Computational complexity and approximability of social welfare optimization in multiagent resource allocation

A central task in multiagent resource allocation, which provides mechanisms to allocate (bundles of) resources to agents, is to maximize social welfare. We assume resources to be indivisible and nonshareable and agents to express their utilities over bundles of resources, where utilities can be represented in the bundle form, the $k$ -additive form, and as straight-line programs. We study the computational complexity of social welfare optimization in multiagent resource allocation, where we consider utilitarian and egalitarian social welfare and social welfare by the Nash product. Solving some of the open problems raised by Chevaleyre et al. (2006) and confirming their conjectures, we prove that egalitarian social welfare optimization is $\mathrm{NP}$ -complete for the bundle form, and both exact utilitarian and exact egalitarian social welfare optimization are $\mathrm{DP}$ -complete, each for both the bundle and the $2$ -additive form, where $\mathrm{DP}$ is the second level of the boolean hierarchy over  $\mathrm{NP}$ . In addition, we prove that social welfare optimization by the Nash product is $\mathrm{NP}$ -complete for both the bundle and the $1$ -additive form, and that the exact variants are $\mathrm{DP}$ -complete for the bundle and the $3$ -additive form. For utility functions represented as straight-line programs, we show $\mathrm{NP}$ -completeness for egalitarian social welfare optimization and social welfare optimization by the Nash product. Finally, we show that social welfare optimization by the Nash product in the $1$ -additive form is hard to approximate, yet we also give fully polynomial-time approximation schemes for egalitarian and Nash product social welfare optimization in the $1$ -additive form with a fixed number of agents.     

A Two-Player Coalition Cooperative Scheme for the Bodyguard Allocation Problem

We address the bodyguard allocation problem (BAP), an optimization problem that illustrates the conflict of interest between two classes of processes with contradictory preferences within a distributed system. While a class of processes prefers to minimize its distance to a particular process called the root, the other class prefers to maximize it; at the same time, all the processes seek to build a communication spanning tree with the maximum social welfare. The two state-of-the-art algorithms for this problem always guarantee the generation of a spanning tree that satisfies a condition of Nash equilibrium in the system; however, such a tree does not necessarily produce the maximum social welfare. In this paper, we propose a two-player coalition cooperative scheme for BAP, which allows some processes to perturb or break a Nash equilibrium to find another one with a better social welfare. By using this cooperative scheme, we propose a new algorithm called FFC-BAP_S for BAP. We present both theoretical and empirical analyses which show that this algorithm produces better quality approximate solutions than former algorithms for BAP.     

Voting almost maximizes social welfare despite limited communication

In cooperative multiagent systems an alternative that maximizes the social welfare—the sum of utilities—can only be selected if each agent reports its full utility function. This may be infeasible in environments where communication is restricted. Employing a voting rule to choose an alternative greatly reduces the communication burden, but leads to a possible gap between the social welfare of the optimal alternative and the social welfare of the one that is ultimately elected. Procaccia and Rosenschein (2006) [13] have introduced the concept of distortion to quantify this gap.In this paper, we present the notion of embeddings into voting rules: functions that receive an agent?s utility function and return the agent?s vote. We establish that very low distortion can be obtained using randomized embeddings, especially when the number of agents is large compared to the number of alternatives. We investigate our ideas in the context of three prominent voting rules with low communication costs: Plurality, Approval, and Veto. Our results arguably provide a compelling reason for employing voting in cooperative multiagent systems.     

EGALITARIAN NEGOTIATIONS IN AGENT SOCIETIES

Achieving fairness among the members of a society is an important issue in many resource allocation problems. The increasing focus of the computer sciences community is motivated by a large panel of applications where other welfare notions do not suit. Centralized approaches are usually used, but they suffer from important drawbacks. Because relationships among society members are not considered, the provided resource allocation may not be achievable in practice. This study seeks to provide an evenly distributed approach based on a multiagent system, which overcomes the main drawbacks of centralized approaches. We provide an adaptive, anytime, and scalable algorithm to hold efficient egalitarian negotiations. Negotiation processes lead to socially efficient allocations as an emergent phenomenon. We also evaluate the “price of the social graph” toward the negotiation efficiency, and we provide the agent behavior to implement in order to achieve fair allocations.     

