mechanism design problem, analytical methods are used to prove that agents' game-theoretically optimal strategies lead to socially desirable outcomes. In many scenarios, traditional mechanism design and auction theory yield clear-cut results; however, there are many situations in which the underlying assumptions of the theory are violated due to the messiness of the real-world. In this paper we review alternative approaches to mechanism design which treat it as an engineering problem and bring to bear engineering design principles, viz.: iterative step-wise refinement of solutions, and satisficing instead of optimization in the face of intractable complexity. We categorize these approaches under the banner of evolutionary mechanism design. We combine Riemannian geometry with the mean field theory of high dimensional chaos to study the nature of signal propagation in generic, deep neural networks with random weights. Our results reveal an order-to-chaos expressivity phase transition, with networks in the chaotic phase computing nonlinear functions whose global curvature grows exponentially with depth but not width. We prove this generic class of deep random functions cannot be efficiently computed by any shallow network, going beyond prior work restricted to the analysis of single functions. Moreover, we formalize and quantitatively demonstrate the long conjectured idea that deep networks can disentangle highly curved manifolds in input space into flat manifolds in hidden space. Our theoretical analysis of the expressive power of deep networks broadly applies to arbitrary nonlinearities, and provides a quantitative underpinning for previously abstract notions about the geometry of deep functions. Many applications in science and engineering lead to models which require solving large-scale fixed point problems, or equivalently, systems of nonlinear equations. Several successful techniques for handling such problems are based on quasi-Newton methods that implicitly update the approximate Jacobian or inverse Jacobian to satisfy a certain secant condition. We present two classes of multisecant methods which allows to take into account a variable number of secant equations at each iteration. The first is the Broyden-like class, of which Broyden’s family is a subclass, and Anderson mixing is a particular member. The second class is that of the nonlinear Eirola-Nevanlinna-type methods. This work was motivated by a problem in electronic structure calculations, whereby a fixed point iteration, known as the self-consistent field (SCF) iteration, is accelerated by various strategies termed ‘mixing’. The field of convention emergence studies how agents involved in repeated coordination games can reach consensus through only local interactions. The literature on this topic is vast and is motivated by human societies, mainly addressing coordination problems between human agents, such as who gets to redial after a dropped telephone call. In contrast, real-world engineering problems, such as coordination in wireless sensor networks, involve agents with limited resources and knowledge and thus pose certain restrictions on the complexity of the coordination mechanisms. Due to these restrictions, strategies proposed for human coordination may not be suitable for engineering applications and need to be further explored in the context of real-world application domains. In this article we take the role of designers of large decentralized multi-agent systems. We investigate the factors that speed up the convergence process of agents arranged in different static and dynamic topologies and under different interaction models, typical for engineering applications. We also study coordination problems both under partial observability and in the presence of faults (or noise). The main contributions of this article are that we propose an approach for emergent coordination, motivated by highly constrained devices, such as wireless nodes and swarm bots, in the absence of a central entity and perform extensive theoretical and empirical studies. Our approach is called Win-Stay Lose-probabilistic-Shift, generalizing two well-known strategies in game theory that have been applied in other domains. We demonstrate that our approach performs well in different settings under limited information and imposes minimal system requirements, due to its simplicity. Moreover, our technique outperforms state-of-the-art coordination mechanisms, guarantees full convergence in any topology and has the property that all convention states are absorbing. What does it mean to fully understand the behavior of a network of adaptive agents? The golden standard typically is the behavior of learning dynamics in potential games, where many evolutionary dynamics, e.g., replicator dynamics, are known to converge to sets of equilibria. Even in such classic settings many questions remain unanswered. We examine issues such as: Point-wise convergence: Does the system always equilibrate, even in the presence of continuums of equilibria? Computing regions of attraction: Given point-wise convergence can we compute the region of asymptotic stability of each equilibrium (e.g., estimate its volume, geometry)? System invariants: Invariant functions remain constant along every system trajectory. This notion is orthogonal to the game theoretic concept of a potential function, which always strictly increases decreases along system trajectories. Do dynamics in potential games exhibit invariant functions? If so, how many? How do these functions look like? Based on these geometric characterizations, we propose a novel quantitative framework for analyzing the efficiency of potential games with many equilibria. The predictions of different equilibria are weighted by their probability to arise under evolutionary dynamics given uniformly random initial conditions. This average case analysis is shown to offer novel insights in classic game theoretic challenges, including quantifying the risk dominance in stag-hunt games and allowing for more nuanced performance analysis in networked coordination and congestion games with large gaps between price of stability and price of anarchy. CCS Concepts: rTheory of computation! Solution concepts in game theory; Convergence and learning in games; In this paper, we propose to tackle the problem of reducing discrepancies between multiple domains referred to as multi-source domain adaptation and consider it under the target shift assumption: in all domains we aim to solve a classification problem with the same output classes, but with labels' proportions differing across them. We design a method based on optimal transport, a theory that is gaining momentum to tackle adaptation problems in machine learning due to its efficiency in aligning probability distributions. Our method performs multi-source adaptation and target shift correction simultaneously by learning the class probabilities of the unlabeled target sample and the coupling allowing to align two (or more) probability distributions. Experiments on both synthetic and real-world data related to satellite image segmentation task show the superiority of the proposed method over the state-of-the-art.