The Study of Delusion in Multiagent Systems

The Study of Delusion in Multiagent Systems Olayide Olorunleke Department of Computer Science University of Saskatchewan, Canada. ARIES Lab oto033@cs....
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The Study of Delusion in Multiagent Systems Olayide Olorunleke Department of Computer Science University of Saskatchewan, Canada. ARIES Lab [email protected]

Gordon McCalla Department of Computer Science University of Saskatchewan, Canada. ARIES Lab [email protected]

Abstract

available in the environment to make decisions. An example of such a coordination approach is the use of focal points (e.g. Fenster et al, 1995; Gervasi and Prencipe, 2003). A second coordination attempt (without communication) assumes that the agents in the system monitor each other’s actions and based on their observations, try to recognize which plan the agent being observed is carrying out (e.g. Genesereth et al, 1986; Huber and Durfee, 1995, Tambe and Rosenbloom, 1995, 1996). This approach is called plan recognition or agent tracking. A third coordination approach that allows communication between agents that has been investigated relies on the notifications that agents send to each other to inform each other of changes that they might be interested in (e.g. Tambe, 1997).

It is generally accepted that an agent needs to build models of other agents in its environment. The content of these models ranges from simple entries, such as agent capabilities, to more complex entries, such as agent intentions, goals, desires, etc. There is the problem that the information stored in these models may not be accurate in terms of matching the actual property of the agent being modelled. When this happens the agent storing the models is said to be deluded about the agent being modelled. This paper discusses our synthesis of ideas on the issue of agent delusion and presents results of some of the work we have carried out in trying to overcome delusion within agent models and in preventing the spread of delusions to other agents’ models when agents communicate/gossip with each other. Keywords agent models; delusion. 1.

Introduction

A multiagent system (MAS) is made up of a set of agents Ags that interact, in some environment, with each other while trying to achieve a system goal (or individual agent goals). The coordination of the agent actions in such systems is important to avoid situations in which one agent’s actions undo another agent’s actions thereby stopping the agents from progressing towards the solution they seek. Various approaches have been explored for achieving such coordination. These coordination approaches are usually characterized as communication-based (i.e. they rely on the exchange of some data between the agents) or communication-free (i.e. agents are not allowed to communicate with each other). An example coordination approach that prohibits communication is the use of information readily

In this paper, our focus is on the coordination approaches that rely on the inference of some internal property of the observed agent based on the actions observed and on the communication (particularly gossip) between agents. In this context, we assume that each agent A ∈ Ags keeps a structure about another agent B ∈ Ags that represents what A believes about B. We represent this structure as modelAB. The content of this structure could be what A believes B’s capabilities are, what A believes B’s intentions are, what A believes B’s reputation is, how much A trusts B to act in a certain way, etc. The point is that modelAB contains some information that A believes about B. Furthermore, we assume that A consults modelAB while making decisions about its actions in the environment and thus that modelAB affects A’s behaviour whenever A chooses to use its contents in decision making. We also assume that A keeps models of each agent in the set OthersA such that OthersA ⊆ Ags, and that A can keep modelATm where Tm represents a team/group of agents in the powerset of Ags, i.e. Tm ∈ P(Ags). The models

stored by each agent may be in various representations such as rules (Kaminka et al, 1998), finite automata (Carmel and Markovitch, 1996), payoff matrices (Gmytrasiewicz et al, 1991), influence diagrams (Suryadi and Gmytrasiewicz, 1999; Zunino and Amandi, 2001), fragments (Olorunleke, 2002), to name a few. We thus define the term agent model as any information stored (irrespective of representation) by an agent A ∈ Ags about another agent B ∈ OthersA | OthersA ⊆ Ags or about a team of agents Tm ∈ P(Ags), and which affects A’s decisions about its activities1. Any agent that stores agent models is doing agent modelling. An agent doing agent modelling (e.g. A) faces two major problems. The first of these problems, which we will not discuss any further in this paper, is the possibility of the large number of models that the agent A must monitor possibly because of the size of the system or the possibility of recursive models (such as modelABA i.e. what A believes B believes A believes, and so on to deeper levels of recursion; Gmytrasiewicz et al, 1991) which could result in A not being able to make decisions in time for the actions to be useful (In fact our work in this direction is also to appear in the proceedings of the AAMAS 2004 conference; Olorunleke and McCalla, 2004). The second problem is related to the accuracy of the content of the models kept by the agents. It is easy to see that an agent’s performance depends on the accuracy of its models if it consults its models when making decisions. To illustrate this, picture a simulated RoboCup game (Kitano et al, 1995) in which A and B ∈ Team (where Team is the team of agents) are playing a formation. If modelAB contains information that B is located at position (a,b), then A can decide to pass the ball to B at position(a,b) where a is on the x-coordinate and b is on the y-coordinate. Now if B was actually located at position (c,d), then A would have just made a wrong decision, and might have just given over control of the ball to the opponent. Such inaccuracies that can exist in the contents of the models are what we refer to as delusion (Olorunleke and McCalla, 2003).