Watershed model parameter estimation and uncertainty in data-limited environments

Parameter uncertainty and sensitivity for a watershed-scale simulation model in Portugal were explored to identify the most critical model parameters in terms of model calibration and prediction. The research is intended to help provide guidance regarding allocation of limited data collection and model parameterization resources for modelers working in any data and resource limited environment. The watershed-scale hydrology and water quality simulation model, Hydrologic Simulation Program – FORTRAN (HSPF), was used to predict the hydrology of Lis River basin in Portugal. The model was calibrated for a 5-year period 1985–1989 and validated for a 4-year period 2003–2006. Agreement between simulated and observed streamflow data was satisfactory considering the performance measures such as Nash–Sutcliffe efficiency (E), deviation runoff (Dv) and coefficient of determination (R²). The Generalized Likelihood Uncertainty Estimation (GLUE) method was used to establish uncertainty bounds for the simulated flow using the Nash–Sutcliffe coefficient as a performance likelihood measure. Sensitivity analysis results indicate that runoff estimations are most sensitive to parameters related to climate conditions, soil and land use. These results state that even though climate conditions are generally most significant in water balance modeling, attention should also focus on land use characteristics as well. Specifically with respect to HSPF, the two most sensitive parameters, INFILT and LZSN, are both directly dependent on soil and land use characteristics.     

Welfare Guarantees for Proportional Allocations

According to the proportional allocation mechanism from the network optimization literature, users compete for a divisible resource – such as bandwidth – by submitting bids. The mechanism allocates to each user a fraction of the resource that is proportional to her bid and collects an amount equal to her bid as payment. Since users act as utility-maximizers, this naturally defines a proportional allocation game. Syrgkanis and Tardos (STOC 2013) quantified the inefficiency of equilibria in this game with respect to the social welfare and presented a lower bound of 26.8 % on the price of anarchy over coarse-correlated and Bayes-Nash equilibria in the full and incomplete information settings, respectively. In this paper, we improve this bound to 50 % over both equilibrium concepts. Our analysis is simpler and, furthermore, we argue that it cannot be improved by arguments that do not take the equilibrium structure into account. We also extend it to settings with budget constraints where we show the first constant bound (between 36 and 50 %) on the price of anarchy of the corresponding game with respect to an effective welfare benchmark that takes budgets into account.     

Optimization-based resource allocation in communication networks

The continuously growing number of applications competing for resources in current communication networks highlights the necessity for efficient resource allocation mechanisms to maximize user satisfaction. Optimization Theory can provide the necessary tools to develop such mechanisms that will allocate network resources optimally and fairly among users. The aim of this paper is to provide a starting point for researchers interested in applying optimization techniques in the resource allocation problem for current communication networks. To achieve that we, first, describe the fundamental optimization theory tools necessary to design optimal resource allocation algorithms. Then, we describe the Network Utility Maximization (NUM) framework, a framework that has already found numerous applications in network optimization, along with some recent advancements of the initial NUM framework. Finally, we summarize some of our recent work in the area and discuss some of the remaining research challenges towards the development of a complete optimization-based resource allocation protocol.     

