Finding Information Sources by Model Sharing in Open Multi-Agent Systems 1

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1 Finding Information Sources by Model Sharing in Open Multi-Agent Systems Jisun Park, K. Suzanne Barber The Laboratory for Intelligent Processes and Systems The University of Texas at Austin 20 E. 24 th Street ACES 5.402, Austin, TX, Abstract. The beliefs of an agent can influence the goal achievement of the agent. In order for an agent to be autonomous an agent should control its beliefs as well as goals. The degree of an agent s belief autonomy is its degree of dependence on others to build its beliefs, which can be controlled by selecting the most appropriate information sources on which to rely. Large, open environments make it difficult for an agent to find the most appropriate information sources since agents only know about a limited number of sources and sources come and go. More challenges arise when the agents are deployed in ad-hoc networks where each agent has a limited number of neighbors with whom it can communicate. This research proposes a method for finding information sources using the evaluation metrics source s trustworthiness, ability to satisfy the agent s information needs, and timeliness of information delivery. Experiments indicate how the extent to which those evaluations are shared among the agents (the degree of model sharing) affects an agent s selection of information sources and thus, its belief autonomy. Introduction Agents in Multi-Agent Systems (MAS) proactively pursue their goals in an environment which includes other agents []. Consequently, autonomy is relational and limited, meaning that an agent s autonomy is both meaningful in relation to the influence of other agents and the autonomy is necessarily limited by the relationship [2]. An agent s beliefs (estimates of the true value of a statement or variable) are essential for an agent to reason when deciding how to accomplish its goals. Thus, an agent s goal achievement is certainly a function of its beliefs. We define the degree of an agent s belief autonomy for a respective goal as the degree of dependence on others to build its belief models; or the degree of control over its beliefs. Since an agent s beliefs may be constructed from information This research was supported in part under a subcontract with ScenPro, Inc. funded by U.S. Department of Defense, Small Business Technology Transfer (STTR) Program, Contract Number F C-093.

2 2 Jisun Park, K. Suzanne Barber acquired from others (e.g. agents), an agent s belief autonomy is key for accurate belief formulation and goal achievement. We argue that an agent s degree of belief autonomy is dependent upon its radius of awareness. An agent s radius of awareness is the extent to which it knows about other information sources in the system. The radius for an individual agent is limited and can change. Therefore, an agent must often rely on other agents to share their knowledge about potential sources. An agent s internal beliefs consist of its derived models of perceived and communicated information about itself, others and the environment. We propose three factors to be considered for achieving an agent s appropriate degree of belief autonomy: trustworthiness, coverage, and cost. In addition, when agents in the environment share their models about other agents (information sources), it is necessary to incorporate these shared models into the agents evaluations about the other agents (information sources). An agent can use s-curve transformations to incorporate the shared models about other agents which may not be known to it. 2 Overview An agent should select the information and information sources to maximize the achievability of the goal which is depending on the respective information and sources. Thus, the degree of belief autonomy as well as the actual dependencies (i.e. dependencies on which beliefs from which information source) is paramount. Agents are the distributed information sources with limited information acquisition and communication. The network of agents is not always complete because an agent can be either physically or logically limited in its communication radius, or not aware of all agents in the system. The degree of model sharing (dms) can also be defined in this context as the distance of neighbors sharing their evaluations of their respective neighbors. The system can be formally described as follows. Na ( i) = { ak ak is a neighbor of ai} KB( ai, gn) = { rk rk is required by a goal gn of ai} PROV ( a ) = { r r is provided by a } i k k i, where Na ( i ) is a set of agents which are the neighbors of a i, KB( ai, gn) is a set of information which is required by agent a i s goal g n, and PROV ( a i ) is a set of information which is provided by a i. When an agent requires information it does not have, the agent needs to find other suppliers of that information. Instead of assuming an oracle which resolves the location of information, we assume multicast of requests and information to and from neighbors. When an agent learns which neighbors can provide the respective information, the agent can exercise control over the selection of the information sources, and thus, control over the acquisition of beliefs (i.e. belief autonomy), deciding from whom to get information the next time.