1

It is possible to extend this definition to allow information stored about other entities in the environment such as humans, relationships, or physical objects.

Our goal in this paper is to present our ideas and views on the problem of delusion and present the work we have been involved in that aims to study how delusion can be overcome and how to prevent delusion from spreading from agent to agent within a multiagent system. The rest of the paper is organized as follows: in section 2 we present our definition of delusion and discuss how delusions arise and some recommendations for avoiding delusions in a MAS. In section 3 we describe a simulation environment we designed to study various strategies for curbing the spread of delusion from agent to agent. In section 4 we discuss important issues in overcoming delusion. We conclude in section 5 with a summary of recommendations for agent modelling and present some future directions needed. 2.

Agent delusion

In the previous section, we stated that agent A keeps modelAB about another agent B such that B is also in the set of agents. This definition allows B to refer to agent A itself, i.e., we could have written modelAB as modelAA. To refer to the model that an agent keeps about itself we will simply write modelA. So our definition of agent modelling supports the idea of self-models. From this definition it also follows that if modelA is inaccurate then A is said to be self-deluded. To illustrate this possibility, consider the source of agent models in I-Help (Greer et al. 2001) where learners needing help (helpees) are put in touch with peers who can help them (helpers). Within I-Help, each learner is represented by a personal agent and the agent’s capabilities are assumed to be the learner’s capabilities in various subject topics. The agent’s initial self-model is supplied by the learner to the agent. This involves supplying a description to the agent such as ratings on various subjects. Based on these supplied models, the I-Help agents then try to match helpers to helpees. Unfortunately, it turns out that often the learners are not good judges of their own capabilities and thus their agents end up being self-deluded. In the same vein, A is also said to be deluded about B if its model of B is inaccurate. This idea of delusions has been referred to as model-entity discrepancies in Touring Machines (Ferguson, 1992). The first question we tackle concerning delusion is about the source of delusions.

2.1 Sources of Delusion Delusions can arise within agent models from various sources. One possible source could be the failure of sensors that the agent depends upon for sensing its environment. A second source could be nature of the domain in which the agents operate. For example, an I-Help agent can become self-deluded due to the models supplied by its learner. A third source for the appearance of delusion in agent models is related to the dynamic nature of the agents being modelled (such as agents that are always moving). A fourth source of delusion in the agent models arises from the way that an agent combines its observations with its models, i.e., an error in the belief revision procedure of an agent can result in the agent being deluded (even if its beliefs are consistent within itself and the procedure is sound and complete). A fifth source of delusions results when agents try to deceive each other by acting in a certain way to lead others into believing that they (the deceiving agent) have a certain property, which they in fact do not (Tambe, 1995). The final source of delusion we discuss in this paper is the possible spread of delusion from one agent to another. This arises when the agents are allowed to gossip with each other either about their observations, or about the contents of their models. While this has advantages (such as an agent getting information outside of the range of its sensors), it also has the disadvantage that delusion can be propagated within the multiagent system as a whole. For example, if A’s sensors fail and A gossips with B about its sensor observations, then B could end up being deluded about the other agent (or object) that the communication was about. 2.2. Avoiding Delusion Attacking the problem of delusion should start right at the cause of the delusions. For example, since an agent can become deluded if its sensors become faulty, then agents should be designed in such a way that the agents are always aware of the working status of their sensors and thus, know when to believe their sensors. Concerning the nature of the environment, we feel that the system designers should find the least likely way to introduce delusions when obtaining models. For example, a more likely way of supplying agent models that are free of delusions in I-Help would be to rely on the past grades of the students in initializing their models

