multi-agent system
argument framework
learn agent
learn from commun
joint deliber
argument protocol
collabor
group
predict accuraci
case-base polici
multi-agent learn
argument
case-base reason

Learning and Joint Deliberation through Argumentation in Multi-Agent Systems Santi Ontañón CCL, Cognitive Computing Lab Georgia Institute of Technology Atlanta, GA 303322/0280 santi@cc.gatech.edu Enric Plaza IIIA, Artificial Intelligence Research Institute CSIC, Spanish Council for Scientific Research Campus UAB, 08193 Bellaterra, Catalonia (Spain) enric@iiia.csic.es ABSTRACT In this paper we will present an argumentation framework for learning agents (AMAL) designed for two purposes: (1) for joint deliberation, and (2) for learning from communication.
The AMAL framework is completely based on learning from examples: the argument preference relation, the argument generation policy, and the counterargument generation policy are case-based techniques.
For join deliberation, learning agents share their experience by forming a committee to decide upon some joint decision.
We experimentally show that the argumentation among committees of agents improves both the individual and joint performance.
For learning from communication, an agent engages into arguing with other agents in order to contrast its individual hypotheses and receive counterexamples; the argumentation process improves their learning scope and individual performance.
Categories and Subject Descriptors I.2.6 [Artificial Intelligence]: Learning; I.2.11 [Artificial Intelligence]: Distributed Artificial Intelligence-Multiagent systems, Intelligent Agents 1.
INTRODUCTION Argumentation frameworks for multi-agent systems can be used for different purposes like joint deliberation, persuasion, negotiation, and conflict resolution.
In this paper we will present an argumentation framework for learning agents, and show that it can be used for two purposes: (1) joint deliberation, and (2) learning from communication.
Argumentation-based joint deliberation involves discussion over the outcome of a particular situation or the appropriate course of action for a particular situation.
Learning agents are capable of learning from experience, in the sense that past examples (situations and their outcomes) are used to predict the outcome for the situation at hand.
However, since individual agents experience may be limited, individual knowledge and prediction accuracy is also limited.
Thus, learning agents that are capable of arguing their individual predictions with other agents may reach better prediction accuracy after such an argumentation process.
Most existing argumentation frameworks for multi-agent systems are based on deductive logic or some other deductive logic formalism specifically designed to support argumentation, such as default logic [3]).
Usually, an argument is seen as a logical statement, while a counterargument is an argument offered in opposition to another argument [4, 13]; agents use a preference relation to resolve conflicting arguments.
However, logic-based argumentation frameworks assume agents with preloaded knowledge and preference relation.
In this paper, we focus on an Argumentation-based Multi-Agent Learning (AMAL) framework where both knowledge and preference relation are learned from experience.
Thus, we consider a scenario with agents that (1) work in the same domain using a shared ontology, (2) are capable of learning from examples, and (3) communicate using an argumentative framework.
Having learning capabilities allows agents effectively use a specific form of counterargument, namely the use of counterexamples.
Counterexamples offer the possibility of agents learning during the argumentation process.
Moreover, learning agents allow techniques that use learnt experience to generate adequate arguments and counterarguments.
Specifically, we will need to address two issues: (1) how to define a technique to generate arguments and counterarguments from examples, and (2)how to define a preference relation over two conflicting arguments that have been induced from examples.
This paper presents a case-based approach to address both issues.
The agents use case-based reasoning (CBR) [1] to learn from past cases (where a case is a situation and its outcome) in order to predict the outcome of a new situation.
We propose an argumentation protocol inside the AMAL framework at supports agents in reaching a joint prediction over a specific situation or problem - moreover, the reasoning needed to support the argumentation process will also be based on cases.
In particular, we present two case-based measures, one for generating the arguments and counterarguments adequate to a particular situation and another for determining preference relation among arguments.
Finally, we evaluate (1) if argumentation between learning agents can produce a joint prediction that improves over individual learning performance and (2) if learning from the counterexamples conveyed during the argumentation process increases the individual performance with precisely those cases being used while arguing among them.
The paper is structured as follows.
Section 2 discusses the relation among argumentation, collaboration and learning.
Then Section 3 introduces our multi-agent CBR (MAC) framework and the notion of justified prediction.
After that, Section 4 formally defines our argumentation framework.
Sections 5 and 6 present our case-based preference relation and argument generation policies respectively.
Later, Section 7 presents the argumentation protocol in our AMAL framework.
After that, Section 8 presents an exemplification of the argumentation framework.
Finally, Section 9 presents an empirical evaluation of our two main hypotheses.
The paper closes with related work and conclusions sections.
2.
ARGUMENTATION,COLLABORATION AND LEARNING Both learning and collaboration are ways in which an agent can improve individual performance.
In fact, there is a clear parallelism between learning and collaboration in multi-agent systems, since both are ways in which agents can deal with their shortcomings.
Let us show which are the main motivations that an agent can have to learn or to collaborate.
• Motivations to learn: - Increase quality of prediction, - Increase efficiency, - Increase the range of solvable problems.
• Motivations to collaborate: - Increase quality of prediction, - Increase efficiency, - Increase the range of solvable problems, - Increase the range of accessible resources.
Looking at the above lists of motivation, we can easily see that learning and collaboration are very related in multi-agent systems.
In fact, with the exception of the last item in the motivations to collaborate list, they are two extremes of a continuum of strategies to improve performance.
An agent may choose to increase performance by learning, by collaborating, or by finding an intermediate point that combines learning and collaboration in order to improve performance.
In this paper we will propose AMAL, an argumentation framework for learning agents, and will also also show how AMAL can be used both for learning from communication and for solving problems in a collaborative way: • Agents can solve problems in a collaborative way via engaging an argumentation process about the prediction for the situation at hand.
Using this collaboration, the prediction can be done in a more informed way, since the information known by several agents has been taken into account.
• Agents can also learn from communication with other agents by engaging an argumentation process.
Agents that engage in such argumentation processes can learn from the arguments and counterexamples received from other agents, and use this information for predicting the outcomes of future situations.
In the rest of this paper we will propose an argumentation framework and show how it can be used both for learning and for solving problems in a collaborative way.
3.
MULTI-AGENT CBR SYSTEMS A Multi-Agent Case Based Reasoning System (MAC) M = {(A1, C1), ..., (An, Cn)} is a multi-agent system composed of A = {Ai, ..., An}, a set of CBR agents, where each agent Ai ∈ A possesses an individual case base Ci.
Each individual agent Ai in a MAC is completely autonomous and each agent Ai has access only to its individual and private case base Ci.
A case base Ci = {c1, ..., cm} is a collection of cases.
Agents in a MAC system are able to individually solve problems, but they can also collaborate with other agents to solve problems.
In this framework, we will restrict ourselves to analytical tasks, i.e. tasks like classification, where the solution of a problem is achieved by selecting a solution class from an enumerated set of solution classes.
In the following we will note the set of all the solution classes by S = {S1, ..., SK }.
Therefore, a case c = P, S is a tuple containing a case description P and a solution class S ∈ S.
In the following, we will use the terms problem and case description indistinctly.
Moreover, we will use the dot notation to refer to elements inside a tuple; e.g., to refer to the solution class of a case c, we will write c.S. Therefore, we say a group of agents perform joint deliberation, when they collaborate to find a joint solution by means of an argumentation process.
However, in order to do so, an agent has to be able to justify its prediction to the other agents (i.e. generate an argument for its predicted solution that can be examined and critiqued by the other agents).
The next section addresses this issue.
3.1 Justified Predictions Both expert systems and CBR systems may have an explanation component [14] in charge of justifying why the system has provided a specific answer to the user.
The line of reasoning of the system can then be examined by a human expert, thus increasing the reliability of the system.
Most of the existing work on explanation generation focuses on generating explanations to be provided to the user.
However, in our approach we use explanations (or justifications) as a tool for improving communication and coordination among agents.
We are interested in justifications since they can be used as arguments.
For that purpose, we will benefit from the ability of some machine learning methods to provide justifications.
A justification built by a CBR method after determining that the solution of a particular problem P was Sk is a description that contains the relevant information from the problem P that the CBR method has considered to predict Sk as the solution of P.
In particular, CBR methods work by retrieving similar cases to the problem at hand, and then reusing their solutions for the current problem, expecting that since the problem and the cases are similar, the solutions will also be similar.
Thus, if a CBR method has retrieved a set of cases C1, ..., Cn to solve a particular problem P the justification built will contain the relevant information from the problem P that made the CBR system retrieve that particular set of cases, i.e. it will contain the relevant information that P and C1, ..., Cn have in common.
For example, Figure 1 shows a justification build by a CBR system for a toy problem (in the following sections we will show justifications for real problems).
In the figure, a problem has two attributes (Traffic_light, and Cars_passing), the retrieval mechanism of the CBR system notices that by considering only the attribute Traffic_light, it can retrieve two cases that predict the same solution: wait.
Thus, since only this attribute has been used, it is the only one appearing in the justification.
The values of the rest of attributes are irrelevant, since whatever their value the solution class would have been the same.
976 The Sixth Intl..
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on Autonomous Agents and Multi-Agent Systems (AAMAS 07) Problem Traffic_light: red Cars_passing: no Case 1 Traffic_light: red Cars_passing: no Solution: wait Case 3 Traffic_light: red Cars_passing: yes Solution: wait Case 4 Traffic_light: green Cars_passing: yes Solution: wait Case 2 Traffic_light: green Cars_passing: no Solution: cross Retrieved cases Solution: wait Justification Traffic_light: red Figure 1: An example of justification generation in a CBR system.
Notice that, since the only relevant feature to decide is Traffic_light (the only one used to retrieve cases), it is the only one appearing in the justification.
In general, the meaning of a justification is that all (or most of) the cases in the case base of an agent that satisfy the justification (i.e. all the cases that are subsumed by the justification) belong to the predicted solution class.
In the rest of the paper, we will use to denote the subsumption relation.
In our work, we use LID [2], a CBR method capable of building symbolic justifications such as the one exemplified in Figure 1.
When an agent provides a justification for a prediction, the agent generates a justified prediction: DEFINITION 3.1.