3 Finding Information Sources by Model Sharing in Open Multi-Agent Systems 3 There are two main issues for an agent constructing the most reliable paths to the information sources. The first is the evaluation metrics for information and information sources (Section 3), and the second is the resultant effect when agents do or do not share the evaluations of other with different degrees of the model sharing (Section 4). 3 Evaluation Metrics In order for an agent to determine its most appropriate degree of belief autonomy for a goal, it must determine () the potential sources that might deliver those beliefs and (2) the quality and efficiency of those sources. The following metrics, trustworthiness, coverage and cost, serve to describe an agent s potential information source(s). 3. Trustworthiness There exist many different representations and management schemes for trustworthiness [3-6]. In this paper, trustworthiness of an information provider from an agent s point of view is defined simply as the reliability of the information provider. Reliability can be defined as the ability of a system or component to perform its required functions under stated conditions for a specified period of time [7] or the probability that a functional unit will perform its required function for a specified interval under stated conditions [7]. It can also be defined as repeatability or consistency [8]. Based on the above definitions, we define reliability as the probability that an agent provides its perceived information consistently and robustly. This definition assumes that a reliable information provider will consistently provide the same beliefs in a given environment if it perceives the same information. Trustworthiness is denoted by Ta ( i, a j), which is the reliability of a j from a i s point of view. This research assumes that an agent keeps track of the reliability of only its own neighbors. This assumption makes a difference in both selecting the potential sources and suggesting the request paths. Reliability of the sources as a trustworthiness evaluation metric is one of the factors for guaranteeing autonomy on beliefs [2] because it is often desirable for an agent to be completely independent from the untrustworthy sources. Consequently, if an agent knows the reliability of potential sources, for respective information the agent can identify on whom to depend for that information. Thus, reliability evaluations are a significant factor for an agent determining an appropriate degree of belief autonomy (degree of dependence). In addition, the degree of model sharing affects an agent s radius of awareness about sources and their reliability. 3.2 Coverage Coverage of an information source is a measure for representing the contribution of the source to an agent s information needs. Depending upon the relative importance of its goals, an agent a might assign a priority weight, PRIO(a,r), to each information requirement r in its knowledge base. Agent a can assign priority to each required

4 4 Jisun Park, K. Suzanne Barber information by examining the number of goals the information helps to satisfy. When prioritization is impossible, we can assume all priorities to be. Given priority weights for information requirements, coverage of goal g n provided by source a j from a i s perspective is defined by the following equation: SourceCoverage( a, a, g ) = i j n rb PROV ( a j) ra KB( ai) PRIO( a, r ) PRIO( a, r ) Given the source coverage for all information sources, we can measure the combined coverage of a i s goal g n : GoalCoverage( a, g ) = Coverage( a, a, g ) i n i j n aj N( ai) In addition, we define TotalCoverage(a i ) accommodating all goals of agent a i as: TotalCoverage( a ) = GoalCoverage( a, g ) i i n n Coverage is a metric for representing the contribution of information sources to a requestor s goal achievement. The degree of information source distribution changes depending on an agent s decision preference 3.3 Cost The cost of getting information affects the performance and efficiency of an agent s decision-making. Even if a source provides the most reliable information, the high cost of information acquisition degrades the system. Timeliness of the information is closely related to the cost because the acquisition of the information is accomplished by a multi-hop request and delivery protocol. Untimely delivery of information can be caused by either delay due to agents or delay due to communication links. As an information consumer, the requesting agent cannot resolve the causes of the untimely reception of the information but can measure the delay. The cost can also be summed up to estimate the total cost of receiving all the information in the KB from a combination of sources. a i s cost of acquiring information from a j and total cost of acquiring a set of information from a combination of information sources are defined as the following equations: k Cost( ai, a j) =, where k is a scaling factor. Timeliness( ai, a j) TotalCost( ai) = Cost( ai, a j) a j N ( ai) PROV ( a j) The total cost is useful measure when an agent wants to select a set of information sources, which is a typical case when an agent has multiple information requirements. i i a b 4 Model Sharing Since a respective agent only knows about a limited number of information sources (known in this paper as the agent s neighbors), it must also rely on other agents to

