Outcome Mtrix bsed Phrse Selection Aln R Wgner Georgi Tech Reserch Institute 50 4 th Street NW, Atlnt GA 0-08 Abstrct This rticle presents method for using outcome mtrices for socil phrse selection. An outcome mtrix is computtionl representtion of interction often used to represent socil decision problem. Typiclly n outcome mtrix lists the potentil ctions tht robot or gent might select nd how the selection of ech possible ction will impct both the gent nd their interctive prtner. Here we exmine the possibility of replcing the socil ctions listed in mtrix with phrses tht could be spoken by the robot. We show tht doing so llows one to utilize severl tools from interdependence theory nd gme theory. Introduction Socil psychologists define interction s influence verbl, physicl or emotionl by one individul on nother (Sers, Peplu, & Tylor, ). This definition of interction centers on the influence individuls hve on one nother. Hence, one s representtion of interction must lso include informtion bout the ctions ech individul is considering, the influence tht the selection of pir of ctions would hve on ech individul, nd informtion bout who is intercting. Outcome mtrices contin ll of this informtion (Wgner, Creting nd Using Mtrix Representtions of Socil Interction, 00). An outcome mtrix not only identifies the individuls intercting but lso contins informtion bout the ctions vilble to both individuls nd the influence tht results from the selection of ech pir of ctions. If we llow socil ction to include verbl sttements then outcome mtrices cn serve s method for deliberting over distinct verbl phrses nd guging how these phrses will impct both the gent nd the humn. Moreover, this pproch llows one to use tools from interdependence nd gme theory for phrse selection (Kelly & Thibut, 8). Copyright 0, Assocition for the Advncement of Artificil Intelligence (www.i.org). All rights reserved. This rticle exmines the use of outcome mtrices s method for phrse selection. We ssume tht the intelligent gent hs t their disposl limited set of known phrses. These phrses serve s the gent s universl set of ctions. From this set, subset of pproprite phrses is selected bsed on the gent s perceptul recognition of the environment. Stereotyping is used to crete further subset of the remining phrses. This finl set of phrses is incorported into the outcome mtrix representtion. An outcome mtrix explicitly represents little informtion relted to common ground. In fct, the only mutul understnding tht the robot nd the humn re ssumed to hve is rudimentry knowledge of how selected phrse would influence both individuls. We rgue tht the robot s use of outcome mtrices for the selection of phrses does in fct ground the phrse with respect to its influence on both individuls. Put nother wy, our method does not ssume or rgue tht the robot hs ny understnding of wht the phrses men. Rther, their vlue during n interction is completely determined by the outcome vlues within the mtrix t tht time. Hence the phrses re grounded in these outcome vlues nd common ground is estblished when these outcome vlues re mutully recognized. This rticle does not exmine the problem of creting or understnding humn-robot dilog. Rther we simply present method by which robot cn select phrse, whether spoken or otherwise, resulting from n interction with person. The key contribution of this pper is to present phrse selection s form of socil ction selection, thereby suggesting tht the phrse selection problem is decision theory problem which cn be represented s n outcome mtrix. Moreover, use of the outcome mtrix representtion leves t our disposl the vrious tools from interdependence theory. For exmple, the outcome mtrix s position in the interdependence spce cn be clculted nd the resulting vlues cn be used to influence the selection of phrse or the robot cn trnsform the mtrix to reflect include its own internl disposition. We exmine the use of these interdependence theory tools in greter detil below.
