Recent Advances

1. Recent Advances Some slides containing formal results are labeled with * in the title fields. These slides may be skipped if only an intuitive tutorial is desired.

2. Common approaches in MAS • Logic-based: Wooldridge 94, Rao and Georgeff 95, Halpern et al. 96. • Game-theoretic: Rosenschein and Zlotkin 94. • Economic: Wellman 92. • Decision-theoretic: Gmytrasiewicz and Durfee 95. • Truth maintenance (default-reasoning)-based: Mason and Johnson 89, Huhns and Bridgeland 91. • Distributed search-based: Yokoo et al. 92.

3. MAS Area of Focus • Task: distributed interpretation • Producing higher level descriptions of the environment from distributed sensing without centralizing the evidence. • Examples of distributed interpretation systems: • Sensor networks. • Medical diagnosis by multiple specialists. • Trouble shooting complex artifacts. • Distributed image interpretation.

4. Recent Advance • Foundation:a probabilistic framework for multiagent distributed interpretation based on multiply sectioned Bayesian networks (MSBNs). • Advance: • Distributed representation of uncertainty knowledge that is consistent with probability theory. • Distributed inference that ensures global consistency. • Agents can be developed by independent designers. • Internal structure/knowledge of agents remains private. • Controversial aspects: • Are cooperative MASs important? • Is homogeneous knowledge representation necessary?

5. Foundations

6. Background • Common approaches for distributed interpretation are based on logic (e.g., blackboard) or default reasoning (e.g., DATMS and DTMS). • Logic-based approaches do not have coherent mechanism to deal with uncertain knowledge. • Default reasoning treats uncertain knowledge as “believed until there is reason to believe otherwise” and not as “believed to a certain degree”. • However, decisions often involve tradeoffs and comparison of strength of belief on states of world or outcomes of actions is thus necessary.

7. Background • Substantial progress has been made in uncertain inference using Bayesian networks (BNs) [Pearl 88]. • Dependencies of domain variables are represented by a DAG. • Strength of dependencies is quantified by an associated jpd. • The jpd is interpreted as the degree of belief of an agent. • Many effective inference algorithms have been developed. • A single-agent paradigm is commonly assumed: • A single processor accesses a single global BN, updates the jpd as evidence becomes available, and answers queries. • This research advances the DTMS approach with a representation of agent’s degree of belief consistent with the probability theory, and advances the single-agent BN approach with a multiagent paradigm and distributed inference algorithm.

8. *Bayesian Networks (BN) • Defi: A BN is a triplet (N,D,P) where • N is a set of random variables, • D is a directed acyclic graph (DAG) whose nodes are labeled by elements of N, • P is a jpd over N specified by probability distributions of each node x in D conditioned on its parents parn(x) in D. • D expresses dependency relations among elements of N. • A variable is independent of its non-descendents given its parents. • Hence P can be expressed as P(N) =  x N P(x | parn(x)).

9. A Trivial Example BN [L & S 88]

10. Multiply Sectioned Bayesian Networks (MSBNs) • Single-agent oriented MSBN [Xiang et al., CI93, AIM93]: • A set of Bayesian subnets that collectively define a BN. • Interface b/w subnets renders them conditionally independent. • Top level structure is a hypertree. • Compiled into a linked junction forest (LJF) for inference. • Coherent inference operations are defined for a LJF. A MSBN (left) and its LJF (right)

11. *The d-sepset: Interface b/w Subnets in a MSBN • Defi: Let Di=(Ni,Ei) (i=1,2) be two DAGs such that their union D is a DAG. I=N1N2 is a d-sepset b/w D1and D2 if for every xI with its parents parn(x) in D, either parn(x)N1 or parn(x) N2. D is said to be sectioned into {D1,D2}. • Theorem: Let a DAG D=(N,E) be sectioned into {D1,…,Dk} and Iij=Ni Nj be the d-sepset b/w Diand Dj. Then for each i,  j Iij d-separates [Pearl88] Ni\ j Iij from N\Ni. • Semantics: If D represents the dependence relations among elements of N, then d-sepset ensures that variables in a subnet are independent of other variables given the d-sepsets of the subnet.