when such information is available. Various environments and domains would most likely present such opportunities, and we feel that agent designers should take advantage of such. In highly dynamic environments it has been previously identified that the content of agent models cannot really be relied upon to make predictions for the long term (Ferguson, 1992; Hu and Wellman, 2001). We agree with this view and the suggestion that the content of the agent models should also be used for decisions only in the short term. What makes a duration short term or long term, however, depends on the particular domain and the properties of the system. In systems that are not so dynamic, agent models can still be used for longer-term decisions, especially when the agents do not change and sensor failures are rare occurrences. This short-term use of models could also be a coping strategy when agents try to deceive each other. An interesting and recent modelling approach, termed active learner modelling (McCalla et al, 2000), considers the agent model to be computed just-in-time (i.e. when needed). The resulting model from this computation is affected by the context surrounding the need for the model, such as, the agents involved, the resources available to the modelling agent, and the purpose for which the model is needed. Because the agent models are created only when needed, the agent models tend to be created for short-term use and thus might be ideal also for avoiding delusion. Ferguson (1992) also suggests that that an agent should make use of as much information as is available to it in making decisions based on its models to avoid discrepancies between the model and the entity being modelled. We feel this also applies to the belief revision procedure that an agent uses. That is an agent should use as much information as is available to it when it reviews its models. The intuition is that the more information is used to model an agent the more accurate the resulting model should be. The final source of delusions we identified earlier in this section is the spread of delusion from agent to agent. This problem suggests that agents should adopt strategies that limit the spread of delusion when agents gossip. The onus mostly lies on the agent receiving the message. This is particularly true in open systems in which any developer can create and run agents. The

next section describes our exploration of various strategies for reducing the spread of delusion via gossip. 3.

The GossipWorld simulator

In this section, we describe the GossipWorld (Olorunleke and McCalla, 2004) that we created to study the impact of various strategies in reducing the spread of delusion. After describing this simulation environment and the results of our experiments, we will make some recommendations concerning which strategy might be ideal in certain situations. Consider agent A located in a 10X10 grid of cells as shown in Figure 1. Each cell in the grid represents a room that can contain a maximum of 3 agents at any time. One of these 3 agents is a stationary agent that either has a certain property (shown by the ‘*’) or not.

Figure 1: GossipWorld - Agent A must visit every room to find out if the light is on or off Agent A’s goal is to find out whether the stationary agents in each of the 100 rooms have the property ‘*’. A can achieve this by visiting every room one after another and noting the property of the stationary agent in the room (we will call this stationary agent the room-agent). A is allowed to move vertically or horizontally from room to room such that it favors unvisited rooms over visited ones. For example, in the figure above, A can either move up, right, down (the grid wraps around), or left (to appear at the last column). It is clear that at the end of the visits, agent A can be sure to have correct models of the room-agents in each of the rooms in the grid (assuming that its sensors are not defective and the stationary agents do not change after being visited). Now lets assume that we have many more agents sharing the same goal as agent A as shown in Figure 2.

Figure 2: GossipWorld - Agents A-R sharing the same goals By allowing agents to gossip with each other, it is obvious that each agent can reduce the number of rooms it needs to visit. Agents can only gossip and share models with each other when they meet in a room. For example, agents A and B can gossip since they are located in the same room. If A and B gossip with one another, then A can learn about the rooms that B has been in that A has not been in and vice versa. After gossiping, A and B concentrate their exploration to those rooms whose agent model is still not known. If we assume that all the agents have perfect sensors and will not lie to each other, then it is possible that the agents can learn about every room-agent without having to visit all of the rooms themselves, and without being deluded about any room-agent at the end of the explorations. To study the spread of delusion among agents, we make agent R’s sensors defective, by causing it to sense the property of a room-agent wrongly. When the room-agent has the property ‘*’, R senses the agent as not having that property, and vice versa. Agent R can however still know the correct state of another room’s room-agent if it got this information through any of the other agents while gossiping with them. When agents A and B gossip in the GossipWorld, A presents a set of models MA ⊆ OthersA and B presents a set of models MB ⊆ OthersB. The set Ω = MA ∩ MB represents the rooms for which both A and B already have a model for the room-agent in that room. The set α = MA\MB represents the models of the room agents that A knows about, but B does not. The set β =MB\MA represents the models of the room agents that B knows about, but A does not. Agent A can learn about the rooms it has not visited by considering the models contained in