5 Finding Information Sources by Model Sharing in Open Multi-Agent Systems 5 share their models describing sources they know about. The degree to which a respective agent shares its knowledge about its neighbors is referred to as the degree of model sharing (dms). An agent s degree of model sharing (dms) is related to its radius of awareness regarding information sources in the system. As the degree of model sharing increases, an agent can evaluate each potential path of an Information Supply Chain more accurately. a 4 REQ REQ REQ REQ a 2 a a 3 INFO INFO INFO INFO a 5 Fig.. Information request multicasting to neighbors with and without the awareness of the indirect neighbors. An agent in an Information Supply Chain receives a request from an agent, and if it cannot provide the information it will request the information from its neighbors. The request is directed to the neighbor which looks like the most appropriate provider based on the agent s models about the providers. The degree of model sharing refers to the degree to which a respective agent shares its knowledge about it neighbors. The knowledge about neighbors which can be shared by the adjacent neighbors includes perceived information, evaluation of neighbors, and suggestion of request paths. They are exchanged between the agents as a form of messages as REQ = [ Info _ id, SUGGESTED _ PATH ], INFO = [ Info, EVAL _ NEIGHBOR]. Fig. depicts an example Information Supply Chain. Focusing on the agent in the middle ( a ), a takes care of two messages request and information. A request message (REQ) includes the information identifications which are required either by a itself or other agents, and suggested paths for the information request. a determines the suggested paths based on the best route given agents known to a and evaluation of other agents given to a. An information message (INFO) contains the information accompanied by the evaluation of neighbors from the provider s point of view. The radius of the evaluations included in the INFO message is decided by dms. Info _ id is a vector of requested information identifications, and Info is the information sent to the requester from the provider. EVAL _ NEIGHBOR is a combined evaluation using the evaluation metrics to describe the potential information sources among the neighbors. Depending on dms, EVAL _ NEIGHBOR contains the models of up to dms hops away from the requesting agent. In Fig., assuming dms is, if a requests information by sending a REQ message, REQ = [ < r >, null], without a suggested path since a does not

6 6 Jisun Park, K. Suzanne Barber have any evaluations about the neighbors of a 3. a3 responds with an INFO message, INFO =< [ r = ><, a4 = 0.5, a5 = 0.9 >, ] including a 3 s evaluations about its neighbors which provide r to a 3 ; in this case, a single number for simplicity. SUGGESTED _ PATH is determined by considering EVAL _ NEIGHBOR. The requesting agent can suggest the expected request route. The suggestion can be injected into the decision-making process of the receivers. An agent must select a set of information sources using its own evaluations of the neighbors and the results of EVAL _ NEIGHBOR for sources beyond it. SUGGESTED _ PATH is a set of suggestions from the receiver of the EVAL _ NEIGHBOR, and it can also affect the decisions about the best sources depending on how much the suggestions are reflected in the decision-making. 5 Shared Models Incorporation Among the evaluation metrics (trustworthiness, cost, coverage) which are the shared models, an agent can use the coverage metric to develop a preference on the sources depending on the preferred degree of distribution among information sources. Cost is related to the timeliness of the information delivery. In a multi-hop delivery system, the delay the requesting agent suffers is accumulated from the origin of the source. Trustworthiness is certainly an important affecting the decision-making, given different degrees of model sharing and it is necessary to integrate the trustworthiness evaluations of () sources originally unknown to the requesting agent but shared by its neighbors (indirect trustworthiness), and (2) its neighbors providing evaluations. When an agent has an access to indirect trustworthiness evaluations, it needs to incorporate those values into the evaluations about its neighbors. In order for an agent to incorporate the indirect trustworthiness values, s-curve transformations can be applied to those values. S-curve transformations clearly promote or diminish values, resulting in semi-binary mapping of indirect trustworthiness values. If an indirect trustworthiness value is more than 0.5, the value is promoted toward. If an indirect trustworthiness value is less than 0.5, the value is demoted toward 0. The incorporation of trustworthiness for the different degrees of the model sharing can be performed by the following equations.,where Tdms ( ai, aj ) T( ai, aj ) σ ( T( am, an )) a is a neighbor of n a, m Tdms ( ai, a ) :incorporated j dist ( ai, an) dms trustworthiness evaluation of a about i a, and, where B is the growth rate. j σ ( x) = + B ( x 0.5) = + e 6 Experiments In the experiments, there are 2 potential information supply chain paths (A,B,C,D,E,F,G,H,I,J,K,L) where each of the paths can be considered as a single