12. *Hypertree MSDAG: Top Level Structure of a MSBN • Defi: Let D be the union of Di (i=1,…,n) where each Di is a connected DAG. D is a hypertree MSDAG if it is a DAG built by the following procedure: • Start with an empty graph. Recursively add a DAG Di called a hypernode, to the existing MSDAG subject to the constraints: • [d-sepset] For each Dj (j<k), Ijk=NjNk is a d-sepset when the two DAGs are isolated. • [Local covering] There exists Di (I<k) such that, for each Dj (j<k;ji), Ijk  Ni . For such Di, Iik is called the hyperlink b/w hypernodes Diand Dk. • Semantics: Each hyperlink renders the two parts of the MSBN that it connects conditionally independent.

13. *Compilation of a MSBN into a Linked Junction Forest • Major steps in compiling a LJF • Convert each DAG (hypernode) into a chordal graph such that all dependence relations are preserved. • Express the chordal graph as a junction tree (JT) of cliques. • Convert each hyperlink (d-sepset) into linkages, each of which is a subset of the d-sepest. • Convert conditional probability distributions in each subnet to belief tables of the corresponding JT and d-sepset. • Let B(Ni) be the belief table on a hypernode and B(Ij) be the belief table on a hyperlink. The joint system belief (JSB) of a LJF is  i B(Ni) /  j B(Ij). • Theorem: JSB of a LJF is equivalent to jpd of its MSBN. • Since each subnet is organized as a tree, a LJF is an equivalent but more effective data structure for inference computation.

14. *Inference in a Single-agent Oriented MSBN • Inference using LJF of a MSBN • Queries of a single user are focused on a single JT at a time, where a query has the form “what is the probability of event A given that B has occured?” • Evidence can be entered incrementally to the JT and queries are answered by local computation only . • As the user shifts attention to another JT, belief propagation is performed only along the hyperpath to the target JT in the hypertree. • Queries can then be entered at the target JT as above. • Theorem: After finite times of attention shifts, answers to queries computed locally are idential to what would be obtained from an equivalent homogeneous BN.

15. What Can be Gained y Using a MSBN? • If a domain consists of loosely coupled subdomains, then... • Knowledge acquisition is natural and modular: Subnet can be built one at a time. • Inference requires only local computation. Attention shift uses only hyperpath. Hence computation is more efficient • Answers to queries are the same as from a homogeneous BN. Structure of a general MSBN (left) and the corresponding hypertree

16. Why Using MSBNs for Distributed Interpretation? • Representation of MSBNs is modular. • Inference in MSBNs is coherent. • The framework of MSBNs is general.

17. Major Issues in Extending MSBNs to MASs • What is the semantics of a subnet? • What is the semantics of the jpd of the MSBN? • How do we build the system by multiple agent developers? • How do we ensure a correct overall structure while protecting the know-how of each developer? • How do we ensure a coherent inference? • What difference does a multi-agent MSBN make relative to a MAS not organized into a MSBN?

18. What is the semantics of a subnet? • In a single-agent MSBN: • The MSBN represents multiple perspectives of a domain hold by a single agent. • Each subnet represents one such perspective. • In a multi-agent MSBN [Xiang, AIJ96] • The MSBN represents multiple agents in a domain, each of which holds one perspective. • Each subnet represents one agent's perspective of the domain. An agent model

19. What is the semantics of the jpd in a MSBN? • If the distribution of each subnet represents one agent's belief, whose belief does the jpd of the MSBN represent? • Example: a computer system. • It processes information coherently as a whole. • Its components are supplied by different vendors. • Observation • As long as vendors follow a protocol in designing component interfaces, the system functions as if it follows a single will.

20. What is the semantics of the jpd in a MSBN? • Another example: a patient sees a doctor. • Patient tells what doctor needs to know for diagnosis. • After doctor reaches a diagnosis, he prescribes a therapy which patient follows. • Observation • Doctor does not experience symptoms. • Patient does not understand how diagnosis is reached. • A coherent belief is demonstrated on symptoms (used by doctor to reach diagnosis) and the diagnosis (therapy is followed by patient).

