Local Utility Function Research Articles

A Hierarchical Multilayer Service Composition Model for Global Virtual Organizations

A major benefit of service composition is the ability to support agile global collaborative virtual organizations. However, being global in nature, collaborative virtual organizations can have several virtual industry clusters (VIC), where each VIC has hundreds to thousands of virtual enterprises that provide functionally similar services exposed as web services. These web services can be differentiated on a high dimensionality of quality of service attributes. The dilemma the virtual enterprise broker is faced with is how to dynamically select the best combination of component services to fulfill a complex consumer need within the shortest time possible. This composite service selection problem remains a Multi-Criteria Decision Making (MCDM) NP hard problem. Although existing MCDM methods based on local planning are linearly scalable for large problems, they lack capabilities to express critical intertask constraints that are practically relevant to service consumers. MCDM global planning methods on the other hand suffer exponential state space explosion making them severely limited for large problems of industrial relevance. This paper proposes HMSCM: Hierarchical Multi-Layer Service Composition Model. HMSCM is based on the theory of Layering as Optimization Decomposition (28-31). We view the service selection process as a layer network where each layer is a subproblem to be solved. The objective of one of the layers is to maximize a local utility function over a subset of web service QoS attributes from a service consumer perspective. The objective of the other layer is to maximize a local utility function over another subset of web service QoS attributes from the perspective of the Virtual enterprise broker. We develop the algorithm: Service Layered Utility Maximization (SLUM) that extends the Mixed Integer programming model in (9). We then formulate the problem at each layer in form of SLUM. Together, the two layers attempt to achieve the global optimization objective of the network. We show analytically how HMSCM overcomes the shortcomings of existing local planning and global planning service selection methods while retaining the strengths from each. i.e HMSCM is able to scale linearly with increasing number of QoS variables and number of web services while being able to enforce global intertask constraints.

Distributed resource allocation in cognitive and cooperative ad hoc networks through joint routing, relay selection and spectrum allocation

Cooperative relaying and dynamic-spectrum-access/cognitive techniques are promising solutions to increase the capacity and reliability of wireless links by exploiting the spatial and frequency diversity of the wireless channel. Yet, the combined use of cooperative relaying and dynamic spectrum access in multi-hop networks with decentralized control is far from being well understood.We study the problem of network throughput maximization in cognitive and cooperative ad hoc networks through joint optimization of routing, relay assignment and spectrum allocation. We derive a decentralized algorithm that solves the power and spectrum allocation problem for two common cooperative transmission schemes, decode-and-forward (DF) and amplify-and-forward (AF), based on convex optimization and arithmetic–geometric mean approximation techniques. We then propose and design a practical medium access control protocol in which the probability of accessing the channel for a given node depends on a local utility function determined as the solution of the joint routing, relay selection, and dynamic spectrum allocation problem. Therefore, the algorithm aims at maximizing the network throughput through local control actions and with localized information only.Through discrete-event network simulations, we finally demonstrate that the protocol provides significant throughput gains with respect to baseline solutions.

Generalized Efficiency Bounds in Distributed Resource Allocation

Game theory is emerging as a popular tool for distributed control of multiagent systems. To take advantage of these game theoretic tools, the interactions of the autonomous agents must be designed within a game-theoretic environment. A central component of this game-theoretic design is the assignment of a local utility function to each agent. One promising approach to utility design is assigning each agent a utility function according to the agent's Shapley value. This method frequently results in games that possess many desirable features, such as the existence of pure Nash equilibria with near-optimal efficiency. In this paper, we explore the relationship between the Shapley value utility design and the resulting efficiency of both pure Nash equilibria and coarse correlated equilibria. To study this relationship, we introduce a simple class of resource allocation problems. Within this class, we derive an explicit relationship between the structure of the resource allocation problem and the efficiency of the resulting equilibria. Lastly, we derive a bicriteria bound for this class of resource allocation problems-a bound on the value of the optimal allocation relative to the value of an equilibrium allocation with additional agents.