A Justified Prediction is a tuple J = A, P, S, D where agent A considers S the correct solution for problem P, and that prediction is justified a symbolic description D such that J.D J.P. Justifications can have many uses for CBR systems [8, 9].
In this paper, we are going to use justifications as arguments, in order to allow learning agents to engage in argumentation processes.
4.
ARGUMENTS AND COUNTERARGUMENTS For our purposes an argument α generated by an agent A is composed of a statement S and some evidence D supporting S as correct.
In the remainder of this section we will see how this general definition of argument can be instantiated in specific kind of arguments that the agents can generate.
In the context of MAC systems, agents argue about predictions for new problems and can provide two kinds of information: a) specific cases P, S , and b) justified predictions: A, P, S, D .
Using this information, we can define three types of arguments: justified predictions, counterarguments, and counterexamples.
A justified prediction α is generated by an agent Ai to argue that Ai believes that the correct solution for a given problem P is α.S, and the evidence provided is the justification α.D.
In the example depicted in Figure 1, an agent Ai may generate the argument α = Ai, P, Wait, (Traffic_light = red) , meaning that the agent Ai believes that the correct solution for P is Wait because the attribute Traffic_light equals red.
A counterargument β is an argument offered in opposition to another argument α.
In our framework, a counterargument consists of a justified prediction Aj, P, S , D generated by an agent Aj with the intention to rebut an argument α generated by another agent Ai, that endorses a solution class S different from that of α.S for the problem at hand and justifies this with a justification D .
In the example in Figure 1, if an agent generates the argument α = Ai, P, Walk, (Cars_passing = no) , an agent that thinks that the correct solution is Wait might answer with the counterargument β = Aj, P, Wait, (Cars_passing = no ∧ Traffic_light = red) , meaning that, although there are no cars passing, the traffic light is red, and the street cannot be crossed.
A counterexample c is a case that contradicts an argument α.
Thus a counterexample is also a counterargument, one that states that a specific argument α is not always true, and the evidence provided is the case c. Specifically, for a case c to be a counterexample of an argument α, the following conditions have to be met: α.D c and α.S = c.S, i.e. the case must satisfy the justification α.D and the solution of c must be different than the predicted by α.
By exchanging arguments and counterarguments (including counterexamples), agents can argue about the correct solution of a given problem, i.e. they can engage a joint deliberation process.
However, in order to do so, they need a specific interaction protocol, a preference relation between contradicting arguments, and a decision policy to generate counterarguments (including counterexamples).
In the following sections we will present these elements.
5.
PREFERENCE RELATION A specific argument provided by an agent might not be consistent with the information known to other agents (or even to some of the information known by the agent that has generated the justification due to noise in training data).
For that reason, we are going to define a preference relation over contradicting justified predictions based on cases.
Basically, we will define a confidence measure for each justified prediction (that takes into account the cases owned by each agent), and the justified prediction with the highest confidence will be the preferred one.
The idea behind case-based confidence is to count how many of the cases in an individual case base endorse a justified prediction, and how many of them are counterexamples of it.
The more the endorsing cases, the higher the confidence; and the more the counterexamples, the lower the confidence.
Specifically, to assess the confidence of a justified prediction α, an agent obtains the set of cases in its individual case base that are subsumed by α.D.
With them, an agent Ai obtains the Y (aye) and N (nay) values: • Y Ai α = |{c ∈ Ci| α.D c.P ∧ α.S = c.S}| is the number of cases in the agent``s case base subsumed by the justification α.D that belong to the solution class α.S, • NAi α = |{c ∈ Ci| α.D c.P ∧ α.S = c.S}| is the number of cases in the agent``s case base subsumed by justification α.D that do not belong to that solution class.
The Sixth Intl..
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on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 977 + + + + + + - - + Figure 2: Confidence of arguments is evaluated by contrasting them against the case bases of the agents.
An agent estimates the confidence of an argument as: CAi (α) = Y Ai α 1 + Y Ai α + NAi α i.e. the confidence on a justified prediction is the number of endorsing cases divided by the number of endorsing cases plus counterexamples.
Notice that we add 1 to the denominator, this is to avoid giving excessively high confidences to justified predictions whose confidence has been computed using a small number of cases.
Notice that this correction follows the same idea than the Laplace correction to estimate probabilities.
Figure 2 illustrates the individual evaluation of the confidence of an argument, in particular, three endorsing cases and one counterexample are found in the case base of agents Ai, giving an estimated confidence of 0.6 Moreover, we can also define the joint confidence of an argument α as the confidence computed using the cases present in the case bases of all the agents in the group: C(α) = i Y Ai α 1 + i Y Ai α + NAi α Notice that, to collaboratively compute the joint confidence, the agents only have to make public the aye and nay values locally computed for a given argument.
In our framework, agents use this joint confidence as the preference relation: a justified prediction α is preferred over another one β if C(α) ≥ C(β).
6.
GENERATION OF ARGUMENTS In our framework, arguments are generated by the agents from cases, using learning methods.
Any learning method able to provide a justified prediction can be used to generate arguments.
For instance, decision trees and LID [2] are suitable learning methods.
Specifically, in the experiments reported in this paper agents use LID.
Thus, when an agent wants to generate an argument endorsing that a specific solution class is the correct solution for a problem P, it generates a justified prediction as explained in Section 3.1.
For instance, Figure 3 shows a real justification generated by LID after solving a problem P in the domain of marine sponges identification.
In particular, Figure 3 shows how when an agent receives a new problem to solve (in this case, a new sponge to determine its order), the agent uses LID to generate an argument (consisting on a justified prediction) using the cases in the case base of the agent.
The justification shown in Figure 3 can be interpreted saying that the predicted solution is hadromerida because the smooth form of the megascleres of the spiculate skeleton of the sponge is of type tylostyle, the spikulate skeleton of the sponge has no uniform length, and there is no gemmules in the external features of the sponge.
Thus, the argument generated will be α = A1, P, hadromerida, D1 .
6.1 Generation of Counterarguments As previously stated, agents may try to rebut arguments by generating counterargument or by finding counterexamples.
Let us explain how they can be generated.
An agent Ai wants to generate a counterargument β to rebut an argument α when α is in contradiction with the local case base of Ai.
Moreover, while generating such counterargument β, Ai expects that β is preferred over α.
For that purpose, we will present a specific policy to generate counterarguments based on the specificity criterion [10].
The specificity criterion is widely used in deductive frameworks for argumentation, and states that between two conflicting arguments, the most specific should be preferred since it is, in principle, more informed.
Thus, counterarguments generated based on the specificity criterion are expected to be preferable (since they are more informed) to the arguments they try to rebut.
However, there is no guarantee that such counterarguments will always win, since, as we have stated in Section 5, agents in our framework use a preference relation based on joint confidence.
Moreover, one may think that it would be better that the agents generate counterarguments based on the joint confidence preference relation; however it is not obvious how to generate counterarguments based on joint confidence in an efficient way, since collaboration is required in order to evaluate joint confidence.
Thus, the agent generating the counterargument should constantly communicate with the other agents at each step of the induction algorithm used to generate counterarguments (presently one of our future research lines).
Thus, in our framework, when an agent wants to generate a counterargument β to an argument α, β has to be more specific than α (i.e. α.D < β.D).
The generation of counterarguments using the specificity criterion imposes some restrictions over the learning method, although LID or ID3 can be easily adapted for this task.
For instance, LID is an algorithm that generates a description starting from scratch and heuristically adding features to that term.
Thus, at every step, the description is made more specific than in the previous step, and the number of cases that are subsumed by that description is reduced.
When the description covers only (or almost only) cases of a single solution class LID terminates and predicts that solution class.
To generate a counterargument to an argument α LID just has to use as starting point the description α.D instead of starting from scratch.
In this way, the justification provided by LID will always be subsumed by α.D, and thus the resulting counterargument will be more specific than α.
However, notice that LID may sometimes not be able to generate counterarguments, since LID may not be able to specialize the description α.D any further, or because the agent Ai has no case inCi that is subsumed by α.D.
Figure 4 shows how an agent A2 that disagreed with the argument shown in Figure 3, generates a counterargument using LID.
Moreover, Figure 4 shows the generation of a counterargument β1 2 for the argument α0 1 (in Figure 3) that is a specialization of α0 1.
978 The Sixth Intl..
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on Autonomous Agents and Multi-Agent Systems (AAMAS 07) Solution: hadromerida Justification: D1 Sponge Spikulate skeleton External features External features Gemmules: no Spikulate Skeleton Megascleres Uniform length: no Megascleres Smooth form: tylostyle Case Base of A1 LID New sponge P Figure 3: Example of a real justification generated by LID in the marine sponges data set.
Specifically, in our experiments, when an agent Ai wants to rebut an argument α, uses the following policy: 1.
Agent Ai uses LID to try to find a counterargument β more specific than α; if found, β is sent to the other agent as a counterargument of α.
2.
If not found, then Ai searches for a counterexample c ∈ Ci of α.
If a case c is found, then c is sent to the other agent as a counterexample of α.
3.
If no counterexamples are found, then Ai cannot rebut the argument α.
7.
ARGUMENTATION-BASED MULTI-AGENT LEARNING The interaction protocol of AMAL allows a group of agents A1, ..., An to deliberate about the correct solution of a problem P by means of an argumentation process.
If the argumentation process arrives to a consensual solution, the joint deliberation ends; otherwise a weighted vote is used to determine the joint solution.
Moreover, AMAL also allows the agents to learn from the counterexamples received from other agents.
The AMAL protocol consists on a series of rounds.
In the initial round, each agent states which is its individual prediction for P. Then, at each round an agent can try to rebut the prediction made by any of the other agents.
The protocol uses a token passing mechanism so that agents (one at a time) can send counterarguments or counterexamples if they disagree with the prediction made by any other agent.
Specifically, each agent is allowed to send one counterargument or counterexample each time he gets the token (notice that this restriction is just to simplify the protocol, and that it does not restrict the number of counterargument an agent can sent, since they can be delayed for subsequent rounds).
When an agent receives a counterargument or counterexample, it informs the other agents if it accepts the counterargument (and changes its prediction) or not.