β , while agent B can learn from the models in α . The question at this point is how should A decide whether to believe β , and how should B decide whether to believe α . 3.1. Strategies We consider three different types of strategies that each agent can adopt when it receives models from any other agent. The first of these strategies is called free model sharing (FMSH). This strategy assumes that the agent does not question whatever information it receives but simply accepts it (i.e. A accepts β into OthersA, and B accepts α into OthersB). At the other end of the spectrum is the reserved model sharing (RMSH) strategy which assumes that an agent will only believe models shared with it in the absence of any evidence that suggests that such shared models cannot be trusted. That is, A will accept β into OthersA iff Ω is empty or Ω contains no disagreements between A and B (and vice versa). Between FMSH and RMSH lies a third type of strategy that is threshold-based. The thresholdbased strategies assume that the agent will compare the ratio of the agreements in Ω and the sum of both the agreements and disagreements in Ω to a threshold value. For ratios above the threshold value the agent would believe the shared models otherwise, it disbelieves the models. Let agree(Ω) be a function that returns the number of times A and B agree in Ω, and disagree(Ω) be the number of times they disagree. We calculate the ratio of agreements (ROA) between A and B as agree(Ω) * 100 ROAAB = agree(Ω) +disagree(Ω) where agree(Ω) +disagree(Ω) = |Ω|. To use the formula above we assume Ω is not empty. If Ω is empty then ROAAB=100. When ROAAB is greater than a threshold then A believes B and vice versa. If the threshold is set at 100 then this approach is equivalent to RMSH and if the threshold is set at 0 the method becomes equivalent to FMSH. 3.2. Experiments and Results In our experiments we use the three strategies we have discussed above. In the threshold based

strategy we vary our threshold from 50 to 100 in increments of 10. We start each experimental setup with agent R as the only source of delusion, and at the end of the experiment we measure both the total delusion in the system (as the sum of the delusions held by each agent), as well as, the number of times agent R gossips. We assume that when agents gossip Mi = Othersi, i.e. agent i will present information about all the room agents it knows so far. An experimental run ends when all the agents have a model of all the room agents (gotten either by observation or gossip). We repeat each run 1000 times and take the average of the total delusion and number of times R gossips in each run to represent the typical total delusion in the system for the number of times R gossips, at the end of the run using any of the strategies discussed.

Figure 3: Total Delusion in the system against number of times agent R gossips. The graph in Figure 3 shows the total delusion in the system plotted against the number of times agent R gossips using each of the strategies. The plot marked thresh50 refers to a threshold value of 50, thresh60 refers to a threshold value of 60, and so on. We do not show the plot for thresh100 because it simply lies on the plot for RMSH as we expected. The first observation from our results (Figure 3) is that after around the 30th gossip by agent R the total delusion in the system changes less rapidly. The explanation for this behavior is that by the time R gossips 30 times the damage to the other agents’ models has already been done, and most of the agents have already found out about every room agent in the grid and thus do not need to gossip anymore. (this is confirmed in Figure 4). We expect this behavior to occur even in a different sized grid or in a grid with a different number of agents (the shape will also remain the same). The specific point at which this happens will change however.

Figure 4 plots the number of times R gossips before all the agents learn models of all room agents, using the various strategies. Figure 4 shows that by the time R gossips 30 times the agents would have completed their explorations under all the strategies. The interesting part of our results lies in the region before R gossips 30 times (in Figure 3).

Figure 4: Times R Gossips before all agents find out about all room agents The FMSH curve in Figure 3 confirms the obvious intuition that free model sharing would allow delusions to spread freely from agent to agent in the system. Also the FMSH shows that the more the deluded agent R gossips the more the amount of delusion in the system. It is worth mentioning at this point that although R was the initial source of the delusions, any agent that believed R could also spread on the delusion to other agents. With RMSH, the delusion in the system rises steadily, but much less rapidly than FMSH. This again confirms that being reserved has the advantage of helping to reduce the transfer of delusion from agent to agent. The disadvantage of RMSH is that it results in agents believing each other only when they agree on each model in Ω or when Ω is empty. This is shown in Figure 5. The y-axis in Figure 5 has been overloaded, that is, the first 2 bars show the number of delusion and the last bar shows number of times R gossips. The table beneath the plot has been added to show the exact values plotted in the graph. Figure 5 shows that although R gossips 30 times it still ends up being deluded about 91% of the room agents while the other agents that were not initially deluded ended up being deluded about only 0.44% of the room agents. The few times that R believed another agent was when Ω was empty. Thus, using RMSH an agent whose sensors fail would begin to disbelieve other agents with perfect sensors and would only tend to believe other agents with failed sensors. Thus, being totally conservative (as in RMSH) is not the way to go. At the same

time, believing every model received is also not the way to go as our experiments have shown. The solution lies somewhere in between being totally conservative and being totally believing.

