Learning to Form Dynamic Committees Santiago Onta˜ n´ on ∗ and Enric Plaza IIIA, Artificial Intelligence Research Institute CSIC, Spanish Council for Scientific Research Campus UAB, 08193 Bellaterra Catalonia (Spain). (santi,enric)@iiia.csic.es, http://www.iiia.csic.es ABSTRACT Learning agents can improve performance when they cooperate with other agents. Specifically, learning agents forming a commit- tee outperform individual agents. This “ensemble effect” is well know for multi-classifier systems in Machine Learning. However, multi-classifier systems assume all data is know to all classifiers while we focus on agents that learn from cases (examples) that are owned and stored individually. In this article we focus on the selec- tion of the agents that join a committee for solving a problem. Our approach is to frame committee membership as a learning task for the convener agent. The committee convener agent learns to form a committee in a dynamic way: at each point in time the convener agent decides whether it is better to invite a new member to join the committee (and which agent to invite) or to close the member- ship. The convener agent performs learning in the space of voting situations, i.e. learns when the current committee voting situation is likely to solve correctly (or not) a problem. The learning pro- cess allows an agent to decide when to individually solve a prob- lem, when it is better to convene a committee, and which individual agents to be invited to join the committee. Our experiments show that learning to form dynamic committees results in smaller com- mittees while maintaining (and sometimes improving) the problem solving accuracy. Categories and Subject Descriptors I.2.11 [Computing Methodologies]: Artificial Intelligence—Dis- tributed Artificial Intelligence; G.3 [Mathematics of Computing]: Distribution functions; I.2.11 [Computing Methodologies]: Arti- ficial Intelligence—Learning General Terms Experimentation ∗ Main author, student Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. To copy otherwise, to republish, to post on servers or to redistribute to lists, requires prior specific permission and/or a fee. Copyright 2002 ACM X-XXXXX-XX-X/XX/XX ...$5.00. Keywords Cooperative CBR, Multiagent CBR, Collaboration Policies. 1. INTRODUCTION A main issue in multiagent systems is how an agent decides when to cooperate with other agents. Specifically we focus on the issue of an agent that has to decide whether it is able to individu- ally solve a problem or asks others to help it to solve the problem forming a Committee. For our purpose, a Committee is a collection of agents that cooperate in solving a problem by casting a vote on a (individually endorsed) solution where the overall solution is that with maximum votes. The voting can have several schemes, major- ity voting or approval voting—we’ll see we will be using bounded weighted approval voting (BWAV). Concerning the incentive of agents to cooperate in the form of a Committee, the basic reason is that they can improve their perfor- mance in solving problems—since we focus on classification tasks, the Committee organization improves (in general) the classification accuracy with respect to individual agents. This called “ensemble effect” is well know for multi-classifier systems in Machine Learn- ing. However, multi-classifier systems assume all data is known to all classifiers while we focus on agents that learn from cases (examples) that are owned and stored individually. The ensemble effect essentially means that when the individual classifiers error is not correlated to other classifiers, the Committee improves with respect to all individual classifiers. A second issue on multiagent cooperation involves the selection of which agents we want to cooperate with. In terms of our current framework, this involves the selection (by a convener agent) of the agents invited to join a Committee. Because of the ensemble effect, the default selection policy is to invite all available and capable agents to join a Committee. However, this process can be expensive or slow if the committee is big, and it is not evident that this policy is the best on all situations. We present a learning framework that unifies both the “when” and “who” issues: learning a decision procedure for when to col- laborate and selecting which agents are better suited for collabo- ration. In this framework the convener agent learns to assess the likelihood that the current committee will give a correct solution. If the likelihood is not high, the convener agent has to invite a new agent to join the Committee and has to decide which agent to in- vite. The initial situation of this framework starts with the convener agent that receives a problem forming a “Committee of one” and then deciding whether the problem can be solved in isolation or it is better to convene a Committee. We present a proactive learning approach, in which an agent per-