7 Finding Information Sources by Model Sharing in Open Multi-Agent Systems 7 instance of decomposed paths from a tree of neighbors. In these experiments, the maximum length of the information supply chain paths is 3 which denotes the number of hops in the path. The trustworthiness evaluations were pre-assigned, and each path in information supply chain is labeled by the supply chain path ID (see Table ). The overall goal of the experiments is to show the effects of different dms values, as well as the effects of s-curve transformations, for the selection of the most appropriate information sources. 6. Evaluating neighbors with trustworthiness In this experiment, only the trustworthiness is used for evaluating the neighbors for different degrees of the model sharing. Fig.2 (a) represents the results with s-curve transformations and Fig.2 (b) represents the results without s-curve transformations. In Table, the information supply chain path IDs and the corresponding MSE values and ranks, when the target location is transferred along each supply chain path, are presented. A path with a smaller MSE value is assigned a higher rank. In Fig.2 (a) and (b), it is shown that increasing dms yields a better evaluation about each path so each neighbor. For example, comparing Fig.2 (a) and (b), we can see that it is hard to distinguish which path is better between A and B when dms is zero although the MSE of A is less than MSE of B. However, if dms is or 2, the evaluation value for A is higher than that for B, meaning A is better than B which is exactly what the MSEs for A and B imply in Table. Trustworthiness Evaluation for each supply chain (w s-curve transform) 3.5 dms 0 dms 2.5 dms 2 Trustworthiness Evaluation for each supply chain (w/o s-curve transform) dms dms dms2 dms.5 dms potential suply chain paths potential supply chain paths (a) (b) Fig. 2. Trustworthiness Evaluation for each supply chain path (a) with s-curve transformation (b) without s-curve transformation In Fig.2 (a) and (b), we can also see that the s-curve transformation yields a better evaluation about each path thus each neighbor. In Fig.2, with dms 2, s-curve transformation yields a higher value for C than for B, and for J than for I which are correct with respect to MSE (MSE for C is less than B, and MSE for J is less than I). However, it is not possible to distinguish which path is better without s-curve transformations between B and C, and between I and J even with dms 2 as in Fig.2 (b). Experimental results certainly advocate maximum dms, s-curve transformation, and the utility of trustworthiness evaluations in selecting information sources. The experimental results which considers both trustworthiness and cost for evaluation show similar results, but are they not shown in this paper because of the lack of room for them.

8 8 Jisun Park, K. Suzanne Barber Table. Potential supply chain paths and corresponding MSE and ranks Supply MSE Chain Path ID value rank MSE Supply Chain Path ID value rank A 0.45 G.26 9 B.04 6 H.0 5 C I.50 D.36 0 J.22 8 E K F.3 7 L Conclusion This research proposes a method for selecting the information sources on which to rely in a large, open environment. Selection is based on the proposed evaluation metrics: source trustworthiness, coverage and cost. We assume that the agent requesting information only knows about its neighbors, the agents it can directly communicate with. The degree of model sharing is the extent to which agents share their evaluations of information sources with their neighbors along a given Information Supply Chain. The requesting agent needs to incorporate the evaluations about other sources it learns about through its neighbors into the evaluations of its neighbors. The s-curve transformation can be applied to incorporate the shared model into the evaluation of neighbors. Experiments indicate that the evaluations and the degree of model sharing will significantly affect the selection of information sources. Additionally, the s-curve transformation for the incorporation of the shared evaluations from neighbors enhances the agent s ability to evaluate its neighbors and other sources. References [] M. J. Wooldridge and N. R. Jennings, "Intelligent Agents: Theory and Practice," Knowledge Engineering Review, vol. 0, pp. 5-52, 995. [2] C. Castelfranchi, "Guarantees for Autonomy in Cognitive Agent Architecture," in Intelligent Agents: ECAI-94 Workshop on Agents Theories, Architectures, and Languages, N. R. Jennings, Ed. Berlin: Springer-Verlag, 995, pp [3] A. F. Dragoni and P. Giorgini, "Learning Agents' Reliability through Bayesian Conditioning: a simulation study," In Proceedings of Learning in DAI Systems, 997. [4] R. Falcone, G. Pezzulo, and C. Castelfranchi, "A fuzzy approach to a belief-based trust computation," in Lecture Notes on Artificial Intelligence, vol. 263, 2003, pp [5] M. Schillo, P. Funk, and M. Rovatsos, "Using Trust for Detecting Deceitful Agents in Artificial Societies," Applied Artificial Intelligence Journal, Special Issue on Deception, Fraud and Trust in Agent Societies, pp , [6] K. S. Barber and J. Kim, "Soft Security: Isolating Unreliable Agents from Society," in Trust, Reputation, and Security: Theories and Practice, Lecture Notes in Artificial Intelligence, M. Singh, Ed.: Springer, 2003, pp [7] IEEE, "IEEE Standard Computer Dictionary: A Compilation of IEEE Standard Computer Glossaries." New York, NY, 990. [8] W. Trochim, The Research Methods Knowledge Base, 2nd ed. Cincinnati, OH: Atomic Dog Publishing, 2000.

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