Moreover, agents have also the opportunity to answer to counterarguments when they receive the token, by trying to generate a counterargument to the counterargument.
When all the agents have had the token once, the token returns to the first agent, and so on.
If at any time in the protocol, all the agents agree or during the last n rounds no agent has generated any counterargument, the protocol ends.
Moreover, if at the end of the argumentation the agents have not reached an agreement, then a voting mechanism that uses the confidence of each prediction as weights is used to decide the final solution (Thus, AMAL follows the same mechanism as human committees, first each individual member of a committee exposes his arguments and discuses those of the other members (joint deliberation), and if no consensus is reached, then a voting mechanism is required).
At each iteration, agents can use the following performatives: • assert(α): the justified prediction held during the next round will be α.
An agent can only hold a single prediction at each round, thus is multiple asserts are send, only the last one is considered as the currently held prediction.
• rebut(β, α): the agent has found a counterargument β to the prediction α.
We will define Ht = αt 1, ..., αt n as the predictions that each of the n agents hold at a round t. Moreover, we will also define contradict(αt i) = {α ∈ Ht|α.S = αt i.S} as the set of contradicting arguments for an agent Ai in a round t, i.e. the set of arguments at round t that support a different solution class than αt i.
The protocol is initiated because one of the agents receives a problem P to be solved.
After that, the agent informs all the other agents about the problem P to solve, and the protocol starts: 1.
At round t = 0, each one of the agents individually solves P, and builds a justified prediction using its own CBR method.
Then, each agent Ai sends the performative assert(α0 i ) to the other agents.
Thus, the agents know H0 = α0 i , ..., α0 n .
Once all the predictions have been sent the token is given to the first agent A1.
2.
At each round t (other than 0), the agents check whether their arguments in Ht agree.
If they do, the protocol moves to step 5.
Moreover, if during the last n rounds no agent has sent any counterexample or counterargument, the protocol also moves to step 5.
Otherwise, the agent Ai owner of the token tries to generate a counterargument for each of the opposing arguments in contradict(αt i) ⊆ Ht (see Section 6.1).
Then, the counterargument βt i against the prediction αt j with the lowest confidence C(αt j) is selected (since αt j is the prediction more likely to be successfully rebutted).
• If βt i is a counterargument, then, Ai locally compares αt i with βt i by assessing their confidence against its individual case base Ci (see Section 5) (notice that Ai is comparing its previous argument with the counterargument that Ai itself has just generated and that is about The Sixth Intl..
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on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 979 Sponge Spikulate skeleton External features External features Gemmules: no Growing: Spikulate Skeleton Megascleres Uniform length: no Megascleres Smooth form: tylostyle Growing Grow: massive Case Base of A2 LID Solution: astrophorida Justification: D2 Figure 4: Generation of a counterargument using LID in the sponges data set.
to send to Aj).
If CAi (βt i ) > CAi (αt i), then Ai considers that βt i is stronger than its previous argument, changes its argument to βt i by sending assert(βt i ) to the rest of the agents (the intuition behind this is that since a counterargument is also an argument, Ai checks if the newly counterargument is a better argument than the one he was previously holding) and rebut(βt i , αt j) to Aj.
Otherwise (i.e. CAi (βt i ) ≤ CAi (αt i)), Ai will send only rebut(βt i , αt j) to Aj.
In any of the two situations the protocol moves to step 3.
• If βt i is a counterexample c, then Ai sends rebut(c, αt j) to Aj.
The protocol moves to step 4.
• If Ai cannot generate any counterargument or counterexample, the token is sent to the next agent, a new round t + 1 starts, and the protocol moves to state 2.
3.
The agent Aj that has received the counterargument βt i , locally compares it against its own argument, αt j, by locally assessing their confidence.
If CAj (βt i ) > CAj (αt j), then Aj will accept the counterargument as stronger than its own argument, and it will send assert(βt i ) to the other agents.
Otherwise (i.e. CAj (βt i ) ≤ CAj (αt j)), Aj will not accept the counterargument, and will inform the other agents accordingly.
Any of the two situations start a new round t + 1, Ai sends the token to the next agent, and the protocol moves back to state 2.
4.
The agent Aj that has received the counterexample c retains it into its case base and generates a new argument αt+1 j that takes into account c, and informs the rest of the agents by sending assert(αt+1 j ) to all of them.
Then, Ai sends the token to the next agent, a new round t + 1 starts, and the protocol moves back to step 2.
5.
The protocol ends yielding a joint prediction, as follows: if the arguments in Ht agree then their prediction is the joint prediction, otherwise a voting mechanism is used to decide the joint prediction.
The voting mechanism uses the joint confidence measure as the voting weights, as follows: S = arg max Sk∈S αi∈Ht|αi.S=Sk C(αi) Moreover, in order to avoid infinite iterations, if an agent sends twice the same argument or counterargument to the same agent, the message is not considered.
8.
EXEMPLIFICATION Let us consider a system composed of three agents A1, A2 and A3.
One of the agents, A1 receives a problem P to solve, and decides to use AMAL to solve it.
For that reason, invites A2 and A3 to take part in the argumentation process.
They accept the invitation, and the argumentation protocol starts.
Initially, each agent generates its individual prediction for P, and broadcasts it to the other agents.
Thus, all of them can compute H0 = α0 1, α0 2, α0 3 .
In particular, in this example: • α0 1 = A1, P, hadromerida, D1 • α0 2 = A2, P, astrophorida, D2 • α0 3 = A3, P, axinellida, D3 A1 starts owning the token and tries to generate counterarguments for α0 2 and α0 3, but does not succeed, however it has one counterexample c13 for α0 3.
Thus, A1 sends the the message rebut( c13, α0 3) to A3.
A3 incorporates c13 into its case base and tries to solve the problem P again, now taking c13 into consideration.
A3 comes up with the justified prediction α1 3 = A3, P, hadromerida, D4 , and broadcasts it to the rest of the agents with the message assert(α1 3).
Thus, all of them know the new H1 = α0 1, α0 2, α1 3 .
Round 1 starts and A2 gets the token.
A2 tries to generate counterarguments for α0 1 and α1 3 and only succeeds to generate a counterargument β1 2 = A2, P, astrophorida, D5 against α1 3.
The counterargument is sent to A3 with the message rebut(β1 2 , α1 3).
Agent A3 receives the counterargument and assesses its local confidence.
The result is that the individual confidence of the counterargument β1 2 is lower than the local confidence of α1 3.
Therefore, A3 does not accept the counterargument, and thus H2 = α0 1, α0 2, α1 3 .
Round 2 starts and A3 gets the token.
A3 generates a counterargument β2 3 = A3, P, hadromerida, D6 for α0 2 and sends it to A2 with the message rebut(β2 3 , α0 2).
Agent A2 receives the counterargument and assesses its local confidence.
The result is that the local confidence of the counterargument β2 3 is higher than the local confidence of α0 2.
Therefore, A2 accepts the counterargument and informs the rest of the agents with the message assert(β2 3 ).
After that, H3 = α0 1, β2 3 , α1 3 .
At Round 3, since all the agents agree (all the justified predictions in H3 predict hadromerida as the solution class) The protocol ends, and A1 (the agent that received the problem) considers hadromerida as the joint solution for the problem P. 9.
EXPERIMENTAL EVALUATION 980 The Sixth Intl..
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on Autonomous Agents and Multi-Agent Systems (AAMAS 07) SPONGE 75 77 79 81 83 85 87 89 91 2 3 4 5 AMAL Voting Individual SOYBEAN 55 60 65 70 75 80 85 90 2 3 4 5 AMAL Voting Individual Figure 5: Individual and joint accuracy for 2 to 5 agents.
In this section we empirically evaluate the AMAL argumentation framework.
We have made experiments in two different data sets: soybean (from the UCI machine learning repository) and sponge (a relational data set).
The soybean data set has 307 examples and 19 solution classes, while the sponge data set has 280 examples and 3 solution classes.
In an experimental run, the data set is divided in 2 sets: the training set and the test set.
The training set examples are distributed among 5 different agents without replication, i.e. there is no example shared by two agents.
In the testing stage, problems in the test set arrive randomly to one of the agents, and their goal is to predict the correct solution.
The experiments are designed to test two hypotheses: (H1) that argumentation is a useful framework for joint deliberation and can improve over other typical methods such as voting; and (H2) that learning from communication improves the individual performance of a learning agent participating in an argumentation process.
Moreover, we also expect that the improvement achieved from argumentation will increase as the number of agents participating in the argumentation increases (since more information will be taken into account).
Concerning H1 (argumentation is a useful framework for joint deliberation), we ran 4 experiments, using 2, 3, 4, and 5 agents respectively (in all experiments each agent has a 20% of the training data, since the training is always distributed among 5 agents).
Figure 5 shows the result of those experiments in the sponge and soybean data sets.
Classification accuracy is plotted in the vertical axis, and in the horizontal axis the number of agents that took part in the argumentation processes is shown.
For each number of agents, three bars are shown: individual, Voting, and AMAL.
The individual bar shows the average accuracy of individual agents predictions; the voting bar shows the average accuracy of the joint prediction achieved by voting but without any argumentation; and finally the AMAL bar shows the average accuracy of the joint prediction using argumentation.
The results shown are the average of 5 10-fold cross validation runs.
Figure 5 shows that collaboration (voting and AMAL) outperforms individual problem solving.
Moreover, as we expected, the accuracy improves as more agents collaborate, since more information is taken into account.
We can also see that AMAL always outperforms standard voting, proving that joint decisions are based on better information as provided by the argumentation process.
For instance, the joint accuracy for 2 agents in the sponge data set is of 87.57% for AMAL and 86.57% for voting (while individual accuracy is just 80.07%).
Moreover, the improvement achieved by AMAL over Voting is even larger in the soybean data set.
The reason is that the soybean data set is more difficult (in the sense that agents need more data to produce good predictions).
These experimental results show that AMAL effectively exploits the opportunity for improvement: the accuracy is higher only because more agents have changed their opinion during argumentation (otherwise they would achieve the same result as Voting).