Figure 5: R does not believe others with RMSH The results obtained from the threshold-based strategies (Figure 3) show that when a threshold value below 80% is used the deluded agent succeeds in passing on its delusions rapidly until after its 10th gossip. A threshold value of 80% and above, however, curbs the effect of the deluded agent much better and the shape of the curve is similar to when the conservative approach is taken. Table 1 shows that when the threshold value is set at 80% agent R is able to lower its delusions about other room agents to 88% from the initial 91% observed with RMSH. The amount of delusions in the other agents models rise a little (from 0.443 to 1.132) while R’s number of gossip still stays at approximately 30 gossips. Table 1: How thresholds affect R's delusions Strategy RMSH Thresh90 Thresh80

Agent R 91.179 90.061 88.095

Others 0.443 0.626 1.132

R Gossips 30.784 29.536 29.288

3.3. Recommendations Based on our observations we recommend that when agents gossip the threshold-based strategy should be used if there is the possibility of sensors failing without the agents knowing. If the agents can tell when their sensors have failed, then the agents should use the RMSH strategy when sensors are working perfectly and the FMSH strategy when the sensors fail. Our

recommendation for the use of threshold-based strategies relies on the assumption (as stated earlier) that agents gossip about everything they know. This assumption is made to ensure that the size of Ω is as large as possible, and thus the decision is made using more information. We suggest threshold values of at least 80%, but the agent designer is encouraged to try other values and pick what they believe is most suitable for their domain. 4. Overcoming Delusion So far we have discussed strategies for avoiding delusion, but these strategies still do not guarantee that an agent will not have any delusions in its models. The second question then is how should an agent get rid of the delusions within its models? Before attempting to answer this question, we should ask the question: is it even possible for an agent to be delusion free? Especially when in a dynamic world. In a dynamic world, agent behaviours are always changing, especially when the agent behaviour depends on the content of its models. If all agents in a system keep changing their behaviour then all other agents will continually need to modify their models to better suit the agents being modelled. This creates the possibility of a moving-target problem in which the entity being modelled is always changing. If the modelled agent changes its behaviour too often, then the modelling agent may never be able converge on an actual correct model or even if it converges on an actual model the agent being modelled could change its behaviour again in the next instant. This suggests that even if agents are able to overcome their delusions, they should still be designed with the ability to cope with some delusion in their models since modelled agents can always change their behaviours or properties being modelled. The ability to cope with delusion can be attained, for instance, by using the contents of models for only short-term predictions (as used by Ferguson, 1992 in Touring Machines), using active models, or by allowing agents to use the content of the models until an observation is made which could not have been predicted by the current model, and when this happens generate a new model that explains the agents behaviour as observed to date (essentially using reinforcement learning). In (Olorunleke and

McCalla, 2003) we discussed an example of such reinforcement learning algorithms in a domain in which we designed agents with various (arithmetic) capabilities with some agents initially deluded about their own and other agent’s capabilities. For space reasons we cannot describe in details this simulated system and the experiments carried out, but we refer the reader to Olorunleke (2002), Olorunleke and McCalla (2003). In this study, agents relied on their observations and gossip received from other agents to incrementally correct their models until the agents were able to converge on the correct model for each agent. This, to us, serves as a confirmation that, in domains that are not so dynamic, reinforcement learning algorithms could be useful in overcoming delusion. One of the lessons we also learnt from this study was that gossip is very useful, particularly in highly deluded societies, if the gossip can be trusted. This lesson formed the basis for our trying to create strategies that ensure that the models shared via gossip do not spread delusion. 5.

Conclusions

Overcoming delusions in agent models is important and is a problem that cannot be ignored if agents are to maintain meaningful interactions. In this paper, we have discussed some sources of delusions and have made recommendations for avoiding and coping with some of the delusions, such as • designing agents to be aware of sensor failures, • minimizing introduction of delusions into agent models when models are initialized for the first time, • using the models for short-term predictions (active modelling might be suitable for this), • making use of as much information as possible when reviewing models, • relying on RMSH if agents can sense when sensors fail and sensors have not failed, • relying on FMSH if agents can sense when sensors fail and sensors have failed, • relying on a threshold-based strategy when it is impossible to tell whether sensors are good or bad. We have made the assumption in GossipWorld that when agents gossip they jointly maximize the size of Ω, and that an agent either believes or disbelieves the content of α or β (whichever is relevant). We hope to further investigate the

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