Rules for trajectory updating in decision based design

Optimization is an indispensable tool in decision based design (DBD). There is an emerging consensus in DBD that the only correct objective to maximize is the decision maker's utility from a design. However, a utility function assessed a priori may not capture the preferences of the decision maker over the entire design space. As a result, when the optimizer searches for the optimal design, it may traverse (or end up) in regions in the design space where the preference order among different solutions is different from that used to build the utility function. For a highly non-convex design space, this can lead to convergence to a grossly suboptimal design depending on where we start the solution search. In this article, we propose two approaches to address this issue. First, we track the trajectory of the solution as generated by the optimizer and generate ranking questions that are presented to the designer to verify the correctness of the utility function, and second we propose backtracking rules if a local utility function is very different from the initially assessed function. We demonstrate our methodology using a mathematical example and a welded-beam design problem.

Convergence of a Multi-Agent Projected Stochastic Gradient Algorithm for Non-Convex Optimization

We introduce a new framework for the convergence analysis of a class of distributed constrained non-convex optimization algorithms in multi-agent systems. The aim is to search for local minimizers of a non-convex objective function which is supposed to be a sum of local utility functions of the agents. The algorithm under study consists of two steps: a local stochastic gradient descent at each agent and a gossip step that drives the network of agents to a consensus. Under the assumption of decreasing stepsize, it is proved that consensus is asymptotically achieved in the network and that the algorithm converges to the set of Karush-Kuhn-Tucker points. As an important feature, the algorithm does not require the double-stochasticity of the gossip matrices. It is in particular suitable for use in a natural broadcast scenario for which no feedback messages between agents are required. It is proved that our results also holds if the number of communications in the network per unit of time vanishes at moderate speed as time increases, allowing potential savings of the network's energy. Applications to power allocation in wireless ad-hoc networks are discussed. Finally, we provide numerical results which sustain our claims.

Pseudo-polynomial functions over finite distributive lattices

In this paper we extend the authors’ previous works by considering a multi-attribute aggregation model based on a composition of a polynomial function over a finite distributive lattice with local utility functions; these are referred to as pseudo-polynomial functions. We present an axiomatization for this class of pseudo-polynomial functions which differs from the previous ones both in flavour and nature, and develop general tools which are then used to obtain all possible such factorizations of a given pseudo-polynomial function.

Local Utility and Multivariate Risk Aversion

We revisit Machina's local utility as a tool to analyze attitudes to multivariate risks. Using martingale embedding techniques, we show that for non-expected utility maximizers choosing between multivariate prospects, aversion to multivariate mean preserving increases in risk is equivalent to the concavity of the local utility functions, thereby generalizing Machina's result in Machina (1982). To analyze comparative risk attitudes within the multivariate extension of rank dependent expected utility of Galichon and Henry (2011), we extend Quiggin's monotone mean and utility preserving increases in risk and show that the useful characterization given in Landsberger and Meilijson (1994) still holds in the multivariate case.

Local Utility and Multivariate Risk Aversion

We revisit Machina's local utility as a tool to analyze attitudes to multivariate risks. Using martingale embedding techniques, we show that for nonexpected utility maximizers choosing between multivariate prospects, aversion to multivariate mean preserving increases in risk is equivalent to the concavity of the local utility functions, thereby generalizing Machina's result in [18]. To analyze comparative risk attitudes within the multivariate extension of rank dependen t expected utility of [10], we extend Quiggin's monotone mean and utility preserving increases in risk and show that the useful characterization given in [17] still holds in the multivariate case.

AXIOMATIZATIONS AND FACTORIZATIONS OF SUGENO UTILITY FUNCTIONS

In this paper we consider a multicriteria aggregation model where local utility functions of different sorts are aggregated using Sugeno integrals, and which we refer to as Sugeno utility functions. We propose a general approach to study such functions via the notion of pseudo-Sugeno integral (or, equivalently, pseudo-polynomial function), which naturally generalizes that of Sugeno integral, and provide several axiomatizations for this class of functions.Moreover, we address and solve the problem of factorizing a Sugeno utility function as a composition q(φ1(x1),…,φn(xn)) of a Sugeno integral q with local utility functions φi, if such a factorization exists.