Concerning H2 (learning from communication in argumentation processes improves individual prediction ), we ran the following experiment: initially, we distributed a 25% of the training set among the five agents; after that, the rest of the cases in the training set is sent to the agents one by one; when an agent receives a new training case, it has several options: the agent can discard it, the agent can retain it, or the agent can use it for engaging an argumentation process.
Figure 6 shows the result of that experiment for the two data sets.
Figure 6 contains three plots, where NL (not learning) shows accuracy of an agent with no learning at all; L (learning), shows the evolution of the individual classification accuracy when agents learn by retaining the training cases they individually receive (notice that when all the training cases have been retained at 100%, the accuracy should be equal to that of Figure 5 for individual agents); and finally LFC (learning from communication) shows the evolution of the individual classification accuracy of learning agents that also learn by retaining those counterexamples received during argumentation (i.e. they learn both from training examples and counterexamples).
Figure 6 shows that if an agent Ai learns also from communication, Ai can significantly improve its individual performance with just a small number of additional cases (those selected as relevant counterexamples for Ai during argumentation).
For instance, in the soybean data set, individual agents have achieved an accuracy of 70.62% when they also learn from communication versus an accuracy of 59.93% when they only learn from their individual experience.
The number of cases learnt from communication depends on the properties of the data set: in the sponges data set, agents have retained only very few additional cases, and significantly improved individual accuracy; namely they retain 59.96 cases in average (compared to the 50.4 cases retained if they do not learn from communication).
In the soybean data set more counterexamples are learnt to significantly improve individual accuracy, namely they retain 87.16 cases in average (compared to 55.27 cases retained if they do not learn from communication).
Finally, the fact that both data sets show a significant improvement points out the adaptive nature of the argumentation-based approach to learning from communication: the useful cases are selected as counterexamples (and no more than those needed), and they have the intended effect.
10.
RELATED WORK Concerning CBR in a multi-agent setting, the first research was on negotiated case retrieval [11] among groups of agents.
Our work on multi-agent case-based learning started in 1999 [6]; later Mc Ginty and Smyth [7] presented a multi-agent collaborative CBR approach (CCBR) for planning.
Finally, another interesting approach is multi-case-base reasoning (MCBR) [5], that deals with The Sixth Intl..
Joint Conf.
on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 981 SPONGE 60 65 70 75 80 85 25% 40% 55% 70% 85% 100% LFC L NL SOYBEAN 20 30 40 50 60 70 80 90 25% 40% 55% 70% 85% 100% LFC L NL Figure 6: Learning from communication resulting from argumentation in a system composed of 5 agents.
distributed systems where there are several case bases available for the same task and addresses the problems of cross-case base adaptation.
The main difference is that our MAC approach is a way to distribute the Reuse process of CBR (using a voting system) while Retrieve is performed individually by each agent; the other multiagent CBR approaches, however, focus on distributing the Retrieve process.
Research on MAS argumentation focus on several issues like a) logics, protocols and languages that support argumentation, b) argument selection and c) argument interpretation.
Approaches for logic and languages that support argumentation include defeasible logic [4] and BDI models [13].
Although argument selection is a key aspect of automated argumentation (see [12] and [13]), most research has been focused on preference relations among arguments.
In our framework we have addressed both argument selection and preference relations using a case-based approach.
11.
CONCLUSIONS AND FUTURE WORK In this paper we have presented an argumentation-based framework for multi-agent learning.
Specifically, we have presented AMAL, a framework that allows a group of learning agents to argue about the solution of a given problem and we have shown how the learning capabilities can be used to generate arguments and counterarguments.
The experimental evaluation shows that the increased amount of information provided to the agents by the argumentation process increases their predictive accuracy, and specially when an adequate number of agents take part in the argumentation.
The main contributions of this work are: a) an argumentation framework for learning agents; b) a case-based preference relation over arguments, based on computing an overall confidence estimation of arguments; c) a case-based policy to generate counterarguments and select counterexamples; and d) an argumentation-based approach for learning from communication.
Finally, in the experiments presented here a learning agent would retain all counterexamples submitted by the other agent; however, this is a very simple case retention policy, and we will like to experiment with more informed policies - with the goal that individual learning agents could significantly improve using only a small set of cases proposed by other agents.
Finally, our approach is focused on lazy learning, and future works aims at incorporating eager inductive learning inside the argumentative framework for learning from communication.
12.
REFERENCES [1] Agnar Aamodt and Enric Plaza.
Case-based reasoning: Foundational issues, methodological variations, and system approaches.
Artificial Intelligence Communications, 7(1):39-59, 1994.
[2] E. Armengol and E. Plaza.
Lazy induction of descriptions for relational case-based learning.
In ECML``2001, pages 13-24, 2001.
[3] Gerhard Brewka.
Dynamic argument systems: A formal model of argumentation processes based on situation calculus.
Journal of Logic and Computation, 11(2):257-282, 2001.
[4] Carlos I. Chesñevar and Guillermo R. Simari.
Formalizing Defeasible Argumentation using Labelled Deductive Systems.
Journal of Computer Science & Technology, 1(4):18-33, 2000.
[5] D. Leake and R. Sooriamurthi.
Automatically selecting strategies for multi-case-base reasoning.
In S. Craw and A. Preece, editors, ECCBR``2002, pages 204-219, Berlin, 2002.
Springer Verlag.
[6] Francisco J. Martín, Enric Plaza, and Josep-Lluis Arcos.
Knowledge and experience reuse through communications among competent (peer) agents.
International Journal of Software Engineering and Knowledge Engineering, 9(3):319-341, 1999.
[7] Lorraine McGinty and Barry Smyth.
Collaborative case-based reasoning: Applications in personalized route planning.
In I. Watson and Q. Yang, editors, ICCBR, number 2080 in LNAI, pages 362-376.
Springer-Verlag, 2001.
[8] Santi Ontañón and Enric Plaza.
Justification-based multiagent learning.
In ICML``2003, pages 576-583.
Morgan Kaufmann, 2003.
[9] Enric Plaza, Eva Armengol, and Santiago Ontañón.
The explanatory power of symbolic similarity in case-based reasoning.
Artificial Intelligence Review, 24(2):145-161, 2005.
[10] David Poole.
On the comparison of theories: Preferring the most specific explanation.
In IJCAI-85, pages 144-147, 1985.
[11] M V Nagendra Prassad, Victor R Lesser, and Susan Lander.
Retrieval and reasoning in distributed case bases.
Technical report, UMass Computer Science Department, 1995.
[12] K. Sycara S. Kraus and A. Evenchik.
Reaching agreements through argumentation: a logical model and implementation.
Artificial Intelligence Journal, 104:1-69, 1998.
[13] N. R. Jennings S. Parsons, C. Sierra.
Agents that reason and negotiate by arguing.
Journal of Logic and Computation, 8:261-292, 1998.
[14] Bruce A. Wooley.
Explanation component of software systems.
ACM CrossRoads, 5.1, 1998.
982 The Sixth Intl..
Joint Conf.
on Autonomous Agents and Multi-Agent Systems (AAMAS 07)

Learning and Joint Deliberation through Argumentation in Multi-Agent Systems
ABSTRACT
In this paper we will present an argumentation framework for learning agents (AMAL) designed for two purposes: (1) for joint deliberation, and (2) for learning from communication.
The AMAL framework is completely based on learning from examples: the argument preference relation, the argument generation policy, and the counterargument generation policy are case-based techniques.
For join deliberation, learning agents share their experience by forming a committee to decide upon some joint decision.
We experimentally show that the argumentation among committees of agents improves both the individual and joint performance.
For learning from communication, an agent engages into arguing with other agents in order to contrast its individual hypotheses and receive counterexamples; the argumentation process improves their learning scope and individual performance.
1.
INTRODUCTION
Argumentation frameworks for multi-agent systems can be used for different purposes like joint deliberation, persuasion, negotiation, and conflict resolution.
In this paper we will present an argumentation framework for learning agents, and show that it can be used for two purposes: (1) joint deliberation, and (2) learning from communication.
Argumentation-based joint deliberation involves discussion over the outcome of a particular situation or the appropriate course of action for a particular situation.
Learning agents are capable of learning from experience, in the sense that past examples (situations and their outcomes) are used to predict the outcome for the situation
at hand.
However, since individual agents experience may be limited, individual knowledge and prediction accuracy is also limited.
Thus, learning agents that are capable of arguing their individual predictions with other agents may reach better prediction accuracy after such an argumentation process.
Most existing argumentation frameworks for multi-agent systems are based on deductive logic or some other deductive logic formalism specifically designed to support argumentation, such as default logic [3]).
Usually, an argument is seen as a logical statement, while a counterargument is an argument offered in opposition to another argument [4, 13]; agents use a preference relation to resolve conflicting arguments.
However, logic-based argumentation frameworks assume agents with preloaded knowledge and preference relation.
In this paper, we focus on an Argumentation-based Multi-Agent Learning (AMAL) framework where both knowledge and preference relation are learned from experience.
Thus, we consider a scenario with agents that (1) work in the same domain using a shared ontology, (2) are capable of learning from examples, and (3) communicate using an argumentative framework.
Having learning capabilities allows agents effectively use a specific form of counterargument, namely the use of counterexamples.
Counterexamples offer the possibility of agents learning during the argumentation process.
Moreover, learning agents allow techniques that use learnt experience to generate adequate arguments and counterarguments.
Specifically, we will need to address two issues: (1) how to define a technique to generate arguments and counterarguments from examples, and (2) how to define a preference relation over two conflicting arguments that have been induced from examples.
This paper presents a case-based approach to address both issues.
The agents use case-based reasoning (CBR) [1] to learn from past cases (where a case is a situation and its outcome) in order to predict the outcome of a new situation.
We propose an argumentation protocol inside the AMAL framework at supports agents in reaching a joint prediction over a specific situation or problem--moreover, the reasoning needed to support the argumentation process will also be based on cases.
In particular, we present two case-based measures, one for generating the arguments and counterarguments adequate to a particular situation and another for determining preference relation among arguments.
Finally, we evaluate (1) if argumentation between learning agents can produce a joint prediction that improves over individual learning performance and (2) if learning from the counterexamples conveyed during the argumentation process increases the individual performance with precisely those cases being used while arguing among them.