On the Efficiency of the Proportional Allocation Mechanism for Divisible Resources

We study the efficiency of the proportional allocation mechanism that is widely used to allocate divisible resources. Each agent submits a bid for each divisible resource and receives a fraction proportional to her bids. We quantify the inefficiency of Nash equilibria by studying the Price of Anarchy (PoA) of the induced game under complete and incomplete information. When agents’ valuations are concave, we show that the Bayesian Nash equilibria can be arbitrarily inefficient, in contrast to the well-known 4/3 bound for pure equilibria Johari and Tsitsiklis (Math. Oper. Res. 29(3), 407–435 2004). Next, we upper bound the PoA over Bayesian equilibria by 2 when agents’ valuations are subadditive, generalizing and strengthening previous bounds on lattice submodular valuations. Furthermore, we show that this bound is tight and cannot be improved by any simple or scale-free mechanism. Then we switch to settings with budget constraints, and we show an improved upper bound on the PoA over coarse-correlated equilibria. Finally, we prove that the PoA is exactly 2 for pure equilibria in the polyhedral environment.     

Surplus equivalence of leveled commitment contracts

In automated negotiation systems consisting of self-interested agents, contracts have traditionally been binding. Leveled commitment contracts—i.e., contracts where each party can decommit by paying a predetermined penalty—were recently shown to improve expected social welfare even if agents decommit strategically in Nash equilibrium. Such contracts differ based on whether agents have to declare their decommitting decisions sequentially or simultaneously, and whether or not agents have to pay the penalties if both decommit. For a given contract, these mechanisms lead to different decommitting thresholds, probabilities, and expected social welfare. However, this paper shows that each of these mechanisms leads to the same social welfare when the contract price and penalties are optimized for each mechanism separately. Our derivations allow agents to construct optimal leveled commitment contracts. We show that such integrative bargaining does not hinder distributive bargaining: the surplus can be divided arbitrarily (as long as each agent benefits), e.g., equally, without compromising optimality. Nonuniqueness questions are answered. We also show that surplus equivalence ceases to hold if agents are not risk neutral.     

基于非合作博弈的变电站无线网络资源研究

无线资源管理对实现资源的有效利用起着至关重要的作用.针对变电站中无线网络资源分配问题,提出了基于非合作博弈的变电站无线网络资源的优化管理算法,解决了全双工系统的无线电资源分配问题.将下行链路与上行链路的联合速率最大化问题建模成为上下行链路信道之间的非合作博弈,提出了基于非合作博弈的迭代算法.该算法有效的实现最佳上行链路与下行链路的资源分配,直到达到纳什均衡.仿真结果表明,该算法实现了快速收敛,与同等资源分配方法相比,可以显著提高全双工的性能.     

The power of verification for one-parameter agents

We initiate the study of mechanisms with verification for one-parameter agents. We give an algorithmic characterization of such mechanisms and show that they are provably better than mechanisms without verification, i.e., those previously considered in the literature. These results are obtained for a number of optimization problems motivated by the Internet and recently studied in the algorithmic mechanism design literature. The characterization can be regarded as an alternative approach to existing techniques to design truthful mechanisms. The construction of such mechanisms reduces to the construction of an algorithm satisfying certain “monotonicity” conditions which, for the case of verification, are much less stringent. In other words, verification makes the construction easier and the algorithm more efficient (both computationally and in terms of approximability).     

Multiagent resource allocation with sharable items

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 value the agent would assign to that bundle in isolation and a congestion cost that depends on the number of agents she has to share each of the resources in her bundle with. The valuation function determining the value and the delay function determining the congestion cost can be agent-dependent. When the agents that share a resource also share control over that resource, then the current users of a resource will require some compensation when a new agent wants to join them using the resource. For this scenario of shared control, we study the existence of distributed negotiation protocols that lead to a social optimum. Depending on constraints on the valuation functions (mainly modularity), on the delay functions (such as convexity), and on the structural complexity of the deals between agents, we prove either the existence of a sequences of deals leading to a social optimum or the convergence of all sequences of deals to such an optimum. We also analyse the length of the path leading to such optimal allocations. For scenarios where the agents using a resource do not have shared control over that resource (i.e., where any agent can use any resource she wants), we study the existence of pure Nash equilibria, i.e., allocations in which no single agent has an incentive to add or drop any of the resources she is currently holding. We provide results for modular valuation functions, we analyse the length of the paths leading to a pure Nash equilibrium, and we relate our findings to results from the literature on congestion games.     