Dual theory of choice with multivariate risks

We propose a multivariate extension of Yaari's dual theory of choice under risk. We show that a decision maker with a preference relation on multidimensional prospects that preserves first order stochastic dominance and satisfies comonotonic independence behaves as if evaluating prospects using a weighted sum of quantiles. Both the notions of quantiles and of comonotonicity are extended to the multivariate framework using optimal transportation maps. Finally, risk averse decision makers are characterized within this framework and their local utility functions are derived. Applications to the measurement of multi-attribute inequality are also discussed.

Recovering a game model from an optimal channel access scheme for WLANs

Idle Sense is an optimal channel access scheme to achieve high throughput with high short-term fairness in IEEE 802.11 style wireless LANs. This paper recovers a non-cooperative game model from the protocol. We show that the control algorithm used by Idle Sense can be reverse-engineered so that each node implicitly maximizes a selfish local utility function. We prove the game has a Nash equilibrium which, under certain conditions, is unique with all nodes sharing the wireless channel equally. We perform extensive numerical simulations to get the equilibrium point for various network sizes and compare the performance of the model with IEEE 802.11 DCF. The achieved throughput at equilibrium is close to optimal.

Foresighted tree configuration games in resource constrained distributed stream mining sensors

We consider the problem of optimizing stream mining applications that are constructed as tree topologies of classifiers and deployed on a set of resource constrained and distributed processing nodes (or sensors). The optimization involves selecting appropriate false-alarm detection tradeoffs (operating points) for each classifier to minimize an end-to-end misclassification penalty, while satisfying resource constraints. We design distributed solutions, by defining tree configuration games, where individual classifiers configure themselves to maximize an appropriate local utility. We define the local utility functions and determine the information that needs to be exchanged across classifiers in order to design the distributed solutions. We analytically show that there is a unique pure strategy Nash equilibrium in operating points, which guarantees convergence of the proposed approach. We develop both myopic strategy, where the utility is purely local to the current classifier, and foresighted strategy, where the utility includes impact of classifier’s actions on successive classifiers. We analytically show that actions determined based on foresighted strategies improve the end-to-end performance of the classifier tree, by deriving an associated probability bound. We also investigate the impact of resource constraints on the classifier action selections for each strategy, and the corresponding application performance. We propose a learning-based approach, which enables each classifier to effectively adapt to the dynamic changes of resource constraints. We evaluate the performance of our solutions on an application for sports scene classification. We show that foresighted strategies result in better performance than myopic strategies in both resource unconstrained and resource constrained scenarios, and asymptotically approach the centralized optimal solution. We also show that the proposed distributed solutions outperform the centralized solution based on the Sequential Quadratic Programming on average in resource unconstrained scenarios.

Consistent mean-variance preferences

Mean-variance utility functions exhibiting a certain set of properties underpin a large body of financial and economic theories. This paper provides a firm choice-theoretic foundation for such a function. Under the assumption that preferences over distributions are utility-representable, we show that the preferences can be represented by a differentiable mean-variance utility function if and only if the preference functional is L p -Frechet differentiable (for ) and the local utility function is quadratic for all distributions. Assuming the conditions for such a mean-variance utility function, we further identify easily interpretable necessary and sufficient conditions on the preferences for each of the properties that the mean-variance utility function is commonly assumed to exhibit in applications of the mean-variance approach. In the light of the characterizations, it is also shown that the apparent inconsistency demonstrated by Borch in a mean-variance model can be ruled out by appropriate restrictions on the mean-variance utility function. Copyright 2011 Oxford University Press 2010 All rights reserved, Oxford University Press.