The paper is structured as follows.
Section 2 discusses the relation among argumentation, collaboration and learning.
Then Sec
tion 3 introduces our multi-agent CBR (MAC) framework and the notion of justified prediction.
After that, Section 4 formally defines our argumentation framework.
Sections 5 and 6 present our case-based preference relation and argument generation policies respectively.
Later, Section 7 presents the argumentation protocol in our AMAL framework.
After that, Section 8 presents an exemplification of the argumentation framework.
Finally, Section 9 presents an empirical evaluation of our two main hypotheses.
The paper closes with related work and conclusions sections.
2.
ARGUMENTATION, COLLABORATION AND LEARNING
3.
MULTI-AGENT CBR SYSTEMS
3.1 Justified Predictions
976 The Sixth Intl. .
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4.
ARGUMENTS AND COUNTERARGUMENTS
5.
PREFERENCE RELATION
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Joint Conf.
on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 977
1 + Yα Ai + NAi
6.
GENERATION OF ARGUMENTS
6.1 Generation of Counterarguments
978 The Sixth Intl. .
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on Autonomous Agents and Multi-Agent Systems (AAMAS 07)
7.
ARGUMENTATION-BASED MULTI-AGENT LEARNING
The Sixth Intl. .
Joint Conf.
on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 979
8.
EXEMPLIFICATION
9.
EXPERIMENTAL EVALUATION
10.
RELATED WORK
Concerning CBR in a multi-agent setting, the first research was on "negotiated case retrieval' [11] among groups of agents.
Our work on multi-agent case-based learning started in 1999 [6]; later Mc Ginty and Smyth [7] presented a multi-agent collaborative CBR approach (CCBR) for planning.
Finally, another interesting approach is multi-case-base reasoning (MCBR) [5], that deals with
The Sixth Intl. .
Joint Conf.
on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 981
Figure 6: Learning from communication resulting from argumentation in a system composed of 5 agents.
distributed systems where there are several case bases available for the same task and addresses the problems of cross-case base adaptation.
The main difference is that our MAC approach is a way to distribute the Reuse process of CBR (using a voting system) while Retrieve is performed individually by each agent; the other multiagent CBR approaches, however, focus on distributing the Retrieve process.
Research on MAS argumentation focus on several issues like a) logics, protocols and languages that support argumentation, b) argument selection and c) argument interpretation.
Approaches for logic and languages that support argumentation include defeasible logic [4] and BDI models [13].
Although argument selection is a key aspect of automated argumentation (see [12] and [13]), most research has been focused on preference relations among arguments.
In our framework we have addressed both argument selection and preference relations using a case-based approach.
11.
CONCLUSIONS AND FUTURE WORK
In this paper we have presented an argumentation-based framework for multi-agent learning.
Specifically, we have presented AMAL, a framework that allows a group of learning agents to argue about the solution of a given problem and we have shown how the learning capabilities can be used to generate arguments and counterarguments.
The experimental evaluation shows that the increased amount of information provided to the agents by the argumentation process increases their predictive accuracy, and specially when an adequate number of agents take part in the argumentation.
The main contributions of this work are: a) an argumentation framework for learning agents; b) a case-based preference relation over arguments, based on computing an overall confidence estimation of arguments; c) a case-based policy to generate counterarguments and select counterexamples; and d) an argumentation-based approach for learning from communication.
Finally, in the experiments presented here a learning agent would retain all counterexamples submitted by the other agent; however, this is a very simple case retention policy, and we will like to experiment with more informed policies--with the goal that individual learning agents could significantly improve using only a small set of cases proposed by other agents.
Finally, our approach is focused on lazy learning, and future works aims at incorporating eager inductive learning inside the argumentative framework for learning from communication.

Learning and Joint Deliberation through Argumentation in Multi-Agent Systems
ABSTRACT
In this paper we will present an argumentation framework for learning agents (AMAL) designed for two purposes: (1) for joint deliberation, and (2) for learning from communication.
The AMAL framework is completely based on learning from examples: the argument preference relation, the argument generation policy, and the counterargument generation policy are case-based techniques.
For join deliberation, learning agents share their experience by forming a committee to decide upon some joint decision.
We experimentally show that the argumentation among committees of agents improves both the individual and joint performance.
For learning from communication, an agent engages into arguing with other agents in order to contrast its individual hypotheses and receive counterexamples; the argumentation process improves their learning scope and individual performance.
1.
INTRODUCTION
Argumentation frameworks for multi-agent systems can be used for different purposes like joint deliberation, persuasion, negotiation, and conflict resolution.
In this paper we will present an argumentation framework for learning agents, and show that it can be used for two purposes: (1) joint deliberation, and (2) learning from communication.
Learning agents are capable of learning from experience, in the sense that past examples (situations and their outcomes) are used to predict the outcome for the situation
at hand.
However, since individual agents experience may be limited, individual knowledge and prediction accuracy is also limited.
Thus, learning agents that are capable of arguing their individual predictions with other agents may reach better prediction accuracy after such an argumentation process.
Most existing argumentation frameworks for multi-agent systems are based on deductive logic or some other deductive logic formalism specifically designed to support argumentation, such as default logic [3]).
However, logic-based argumentation frameworks assume agents with preloaded knowledge and preference relation.
In this paper, we focus on an Argumentation-based Multi-Agent Learning (AMAL) framework where both knowledge and preference relation are learned from experience.
Thus, we consider a scenario with agents that (1) work in the same domain using a shared ontology, (2) are capable of learning from examples, and (3) communicate using an argumentative framework.
Having learning capabilities allows agents effectively use a specific form of counterargument, namely the use of counterexamples.
Counterexamples offer the possibility of agents learning during the argumentation process.
Moreover, learning agents allow techniques that use learnt experience to generate adequate arguments and counterarguments.
This paper presents a case-based approach to address both issues.
The agents use case-based reasoning (CBR) [1] to learn from past cases (where a case is a situation and its outcome) in order to predict the outcome of a new situation.
We propose an argumentation protocol inside the AMAL framework at supports agents in reaching a joint prediction over a specific situation or problem--moreover, the reasoning needed to support the argumentation process will also be based on cases.
In particular, we present two case-based measures, one for generating the arguments and counterarguments adequate to a particular situation and another for determining preference relation among arguments.
Finally, we evaluate (1) if argumentation between learning agents can produce a joint prediction that improves over individual learning performance and (2) if learning from the counterexamples conveyed during the argumentation process increases the individual performance with precisely those cases being used while arguing among them.
The paper is structured as follows.
Section 2 discusses the relation among argumentation, collaboration and learning.
Then Sec
tion 3 introduces our multi-agent CBR (MAC) framework and the notion of justified prediction.
After that, Section 4 formally defines our argumentation framework.
Sections 5 and 6 present our case-based preference relation and argument generation policies respectively.
Later, Section 7 presents the argumentation protocol in our AMAL framework.
After that, Section 8 presents an exemplification of the argumentation framework.
Finally, Section 9 presents an empirical evaluation of our two main hypotheses.
The paper closes with related work and conclusions sections.
10.
RELATED WORK
Concerning CBR in a multi-agent setting, the first research was on "negotiated case retrieval' [11] among groups of agents.
Our work on multi-agent case-based learning started in 1999 [6]; later Mc Ginty and Smyth [7] presented a multi-agent collaborative CBR approach (CCBR) for planning.
The Sixth Intl. .
Joint Conf.
on Autonomous Agents and Multi-Agent Systems (AAMAS 07) 981
Figure 6: Learning from communication resulting from argumentation in a system composed of 5 agents.
Research on MAS argumentation focus on several issues like a) logics, protocols and languages that support argumentation, b) argument selection and c) argument interpretation.
Approaches for logic and languages that support argumentation include defeasible logic [4] and BDI models [13].
Although argument selection is a key aspect of automated argumentation (see [12] and [13]), most research has been focused on preference relations among arguments.
In our framework we have addressed both argument selection and preference relations using a case-based approach.
11.
CONCLUSIONS AND FUTURE WORK
In this paper we have presented an argumentation-based framework for multi-agent learning.
Specifically, we have presented AMAL, a framework that allows a group of learning agents to argue about the solution of a given problem and we have shown how the learning capabilities can be used to generate arguments and counterarguments.
The main contributions of this work are: a) an argumentation framework for learning agents; b) a case-based preference relation over arguments, based on computing an overall confidence estimation of arguments; c) a case-based policy to generate counterarguments and select counterexamples; and d) an argumentation-based approach for learning from communication.
Finally, our approach is focused on lazy learning, and future works aims at incorporating eager inductive learning inside the argumentative framework for learning from communication.

Learning and Joint Deliberation through Argumentation in Multi-Agent Systems
ABSTRACT
In this paper we will present an argumentation framework for learning agents (AMAL) designed for two purposes: (1) for joint deliberation, and (2) for learning from communication.
The AMAL framework is completely based on learning from examples: the argument preference relation, the argument generation policy, and the counterargument generation policy are case-based techniques.
For join deliberation, learning agents share their experience by forming a committee to decide upon some joint decision.
We experimentally show that the argumentation among committees of agents improves both the individual and joint performance.
For learning from communication, an agent engages into arguing with other agents in order to contrast its individual hypotheses and receive counterexamples; the argumentation process improves their learning scope and individual performance.
1.
INTRODUCTION
Argumentation frameworks for multi-agent systems can be used for different purposes like joint deliberation, persuasion, negotiation, and conflict resolution.
In this paper we will present an argumentation framework for learning agents, and show that it can be used for two purposes: (1) joint deliberation, and (2) learning from communication.
Argumentation-based joint deliberation involves discussion over the outcome of a particular situation or the appropriate course of action for a particular situation.
Learning agents are capable of learning from experience, in the sense that past examples (situations and their outcomes) are used to predict the outcome for the situation
at hand.
However, since individual agents experience may be limited, individual knowledge and prediction accuracy is also limited.
Thus, learning agents that are capable of arguing their individual predictions with other agents may reach better prediction accuracy after such an argumentation process.