On the structure and complexity of worst-case equilibria

In the resource allocation game introduced by Koutsoupias and Papadimitriou, n$n$ jobs of different weights are assigned to m$m$ identical machines by selfish agents. For this game, it has been conjectured by several authors that the fully mixed Nash equilibrium (FMNE) is the worst possible w.r.t. the expected maximum load over all machines. Assuming the validity of this conjecture, computing a worst-case Nash equilibrium for a given instance was trivial, and approximating the Price of Anarchy for this instance would be possible by approximating the expected social cost of the FMNE by applying a known FPRAS.     

Resource virtualization methodology for on-demand allocation in cloud computing systems

The resources’ heterogeneity and unbalanced capability, together with the diversity of resource requirements in cloud computing systems, have produced great contradictions between resources’ tight coupling characteristics and user’s multi-granularities requirements. We propose a resource virtualization model and its on-demand allocation oriented infrastructure mainly providing computing services to solve that problem. A loosely coupled resource environment centered on resource users is created to complete a mapping from physical view of resources to logic view of resources. Heuristic resource combination algorithm (HRCA) is proposed to transform physical resources to logic resources, which meets two requirements: randomness in combination and fluctuation control to the size of resources granularities. On the basis of the appraisal indexes presented for the on-demand allocation, resource matching algorithm (RMA), targeting at resource satisfaction with the highest resource utilization, is designed to reuse resources. RMA can satisfy users’ requirement in limited time and keep resource satisfaction in the highest level in the condition of logic resources granularities being less than their required size. Resource reconfiguration algorithm (RRA) is presented to implement resource matching in the condition that virtual computing resource pool cannot match granularities of resource requirements. RRA assures the lowest resource refusal rate and the greatest resource satisfaction. We verify the effectiveness, performance and accuracy of algorithms in implementing the goal of resource virtualization centered on resource users and on-demand allocation.     

Positional scoring-based allocation of indivisible goods

We define a family of rules for dividing m indivisible goods among agents, parameterized by a scoring vector and a social welfare aggregation function. We assume that agents’ preferences over sets of goods are additive, but that the input is ordinal: each agent reports her preferences simply by ranking single goods. Similarly to positional scoring rules in voting, a scoring vector \(s = (s_1, \ldots , s_m)\) consists of m nonincreasing, nonnegative weights, where \(s_i\) is the score of a good assigned to an agent who ranks it in position i. The global score of an allocation for an agent is the sum of the scores of the goods assigned to her. The social welfare of an allocation is the aggregation of the scores of all agents, for some aggregation function \(\star \) such as, typically, \(+\) or \(\min \). The rule associated with s and \(\star \) maps a profile to (one of) the allocation(s) maximizing social welfare. After defining this family of rules, and focusing on some key examples, we investigate some of the social-choice-theoretic properties of this family of rules, such as various kinds of monotonicity, and separability. Finally, we focus on the computation of winning allocations, and on their approximation: we show that for commonly used scoring vectors and aggregation functions this problem is NP-hard and we exhibit some tractable particular cases.     

基于纳什议价的对等网络资源分配

针对对等(P2P)网络中普遍存在的自由下载问题,提出保证节点最小服务质量的一种基于纳什议价的资源分配方案。首先,建立保证节点最小服务质量的理论模型,分析表明合作博弈的节点议价权力与其最大贡献能力正相关,非合作博弈节点的议价权力与其最大贡献能力负相关,因此,合作节点比非合作节点获得更多的资源;其次,证明了合作博弈中节点的相对议价权力越大,节点获得的资源越多,收益越大,反之亦然。最后,通过仿真验证系统保证节点获得最小服务质量的前提下,合作节点获得的资源与节点的初始资源分配和纳什议价权力等因素相关;初始资源分配与节点的最大贡献能力呈正相关,并随着节点数目的增加而减少;议价权力随着节点数目的增加而下降,节点获得的资源随着节点议价权力的增加而增加。该方案与经典保证公平性的平均资源分配方案相比,合作节点能获得更多的资源。仿真结果验证了理论分析中在保证节点服务质量前提下,节点议价权力越大,获得的资源越多。     