21. What is the semantics of the jpd in a MSBN? • Due to the way the jpd of a MSBN is defined, there exists a unique jpd [Xiang, AIJ96] such that • its marginalization to each subnet is identical to the distribution of the subnet; • adjacent subnets are conditionally independent given their interface. • Implication: If agents are (1) cooperative, (2) independent conditioned on interface, and (3) initially consistent, then the jpd of the MSBN represents a unique collective belief • identical to each agent's belief within its subdomain, • and supplemental to its belief outside its subdomain.

22. How do we ensure coherent inference? • Issue arising: • In a single-agent MSBN, evidence is entered one subnet at a time. • In a multi-agent MSBN, evidence are entered asynchronously at multiple subnets in parallel. • Solution: extended inference operations [Xiang, AIJ96]. CommunicateBelief CollectNewBelief DistributeBelief

23. How do we ensure coherent inference? • CollectNewBelief: Initiated at an agent to activate an inward propagation towards the agent.

24. How do we ensure coherent inference? • DistributeBelief: Initiated at an agent to activate an outward propagation.

25. How do we ensure coherent inference? • Theorem: After CommunicateBelief, answers to queries from any agent is identical to what is obtained from an equivalent homogeneous BN. • Implication: Distribution causes no loss of coherence. • Complexity of inference computation • Inference at one agent: O(k 2^m), where m is the maximal size of a clique and k is the number of cliques in the JT. • CommunicateBelief: O(t g k 2**m), where t is the number of agents and g is the maximal number of linkages in a hyperlink.

26. How do we ensure coherent inference? • Theorem: Between successive CommunicateBeliefs, answers to queries from any agent X is identical to what would be obtained in an equivalent homogeneous BN where only evidence in the bottom are entered. Evidence to A Evidence to A ... ... Evidence to W Evidence to W Evidence to X Evidence to X Evidence to Y Evidence to Y Evidence to Z Evidence to Z t CommunicateBelief CommunicateBelief t

27. How to build a MSBN by multiple developers? • How to ensure system coherence without disclosing structure and distribution of individual subnets? • It is possible if • the interface of each subnet renders it conditionally independent of others; and • adjacent agents agree on an initial belief of their interface. • Solution [Xiang, AI96]: • A single integrater with the knowledge of agents interface puts agents into a hypertree. • Agents negotiate to achieve initial belief on interface.

28. Global structure vs each agent's know-how • Structures of subnets in a MSBN collectively define a directed acyclic graph (DAG). • Local acyclicity doesn't warrant global acyclicity. • Algorithms to test acyclicity based on topological sorting are well known. However, a central representation of the graph is assumed.

29. Global structure vs each agent's know-how • If each subnet’s structure is unknown to others, how can we ensure acyclicity of the MSBN? • A distributed algorithm has been developed that has the following features [Xiang, FLAIRS96]: • Each agent provides only info on whether a shared node has a parent or a child in its DAG, plus some flag info. • The acyclicity of the MSBN can be correctly determined.

30. What if agents are not organized into a MSBN? • Belief propagation in a MSBN proceeds along hypertree in a regulated fashion. • What happens otherwise? • Circular evidence propagation causes no problem if agents are logical. • But it causes false belief if agent’s knowledge is uncertain. Agent X Agent Y Agent W Agent Z • Not knowing message from Y is based on evidence originated from itself, Z counts the same info twice.

31. Prospects

32. Prospects for distributed interpretation • A framework is provided for tasks that rely on uncertain knowledge and distributed inference without sacrifice of coherence in the interpretation. • The framework protects individual agent developer’s know-how and hence encourages cooperation of many agent developers in building MASs in large and complex domains. • Ex. Systems for trouble-shooting complex artifacts.

33. Prospects for distributed interpretation • The framework suggests standardization of agent interfaces in large and complex domains where knowledge sources are naturally distributed and separately owned. • The framework suggests future research directions: • Dynamic formulation of multiagent MSBNs. • Incorporation of decision making. • Incorporation of temporal inference.