Most existing argumentation frameworks for multi-agent systems are based on deductive logic or some other deductive logic formalism specifically designed to support argumentation, such as default logic [3]).
Usually, an argument is seen as a logical statement, while a counterargument is an argument offered in opposition to another argument [4, 13]; agents use a preference relation to resolve conflicting arguments.
However, logic-based argumentation frameworks assume agents with preloaded knowledge and preference relation.
In this paper, we focus on an Argumentation-based Multi-Agent Learning (AMAL) framework where both knowledge and preference relation are learned from experience.
Thus, we consider a scenario with agents that (1) work in the same domain using a shared ontology, (2) are capable of learning from examples, and (3) communicate using an argumentative framework.
Having learning capabilities allows agents effectively use a specific form of counterargument, namely the use of counterexamples.
Counterexamples offer the possibility of agents learning during the argumentation process.
Moreover, learning agents allow techniques that use learnt experience to generate adequate arguments and counterarguments.
Specifically, we will need to address two issues: (1) how to define a technique to generate arguments and counterarguments from examples, and (2) how to define a preference relation over two conflicting arguments that have been induced from examples.
This paper presents a case-based approach to address both issues.
The agents use case-based reasoning (CBR) [1] to learn from past cases (where a case is a situation and its outcome) in order to predict the outcome of a new situation.
We propose an argumentation protocol inside the AMAL framework at supports agents in reaching a joint prediction over a specific situation or problem--moreover, the reasoning needed to support the argumentation process will also be based on cases.
In particular, we present two case-based measures, one for generating the arguments and counterarguments adequate to a particular situation and another for determining preference relation among arguments.
Finally, we evaluate (1) if argumentation between learning agents can produce a joint prediction that improves over individual learning performance and (2) if learning from the counterexamples conveyed during the argumentation process increases the individual performance with precisely those cases being used while arguing among them.
The paper is structured as follows.
Section 2 discusses the relation among argumentation, collaboration and learning.
Then Sec
tion 3 introduces our multi-agent CBR (MAC) framework and the notion of justified prediction.
After that, Section 4 formally defines our argumentation framework.
Sections 5 and 6 present our case-based preference relation and argument generation policies respectively.
Later, Section 7 presents the argumentation protocol in our AMAL framework.
After that, Section 8 presents an exemplification of the argumentation framework.
Finally, Section 9 presents an empirical evaluation of our two main hypotheses.
The paper closes with related work and conclusions sections.
2.
ARGUMENTATION, COLLABORATION AND LEARNING
Both learning and collaboration are ways in which an agent can improve individual performance.
In fact, there is a clear parallelism between learning and collaboration in multi-agent systems, since both are ways in which agents can deal with their shortcomings.
Let us show which are the main motivations that an agent can have to learn or to collaborate.
• Motivations to learn:--Increase quality of prediction,--Increase efficiency,--Increase the range of solvable problems.
• Motivations to collaborate:--Increase quality of prediction,--Increase efficiency,--Increase the range of solvable problems,--Increase the range of accessible resources.
Looking at the above lists of motivation, we can easily see that learning and collaboration are very related in multi-agent systems.
In fact, with the exception of the last item in the motivations to collaborate list, they are two extremes of a continuum of strategies to improve performance.
An agent may choose to increase performance by learning, by collaborating, or by finding an intermediate point that combines learning and collaboration in order to improve performance.
In this paper we will propose AMAL, an argumentation framework for learning agents, and will also also show how AMAL can be used both for learning from communication and for solving problems in a collaborative way:
• Agents can solve problems in a collaborative way via engaging an argumentation process about the prediction for the situation at hand.
Using this collaboration, the prediction can be done in a more informed way, since the information known by several agents has been taken into account.
• Agents can also learn from communication with other agents by engaging an argumentation process.
Agents that engage in such argumentation processes can learn from the argu
ments and counterexamples received from other agents, and use this information for predicting the outcomes of future situations.
In the rest of this paper we will propose an argumentation framework and show how it can be used both for learning and for solving problems in a collaborative way.
3.
MULTI-AGENT CBR SYSTEMS
A Multi-Agent Case Based Reasoning System (MAC) M = {(Al, Cl),..., (An, Cn)} is a multi-agent system composed of A = {Ai,..., An}, a set of CBR agents, where each agent Ai ∈ A possesses an individual case base Ci.
Each individual agent Ai in a MAC is completely autonomous and each agent Ai has access only to its individual and private case base Ci.
A case base Ci = {cl,..., cm} is a collection of cases.
Agents in a MAC system are able to individually solve problems, but they can also collaborate with other agents to solve problems.
In this framework, we will restrict ourselves to analytical tasks, i.e. tasks like classification, where the solution of a problem is achieved by selecting a solution class from an enumerated set of solution classes.
In the following we will note the set of all the solution classes by S = {Sl,..., SK}.
Therefore, a case c = (P, S) is a tuple containing a case description P and a solution class S ∈ S.
In the following, we will use the terms problem and case description indistinctly.
Moreover, we will use the dot notation to refer to elements inside a tuple; e.g., to refer to the solution class of a case c, we will write c.S. Therefore, we say a group of agents perform joint deliberation, when they collaborate to find a joint solution by means of an argumentation process.
However, in order to do so, an agent has to be able to justify its prediction to the other agents (i.e. generate an argument for its predicted solution that can be examined and critiqued by the other agents).
The next section addresses this issue.
3.1 Justified Predictions
Both expert systems and CBR systems may have an explanation component [14] in charge of justifying why the system has provided a specific answer to the user.
The line of reasoning of the system can then be examined by a human expert, thus increasing the reliability of the system.
Most of the existing work on explanation generation focuses on generating explanations to be provided to the user.
However, in our approach we use explanations (or justifications) as a tool for improving communication and coordination among agents.
We are interested in justifications since they can be used as arguments.
For that purpose, we will benefit from the ability of some machine learning methods to provide justifications.
A justification built by a CBR method after determining that the solution of a particular problem P was Sk is a description that contains the relevant information from the problem P that the CBR method has considered to predict Sk as the solution of P.
In particular, CBR methods work by retrieving similar cases to the problem at hand, and then reusing their solutions for the current problem, expecting that since the problem and the cases are similar, the solutions will also be similar.
Thus, if a CBR method has retrieved a set of cases Cl,..., Cn to solve a particular problem P the justification built will contain the relevant information from the problem P that made the CBR system retrieve that particular set of cases, i.e. it will contain the relevant information that P and Cl,..., Cn have in common.
For example, Figure 1 shows a justification build by a CBR system for a toy problem (in the following sections we will show justifications for real problems).
In the figure, a problem has two attributes (Traffic_light, and Cars_passing), the retrieval mechanism of the CBR system notices that by considering only the attribute Traffic_light, it can retrieve two cases that predict the same solution: wait.
Thus, since only this attribute has been used, it is the only one appearing in the justification.
The values of the rest of attributes are irrelevant, since whatever their value the solution class would have been the same.
976 The Sixth Intl. .
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Figure 1: An example of justification generation in a CBR system.
Notice that, since the only relevant feature to decide is Traffic_light (the only one used to retrieve cases), it is the only one appearing in the justification.
In general, the meaning of a justification is that all (or most of) the cases in the case base of an agent that satisfy the justification (i.e. all the cases that are subsumed by the justification) belong to the predicted solution class.
In the rest of the paper, we will use C to denote the subsumption relation.
In our work, we use LID [2], a CBR method capable of building symbolic justifications such as the one exemplified in Figure 1.
When an agent provides a justification for a prediction, the agent generates a justified prediction:
Justifications can have many uses for CBR systems [8, 9].
In this paper, we are going to use justifications as arguments, in order to allow learning agents to engage in argumentation processes.
4.
ARGUMENTS AND COUNTERARGUMENTS
For our purposes an argument α generated by an agent A is composed of a statement S and some evidence D supporting S as correct.
In the remainder of this section we will see how this general definition of argument can be instantiated in specific kind of arguments that the agents can generate.
In the context of MAC systems, agents argue about predictions for new problems and can provide two kinds of information: a) specific cases (P, S), and b) justified predictions: (A, P, S, D).
Using this information, we can define three types of arguments: justified predictions, counterarguments, and counterexamples.
A justified prediction α is generated by an agent Ai to argue that Ai believes that the correct solution for a given problem P is α.S, and the evidence provided is the justification α.D.
In the example depicted in Figure 1, an agent Ai may generate the argument α = (Ai, P, Wait, (Traffic-light = red)), meaning that the agent Ai believes that the correct solution for P is Wait because the attribute Traffic-light equals red.
A counterargument β is an argument offered in opposition to another argument α.
In our framework, a counterargument consists of a justified prediction (Aj, P, S', D') generated by an agent Aj with the intention to rebut an argument α generated by another agent Ai, that endorses a solution class S' different from that of α.S for the problem at hand and justifies this with a justification D'.
In the example in Figure 1, if an agent generates the argument α = (Ai, P, Walk, (Cars-passing = no)), an agent that thinks that the correct solution is Wait might answer with the counterargument β = (Aj, P, Wait, (Cars-passing = no n Traffic-light = red)), meaning that, although there are no cars passing, the traffic light is red, and the street cannot be crossed.
A counterexample c is a case that contradicts an argument α.
Thus a counterexample is also a counterargument, one that states that a specific argument α is not always true, and the evidence provided is the case c. Specifically, for a case c to be a counterexample of an argument α, the following conditions have to be met: α.D C c and α.S = ~ c.S, i.e. the case must satisfy the justification α.D and the solution of c must be different than the predicted by α.
By exchanging arguments and counterarguments (including counterexamples), agents can argue about the correct solution of a given problem, i.e. they can engage a joint deliberation process.
However, in order to do so, they need a specific interaction protocol, a preference relation between contradicting arguments, and a decision policy to generate counterarguments (including counterexamples).
In the following sections we will present these elements.
5.
PREFERENCE RELATION
A specific argument provided by an agent might not be consistent with the information known to other agents (or even to some of the information known by the agent that has generated the justification due to noise in training data).
For that reason, we are going to define a preference relation over contradicting justified predictions based on cases.