Learning vector quantization with adaptive metrics for online figure-ground segmentation

Learning vector quantization with adaptive metrics for online figure-ground segmentation

Reverse-Engineering MAC: A Non-Cooperative Game Model

This paper reverse-engineers backoff-based random-access MAC protocols in ad-hoc networks. We show that the contention resolution algorithm in such protocols is implicitly participating in a non-cooperative game. Each link attempts to maximize a selfish local utility function, whose exact shape is reverse-engineered from the protocol description, through a stochastic subgradient method in which the link updates its persistence probability based on its transmission success or failure. We prove that existence of a Nash equilibrium is guaranteed in general. Then we establish the minimum amount of backoff aggressiveness needed, as a function of density of active users, for uniqueness of Nash equilibrium and convergence of the best response strategy. Convergence properties and connection with the best response strategy are also proved for variants of the stochastic-subgradient-based dynamics of the game. Together with known results in reverse-engineering TCP and BGP, this paper further advances the recent efforts in reverse-engineering layers 2-4 protocols. In contrast to the TCP reverse-engineering results in earlier literature, MAC reverse-engineering highlights the non-cooperative nature of random access.

Decentralized Utility-based Sensor Network Design

Wireless sensor networks consist of energy-constrained sensor nodes operating unattended in highly dynamic environments. In this paper, we advocate a systematic decentralized approach towards the design of such networks based on utility functions. A local utility function is defined for each sensor node in the network. While each sensor node “selfishly” optimizes its own utility, the network as a “whole” converges to a desired global objective. For the purpose of demonstrating our approach, we consider the following two separate case studies for data gathering in sensor networks: (a) construction of a load balanced tree and (b) construction of an energy balanced tree. Our work suggests a significant departure from the existing view of sensor networks as consisting of cooperative nodes, i.e. “selfish”sensor nodes is a useful paradigm for designing efficient distributed algorithms for these networks.

Local Utility Functions and Local Probability Transformations

This note shows that, under appropriate conditions, preferences may be locally approximated by the linear utility or risk-neutral preference functional associated with a local probability transformation.

First-order risk aversion and non-differentiability

First-order risk aversion happens when the risk premiumπ a decision maker is willing to pay to avoid the lottery\(t \cdot \tilde \varepsilon , E[\tilde \varepsilon ] = 0\), is proportional, for smallt, tot. Equivalently,\(\partial \pi /\partial t|_{ t = 0^ + } > 0\). We show that first-order risk aversion is equivalent to a certain non-differentiability of some of the local utility functions (Machina [7]).

Preference modelling by estimating local utility functions for multiobjective optimization

This paper is intended to design goal programming models for capturing the decision maker's (DM's) preference information and for supporting the search for the best compromise solutions in multiobjective optimization. At first, a linear goal programming model is built to estimate piecewise linear local utility functions based on pairwise comparisons of efficient solutions as well as objectives. The interactive step trade-off method (ISTM) is employed to generate a typical subset of efficient solutions of a multiobjective problem. Another general goal programming model is then constructed to embed the estimated utility functions in the original multiobjective problem for utility optimization using ordinary nonlinear programming algorithms. This technique, consisting of the ISTM method and the newly investigated search process, facilitates the identification and elimination of possible inconsistent information which may exist in the DM's preferences. It also provides various ways to carry out post-optimality analysis to test the robustness of the obtained best solutions. A modified nonlinear multiobjective management problem is taken as example to demonstrate the technique.

A Schur Concave Characterization of Risk Aversion for Non-expected Utility Preferences

This paper extends Machina′s (Econometrica50 (1982), 277-323) characterization of risk aversion for Fréchet differentiable non-expected utility preferences to the class of continuous non-expected utility preferences without imposing any differentiability requirement. The necessary and sufficient condition for risk aversion is derived in terms of the Schur concavity of the preference functional when evaluated on finite lotteries with equal probabilities. The latter is characterized by its marginal-rate-of-substitution between a high-income state and a low-income state being not less than unity. Correspondingly, the more risk averse the preference ordering, the greater is its marginal-rate-of-substitution between a high-income state and a low-income state. Finally, we apply our results to characterize individual as well as comparative risk aversion for the class of Gâteaux differentiable preferences in terms of the concavity of the Gâteaux derivative or local utility function. This extends Machina′s Fréchet-based local expected utility analysis to the larger class of Gâteaux differentiable preferences. Journal of Economic Literature Classification Number: D81.