Relted Work Mny reserchers hve exmined humn-robot dilog. Much reserch hs been devoted to developing robots tht lern the words for objects in n environment (Chuhn & Lopes, 00)(Iwhshi, Sugiur, Tguchi, Ngl, & Tniguchi, 00). Others hve focused on specific portions of dilog such s djectives (Petrosino & Gold, 00) or sptil lnguge (Skubic, Perznowski, Schultz, & Adms, 00). Investigtions of timing nd turn-tking re plentiful (Cho & Thomz, 00) (Spiliotopoulos & etl, 00). Scheutz et l. developed n rchitecture tht expressed nd verblly responded to humn s ffect(scheutz, Schermerhorn, & Krmer, 006). Representtions for interction hve long history in socil psychology nd gme theory (Kelly & Thibut, 8)(Osborne & Rubinstein, 4). Interdependence theory, type of socil exchnge theory, is psychologicl theory developed s mens for understnding nd nlyzing interpersonl situtions nd interction (Kelly & Thibut, 8). The term interdependence specifies the extent to which one individul of dyd influences the other. Interdependence theory is bsed on the clim tht people djust their interctive behvior in response to their perception of socil sitution s pttern of rewrds nd costs. Thus, ech choice of interctive behvior by n individul offers the possibility of specific rewrds nd costs lso known s outcomes fter the interction. Interdependence theory represents interction nd socil situtions computtionlly s n outcome mtrix (Figure ). An outcome mtrix represents n interction by expressing the outcomes fforded to ech intercting individul with respect ech pir of potentil behviors chosen by the individuls. Individul Independent versus Dependent mtrices Independent Socil Sitution Individul Dependent Socil Sitution Figure. An exmple of n independent sitution is depicted on the left nd n exmple of dependent sitution is depicted on the right. In the exmple of n independent sitution,, the ction selection of the second individul does not hve n effect the outcome received by the first individul. In the dependent exmple, on the other hnd, the ction selection of the second individul results in gin or lose of 6 units of outcome ( mesure of utility) by the first individul. Individul Individul Representing Interction The outcome mtrix is stndrd computtionl representtion for interction (Kelly & Thibut, 8). It is composed of informtion bout the individuls intercting, including their identity, the interctive ctions they re deliberting over, nd sclr outcome vlues representing the rewrd minus the cost, or the outcomes, for ech individul. Thus, n outcome mtrix explicitly represents informtion tht is criticl to interction. Typiclly, the identity of the intercting individuls is listed long the dimensions of the mtrix. Figure depicts n interction involving two individuls. In this rticle the term individul is used to indicte either humn or socil robot or gent. We will focus on interction involving two individuls dydic interction. An outcome mtrix cn, however, represent interction involving more thn two individuls. The rows nd columns of the mtrix consist of list of ctions vilble to ech individul during the interction. Finlly, sclr outcome is ssocited with ech ction pir for ech individul. Outcomes represent unitless chnges in the robot, gent, or humn s utility. Thus, for exmple, n outcome of zero reflects the fct tht no chnge in the individul s utility will result from the mutul selection of tht ction pir. Becuse outcome mtrices re computtionl representtions, it is possible to describe them formlly. Doing so llows for powerful nd generl descriptions of interction. The nottion presented here drws hevily from gme theory (Osborne & Rubinstein, 4). A representtion of interction consists of ) finite set N of intercting individuls; ) for ech individul i N i nonempty set A of ctions; ) the utility obtined by ech individul for ech combintion of ctions tht could hve i i been selected (Gibbons, ). Let A be n j rbitrry ction j from individul i s set of ctions. Let N ( j, K, k ) denote combintion of ctions, one for ech individul, nd let u i denote individul i s utility i N function: u ( j, K, k ) R is the utility received by individul i if the individuls choose the ctions N ( j, K, k ). The term O is used to denote n outcome mtrix. The superscript -i is used to express individul i's i prtner. Thus, for exmple, A denotes the ction set of i individul i nd A denotes the ction set of individul i s interctive prtner. Phrses s Outcome Mtrix Actions Verbl sttements cn hve powerful influence both on one s self nd on one s interctive prtner. As mentioned