Basically, we will define a confidence measure for each justified prediction (that takes into account the cases owned by each agent), and the justified prediction with the highest confidence will be the preferred one.
The idea behind case-based confidence is to count how many of the cases in an individual case base endorse a justified prediction, and how many of them are counterexamples of it.
The more the endorsing cases, the higher the confidence; and the more the counterexamples, the lower the confidence.
Specifically, to assess the confidence of a justified prediction α, an agent obtains the set of cases in its individual case base that are subsumed by α.D.
With them, an agent Ai obtains the Y (aye) and N (nay) values:
• Y Ai α = I1c E CiI α.D C c.P n α.S = c.S} I is the number of cases in the agent's case base subsumed by the justification α.D that belong to the solution class α.S, • NAi
α = I1c E CiI α.D C c.P n α.S = ~ c.S} I is the number of cases in the agent's case base subsumed by justification α.D that do not belong to that solution class.
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Figure 2: Confidence of arguments is evaluated by contrasting them against the case bases of the agents.
An agent estimates the confidence of an argument as:
1 + Yα Ai + NAi
α i.e. the confidence on a justified prediction is the number of endorsing cases divided by the number of endorsing cases plus counterexamples.
Notice that we add 1 to the denominator, this is to avoid giving excessively high confidences to justified predictions whose confidence has been computed using a small number of cases.
Notice that this correction follows the same idea than the Laplace correction to estimate probabilities.
Figure 2 illustrates the individual evaluation of the confidence of an argument, in particular, three endorsing cases and one counterexample are found in the case base of agents Ai, giving an estimated confidence of 0.6 Moreover, we can also define the joint confidence of an argument α as the confidence computed using the cases present in the case bases of all the agents in the group:
Notice that, to collaboratively compute the joint confidence, the agents only have to make public the aye and nay values locally computed for a given argument.
In our framework, agents use this joint confidence as the preference relation: a justified prediction α is preferred over another one,3 if C (α) ≥ C (,3).
6.
GENERATION OF ARGUMENTS
In our framework, arguments are generated by the agents from cases, using learning methods.
Any learning method able to provide a justified prediction can be used to generate arguments.
For instance, decision trees and LID [2] are suitable learning methods.
Specifically, in the experiments reported in this paper agents use LID.
Thus, when an agent wants to generate an argument endorsing that a specific solution class is the correct solution for a problem P, it generates a justified prediction as explained in Section 3.1.
For instance, Figure 3 shows a real justification generated by LID after solving a problem P in the domain of marine sponges identification.
In particular, Figure 3 shows how when an agent receives a new problem to solve (in this case, a new sponge to determine its order), the agent uses LID to generate an argument (consisting on a justified prediction) using the cases in the case base of the agent.
The justification shown in Figure 3 can be interpreted saying that "the predicted solution is hadromerida because the smooth form of the megascleres of the spiculate skeleton of the sponge is of type tylostyle, the spikulate skeleton of the sponge has no uniform length, and there is no gemmules in the external features of the sponge".
Thus, the argument generated will be α = (Ar, P, hadromerida, Dr).
6.1 Generation of Counterarguments
As previously stated, agents may try to rebut arguments by generating counterargument or by finding counterexamples.
Let us explain how they can be generated.
An agent Ai wants to generate a counterargument,3 to rebut an argument α when α is in contradiction with the local case base of Ai.
Moreover, while generating such counterargument,3, Ai expects that,3 is preferred over α.
For that purpose, we will present a specific policy to generate counterarguments based on the specificity criterion [10].
The specificity criterion is widely used in deductive frameworks for argumentation, and states that between two conflicting arguments, the most specific should be preferred since it is, in principle, more informed.
Thus, counterarguments generated based on the specificity criterion are expected to be preferable (since they are more informed) to the arguments they try to rebut.
However, there is no guarantee that such counterarguments will always win, since, as we have stated in Section 5, agents in our framework use a preference relation based on joint confidence.
Moreover, one may think that it would be better that the agents generate counterarguments based on the joint confidence preference relation; however it is not obvious how to generate counterarguments based on joint confidence in an efficient way, since collaboration is required in order to evaluate joint confidence.
Thus, the agent generating the counterargument should constantly communicate with the other agents at each step of the induction algorithm used to generate counterarguments (presently one of our future research lines).
Thus, in our framework, when an agent wants to generate a counterargument,3 to an argument α,,3 has to be more specific than α (i.e. α.D ❁,3.
D).
The generation of counterarguments using the specificity criterion imposes some restrictions over the learning method, although LID or ID3 can be easily adapted for this task.
For instance, LID is an algorithm that generates a description starting from scratch and heuristically adding features to that term.
Thus, at every step, the description is made more specific than in the previous step, and the number of cases that are subsumed by that description is reduced.
When the description covers only (or almost only) cases of a single solution class LID terminates and predicts that solution class.
To generate a counterargument to an argument α LID just has to use as starting point the description α.D instead of starting from scratch.
In this way, the justification provided by LID will always be subsumed by α.D, and thus the resulting counterargument will be more specific than α.
However, notice that LID may sometimes not be able to generate counterarguments, since LID may not be able to specialize the description α.D any further, or because the agent Ai has no case inCi that is subsumed by α.D.
Figure 4 shows how an agent A2 that disagreed with the argument shown in Figure 3, generates a counterargument using LID.
Moreover, Figure 4 shows the generation of a counterargument,3 r2 for the argument α0r (in Figure 3) that is a specialization of α0r.
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Figure 3: Example of a real justification generated by LID in the marine sponges data set.
Specifically, in our experiments, when an agent Ai wants to rebut an argument α, uses the following policy:
1.
Agent Ai uses LID to try to find a counterargument β more specific than α; if found, β is sent to the other agent as a counterargument of α.
2.
If not found, then Ai searches for a counterexample c E Ci of α.
If a case c is found, then c is sent to the other agent as a counterexample of α.
3.
If no counterexamples are found, then Ai cannot rebut the argument α.
7.
ARGUMENTATION-BASED MULTI-AGENT LEARNING
The interaction protocol of AMAL allows a group of agents A1,..., An to deliberate about the correct solution of a problem P by means of an argumentation process.
If the argumentation process arrives to a consensual solution, the joint deliberation ends; otherwise a weighted vote is used to determine the joint solution.
Moreover, AMAL also allows the agents to learn from the counterexamples received from other agents.
The AMAL protocol consists on a series of rounds.
In the initial round, each agent states which is its individual prediction for P. Then, at each round an agent can try to rebut the prediction made by any of the other agents.
The protocol uses a token passing mechanism so that agents (one at a time) can send counterarguments or counterexamples if they disagree with the prediction made by any other agent.
Specifically, each agent is allowed to send one counterargument or counterexample each time he gets the token (notice that this restriction is just to simplify the protocol, and that it does not restrict the number of counterargument an agent can sent, since they can be delayed for subsequent rounds).
When an agent receives a counterargument or counterexample, it informs the other agents if it accepts the counterargument (and changes its prediction) or not.
Moreover, agents have also the opportunity to answer to counterarguments when they receive the token, by trying to generate a counterargument to the counterargument.
When all the agents have had the token once, the token returns to the first agent, and so on.
If at any time in the protocol, all the agents agree or during the last n rounds no agent has generated any counterargument, the protocol ends.
Moreover, if at the end of the argumentation the agents have not reached an agreement, then a voting mechanism that uses the confidence of each prediction as weights is used to decide the final solution (Thus, AMAL follows the same mechanism as human committees, first each individual member of a committee exposes his arguments and discuses those of the other members (joint deliberation), and if no consensus is reached, then a voting mechanism is required).
At each iteration, agents can use the following performatives:
• assert (α): the justified prediction held during the next round will be α.
An agent can only hold a single prediction at each round, thus is multiple asserts are send, only the last one is considered as the currently held prediction.
• rebut (β, α): the agent has found a counterargument β to the prediction α.
We will define Ht = (αt1,..., αtn) as the predictions that each of the n agents hold at a round t. Moreover, we will also define contradict (αti) = {α E Ht | α.S = ~ αti.S} as the set of contradicting arguments for an agent Ai in a round t, i.e. the set of arguments at round t that support a different solution class than αti.
The protocol is initiated because one of the agents receives a problem P to be solved.
After that, the agent informs all the other agents about the problem P to solve, and the protocol starts:
1.
At round t = 0, each one of the agents individually solves P, and builds a justified prediction using its own CBR method.
Then, each agent Ai sends the performative assert (α0i) to the other agents.
Thus, the agents know H0 = (α0i,..., α0n).
Once all the predictions have been sent the token is given to the first agent A1.
2.
At each round t (other than 0), the agents check whether their arguments in Ht agree.
If they do, the protocol moves to step 5.
Moreover, if during the last n rounds no agent has sent any counterexample or counterargument, the protocol also moves to step 5.
Otherwise, the agent Ai owner of the token tries to generate a counterargument for each of the opposing arguments in contradict (αti) C Ht (see Section 6.1).
Then, the counterargument βti against the prediction αtj with the lowest confidence C (αtj) is selected (since αtj is the prediction more likely to be successfully rebutted).
• If βti is a counterargument, then, Ai locally compares αti with βti by assessing their confidence against its individual case base Ci (see Section 5) (notice that Ai is comparing its previous argument with the counterargument that Ai itself has just generated and that is about
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Figure 4: Generation of a counterargument using LID in the sponges data set.
to send to Aj).
If CAi (,3 ti)> CAi (αti), then Ai considers that,3 ti is stronger than its previous argument, changes its argument to,3 ti by sending assert (,3 ti) to the rest of the agents (the intuition behind this is that since a counterargument is also an argument, Ai checks if the newly counterargument is a better argument than the one he was previously holding) and rebut (,3 ti, αtj) to Aj.
Otherwise (i.e. CAi (,3 ti) <CAi (αti)), Ai will send only rebut (,3 ti, αtj) to Aj.
In any of the two situations the protocol moves to step 3.
• If,3 ti is a counterexample c, then Ai sends rebut (c, αtj) to Aj.
The protocol moves to step 4.