Joint Quality Enhancement and Power Control for Wireless Visual Sensor Networks based on the Nash Bargaining Solution

We propose a cooperative method for resource allocation with power control in a multihop Direct Sequence Code Division Multiple Access Wireless Visual Sensor Network (WVSN). Typical multihop WVSNs consist of visual sensors that record different scenes and relay nodes that retransmit video data until the base station is reached. The error prone wireless environment contributes to the end-to-end video quality degradation. Moreover, the limited battery life span of the network nodes poses challenges on the management of power consumption. The different resource requirements of the WVSN nodes necessitate a quality-driven and power-aware resource allocation mechanism. We formulate the joint Quality Enhancement and Power Control problem based on a utility function that reflects both the benefit in terms of video quality and the cost in terms of transmission power. This function is employed by the Nash Bargaining Solution, which achieves higher fairness in terms of end-to-end video quality among all nodes. For the fairness assessment, a new metric is introduced. The experiments demonstrate the effectiveness of the proposed approach and explain the video quality-power consumption tradeoff as well as the resulting fairness-power consumption tradeoff.     

Social-welfare based task allocation for multi-robot systems with resource constraints

This paper aims to propose a distributed task allocation algorithm for a team of robots that have constraints on energy resources and operate in an unknown dynamic environment. The objective of the allocation is to maximize task completion ratio while minimizing resource usage. The approach we propose is inspired by the social welfare in economics that helps extend the combined operational lifetime of the team by balancing resource consumptions among robots. This social welfare based task allocation method positions a robot team appropriately in preparedness for dynamic future events and enables to achieve the objectives of the system flexibly depending on the application context. Our simulation-based experiments show that the proposed algorithm outperforms a typical market-based approach in various scenarios.     

基于MAS市场机制的动态计算资源调度模型研究

针对动态计算网格资源调度问题,结合多Agent系统(multi agent syste,MAS)协同技术和市场竞价博弈机制,对计算网格资源分配技术进行了深入研究,提出了能够反映供求关系的基于市场经济的网格资源调度模型,该模型一方面能够充分利用消费者Agent的协商能力,另一方面能够充分考虑消费者的行为,使得消费者的资源申请和分配具有较高的合理性和有效性.同时,设计了消费者的效用函数,论证了资源分配博弈中Nash均衡点的存在性和惟一性以及Nash均衡解.基于所提资源调度模型,设计了一种网格资源调度算法.仿真实验表明,资源调度算法能够为消费者的资源数量提供参考,规范消费者竞价,从而使得整个资源的分配趋于合理.     

A game-theoretic method of fair resource allocation for cloud computing services

As cloud-based services become more numerous and dynamic, resource provisioning becomes more and more challenging. A QoS constrained resource allocation problem is considered in this paper, in which service demanders intend to solve sophisticated parallel computing problem by requesting the usage of resources across a cloud-based network, and a cost of each computational service depends on the amount of computation. Game theory is used to solve the problem of resource allocation. A practical approximated solution with the following two steps is proposed. First, each participant solves its optimal problem independently, without consideration of the multiplexing of resource assignments. A Binary Integer Programming method is proposed to solve the independent optimization. Second, an evolutionary mechanism is designed, which changes multiplexed strategies of the initial optimal solutions of different participants with minimizing their efficiency losses. The algorithms in the evolutionary mechanism take both optimization and fairness into account. It is demonstrated that Nash equilibrium always exists if the resource allocation game has feasible solutions.