• If Ai cannot generate any counterargument or counterexample, the token is sent to the next agent, a new round t + 1 starts, and the protocol moves to state 2.
3.
The agent Aj that has received the counterargument,3 ti, locally compares it against its own argument, αtj, by locally assessing their confidence.
If CAj (,3 ti)> CAj (αtj), then Aj will accept the counterargument as stronger than its own argument, and it will send assert (,3 ti) to the other agents.
Otherwise (i.e. CAj (,3 ti) <CAj (αtj)), Aj will not accept the counterargument, and will inform the other agents accordingly.
Any of the two situations start a new round t + 1, Ai sends the token to the next agent, and the protocol moves back to state 2.
4.
The agent Aj that has received the counterexample c retains it into its case base and generates a new argument αt +1
j that takes into account c, and informs the rest of the agents by sending assert (αt +1 j) to all of them.
Then, Ai sends the token to the next agent, a new round t + 1 starts, and the protocol moves back to step 2.
5.
The protocol ends yielding a joint prediction, as follows: if the arguments in Ht agree then their prediction is the joint prediction, otherwise a voting mechanism is used to decide the joint prediction.
The voting mechanism uses the joint confidence measure as the voting weights, as follows: Moreover, in order to avoid infinite iterations, if an agent sends twice the same argument or counterargument to the same agent, the message is not considered.
8.
EXEMPLIFICATION
Let us consider a system composed of three agents A1, A2 and A3.
One of the agents, A1 receives a problem P to solve, and decides to use AMAL to solve it.
For that reason, invites A2 and A3 to take part in the argumentation process.
They accept the invitation, and the argumentation protocol starts.
Initially, each agent generates its individual prediction for P, and broadcasts it to the other agents.
Thus, all of them can compute H0 = (α0 1, α02, α03).
In particular, in this example:
• α01 = (A1, P, hadromerida, D1) • α02 = (A2, P, astrophorida, D2) • α03 = (A3, P, axinellida, D3)
A1 starts owning the token and tries to generate counterarguments for α02 and α0 3, but does not succeed, however it has one counterexample c13 for α0 3.
Thus, A1 sends the the message rebut (c13, α03) to A3.
A3 incorporates c13 into its case base and tries to solve the problem P again, now taking c13 into consideration.
A3 comes up with the justified prediction α13 = (A3, P, hadromerida, D4), and broadcasts it to the rest of the agents with the message assert (α13).
Thus, all of them know the new H1 = (α0 1, α02, α13).
Round 1 starts and A2 gets the token.
A2 tries to generate counterarguments for α01 and α13 and only succeeds to generate a counterargument,312 = (A2, P, astrophorida, D5) against α1 3.
The counterargument is sent to A3 with the message rebut (,312, α13).
Agent A3 receives the counterargument and assesses its local confidence.
The result is that the individual confidence of the counterargument,31 2 is lower than the local confidence of α1 3.
Therefore, A3 does not accept the counterargument, and thus H2 = (α0 1, α02, α13).
Round 2 starts and A3 gets the token.
A3 generates a counterargument,32 3 = (A3, P, hadromerida, D6) for α02 and sends it to A2 with the message rebut (,32 3, α02).
Agent A2 receives the counterargument and assesses its local confidence.
The result is that the local confidence of the counterargument,323 is higher than the local confidence of α0 2.
Therefore, A2 accepts the counterargument and informs the rest of the agents with the message assert (,323).
After that, H3 = (α0 1,,32 3, α13).
At Round 3, since all the agents agree (all the justified predictions in H3 predict hadromerida as the solution class) The protocol ends, and A1 (the agent that received the problem) considers hadromerida as the joint solution for the problem P.
9.
EXPERIMENTAL EVALUATION
Figure 5: Individual and joint accuracy for 2 to 5 agents.
In this section we empirically evaluate the AMAL argumentation framework.
We have made experiments in two different data sets: soybean (from the UCI machine learning repository) and sponge (a relational data set).
The soybean data set has 307 examples and 19 solution classes, while the sponge data set has 280 examples and 3 solution classes.
In an experimental run, the data set is divided in 2 sets: the training set and the test set.
The training set examples are distributed among 5 different agents without replication, i.e. there is no example shared by two agents.
In the testing stage, problems in the test set arrive randomly to one of the agents, and their goal is to predict the correct solution.
The experiments are designed to test two hypotheses: (H1) that argumentation is a useful framework for joint deliberation and can improve over other typical methods such as voting; and (H2) that learning from communication improves the individual performance of a learning agent participating in an argumentation process.
Moreover, we also expect that the improvement achieved from argumentation will increase as the number of agents participating in the argumentation increases (since more information will be taken into account).
Concerning H1 (argumentation is a useful framework for joint deliberation), we ran 4 experiments, using 2, 3, 4, and 5 agents respectively (in all experiments each agent has a 20% of the training data, since the training is always distributed among 5 agents).
Figure 5 shows the result of those experiments in the sponge and soybean data sets.
Classification accuracy is plotted in the vertical axis, and in the horizontal axis the number of agents that took part in the argumentation processes is shown.
For each number of agents, three bars are shown: individual, Voting, and AMAL.
The individual bar shows the average accuracy of individual agents predictions; the voting bar shows the average accuracy of the joint prediction achieved by voting but without any argumentation; and finally the AMAL bar shows the average accuracy of the joint prediction using argumentation.
The results shown are the average of 5 10-fold cross validation runs.
Figure 5 shows that collaboration (voting and AMAL) outperforms individual problem solving.
Moreover, as we expected, the accuracy improves as more agents collaborate, since more information is taken into account.
We can also see that AMAL always outperforms standard voting, proving that joint decisions are based on better information as provided by the argumentation process.
For instance, the joint accuracy for 2 agents in the sponge data set is of 87.57% for AMAL and 86.57% for voting (while individual accuracy is just 80.07%).
Moreover, the improvement achieved by AMAL over Voting is even larger in the soybean data set.
The reason is that the soybean data set is more "difficult' (in the sense that agents need more data to produce good predictions).
These experimental results show that AMAL effectively exploits the opportunity for improvement: the accuracy is higher only because more agents have changed their opinion during argumentation (otherwise they would achieve the same result as Voting).
Concerning H2 (learning from communication in argumentation processes improves individual prediction), we ran the following experiment: initially, we distributed a 25% of the training set among the five agents; after that, the rest of the cases in the training set is sent to the agents one by one; when an agent receives a new training case, it has several options: the agent can discard it, the agent can retain it, or the agent can use it for engaging an argumentation process.
Figure 6 shows the result of that experiment for the two data sets.
Figure 6 contains three plots, where NL (not learning) shows accuracy of an agent with no learning at all; L (learning), shows the evolution of the individual classification accuracy when agents learn by retaining the training cases they individually receive (notice that when all the training cases have been retained at 100%, the accuracy should be equal to that of Figure 5 for individual agents); and finally LFC (learning from communication) shows the evolution of the individual classification accuracy of learning agents that also learn by retaining those counterexamples received during argumentation (i.e. they learn both from training examples and counterexamples).
Figure 6 shows that if an agent Ai learns also from communication, Ai can significantly improve its individual performance with just a small number of additional cases (those selected as relevant counterexamples for Ai during argumentation).
For instance, in the soybean data set, individual agents have achieved an accuracy of 70.62% when they also learn from communication versus an accuracy of 59.93% when they only learn from their individual experience.
The number of cases learnt from communication depends on the properties of the data set: in the sponges data set, agents have retained only very few additional cases, and significantly improved individual accuracy; namely they retain 59.96 cases in average (compared to the 50.4 cases retained if they do not learn from communication).
In the soybean data set more counterexamples are learnt to significantly improve individual accuracy, namely they retain 87.16 cases in average (compared to 55.27 cases retained if they do not learn from communication).
Finally, the fact that both data sets show a significant improvement points out the adaptive nature of the argumentation-based approach to learning from communication: the useful cases are selected as counterexamples (and no more than those needed), and they have the intended effect.
10.
RELATED WORK
Concerning CBR in a multi-agent setting, the first research was on "negotiated case retrieval' [11] among groups of agents.
Our work on multi-agent case-based learning started in 1999 [6]; later Mc Ginty and Smyth [7] presented a multi-agent collaborative CBR approach (CCBR) for planning.
Finally, another interesting approach is multi-case-base reasoning (MCBR) [5], that deals with
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Figure 6: Learning from communication resulting from argumentation in a system composed of 5 agents.
distributed systems where there are several case bases available for the same task and addresses the problems of cross-case base adaptation.
The main difference is that our MAC approach is a way to distribute the Reuse process of CBR (using a voting system) while Retrieve is performed individually by each agent; the other multiagent CBR approaches, however, focus on distributing the Retrieve process.
Research on MAS argumentation focus on several issues like a) logics, protocols and languages that support argumentation, b) argument selection and c) argument interpretation.
Approaches for logic and languages that support argumentation include defeasible logic [4] and BDI models [13].
Although argument selection is a key aspect of automated argumentation (see [12] and [13]), most research has been focused on preference relations among arguments.
In our framework we have addressed both argument selection and preference relations using a case-based approach.
11.
CONCLUSIONS AND FUTURE WORK
In this paper we have presented an argumentation-based framework for multi-agent learning.
Specifically, we have presented AMAL, a framework that allows a group of learning agents to argue about the solution of a given problem and we have shown how the learning capabilities can be used to generate arguments and counterarguments.
The experimental evaluation shows that the increased amount of information provided to the agents by the argumentation process increases their predictive accuracy, and specially when an adequate number of agents take part in the argumentation.
The main contributions of this work are: a) an argumentation framework for learning agents; b) a case-based preference relation over arguments, based on computing an overall confidence estimation of arguments; c) a case-based policy to generate counterarguments and select counterexamples; and d) an argumentation-based approach for learning from communication.
Finally, in the experiments presented here a learning agent would retain all counterexamples submitted by the other agent; however, this is a very simple case retention policy, and we will like to experiment with more informed policies--with the goal that individual learning agents could significantly improve using only a small set of cases proposed by other agents.
Finally, our approach is focused on lazy learning, and future works aims at incorporating eager inductive learning inside the argumentative framework for learning from communication.