Using Context nd Stereotypes to refine the set of Phrses Universl Set of Phrses Context Subset Prtner Subset I cn ssist with the xe I cn ssist with the bton I cn ssist with stethoscope 4 How cn I help you? 5 Do you wnt coffee? 6 Yes No? I cn ssist with the xe I cn ssist with the bton I cn ssist with the xe Imge exmple from experiment Figure The figure bove depicts the itertive refinement of set of phrses bsed on context nd stereotyping. The robot begins with universl set of phrses (left). Recognition of tools in the environment refines the possible set of phrses to be pplicble to the context involving the tools locted. Next, perceptul fetures relted to the stereotype of fire fighter re recognized. These fetures refine the set of phrses down to single phrse. n outcome mtrix cts s computtionl representtion of interction. The informtion contined within n outcome mtrix explicitly represents the decision problem fced by the gent or robot. We rgue tht this decision problem often involves selecting the most pproprite verbl sttement. In this cse we consider the robot to hve set such tht is verbl sttement. The selection of the verbl sttement will result in outcome, for the robot nd its prtner. The robot selects the sttement bsed only on the outcome vlues. Still, the outcome vlues themselves my be influenced by mny different fctors, such s the context or chrcteristics of the interctive prtner. The robot or gent thus hs finite, but possibly lrge, set of phrses representing the ctions vilble to it. This universl set of phrses,, includes ll possible phrses vilble to the robot in ll contexts nd with ll prtners. At this point we do not offer insight s to how the robot genertes or constructs such set. Lerning phrses from interctions with others seems to be the most obvious route. Keep in mind, however, tht for this process to be vible, the robot must lso lern the outcome vlues for such phrses. Simply lerning the phrse itself would not be of vlue. Refining the Set of Phrses Socil scientists clim tht interction is function of both interctive individuls (A nd B) nd the context (C), formlly,, (Rusbult & Vn Lnge, 00). With respect to interctive phrse selection, the robot must hve process for down selecting the set of possible phrses to those phrses vilble for given prtner in given context. In the section tht follows we describe such process. We propose tht the context nd interctive prtner operte by selecting subsets of universl set of phrses. The robot begins with universl set of phrses representing ll phrses it hs vilble. At strtup, the robot surveys its environment generting context vector,, which includes perceptul informtion relted to the robot s context. The context vector nd the universl set of phrses re used s input to function tht produces subset of phrses vilble in tht prticulr context. Next or possibly concurrently, the robot genertes prtner feture vector,, tht includes perceptul informtion relted to the robot s interctive prtner. The prtner feture vector nd the context relted subset of phrses re used s input to function generted further subset of phrses.
Allowing Disposition to Influence Phrse Selection Robot s Phrses No, I don t see ny reson to Yes, I ll do whtever you need No, I won t let you succeed No, but I ll help myself If you help me Let s help ech other Mtrix Will you help me? 0-8 0 0-4 - 0 6 Disposition Egoist Altruist Mlevolent Competitive Fir Coopertive Figure The figure bove depicts sitution in which the humn sks the question, Will you help me? The robot hs severl different potentil phrses to choose from. Below the mtrix underneth ech potentil robot phrse, the robot disposition tht would choose tht phrse is listed. For exmple, mlevolent disposition would choose the phrse No, I won t let you succeed. Stereotypes nd stereotyping llow for the lerning of ctegories of individuls. Sers, Peplu nd Tylor define stereotype s n interpersonl schem relting perceptul fetures to distinctive clusters of trits (Sers, Peplu, & Tylor, ). A stereotype is type of generlized model of one s prtner used to represent collection or ctegory of individul prtner models. The cretion of stereotypes requires the cretion of these generlized prtner models. Moreover, to be useful, techniques must exist which re cpble of mtching new interctive prtner s perceptul fetures to n existing stereotype. In previous work we developed lgorithms for stereotype building nd for mtching new prtner to n existing stereotype (Wgner, Extended Abstrct: Using Stereotypes to Understnd One's Interctive Prtner, 00). With respect to phrse selection, the use of stereotypes llows the robot to mtch collections of phrses to the prticulr ctegories of people. Figure presents n exmple in which we hve used this process of refining the set of phrses. In this exmple the robot begins with seven phrses in the universl set. The robot recognizes prticulr objects in the environment. These objects mp to prticulr subset of the universl phrse set. Next, the robot uses the perceptul chrcteristics of the person to crete feture vector. This feture vector is used to select stereotype. The selected stereotype includes informtion relted to which phrses remin vible during the interction. The ordering of the refinement steps is not importnt; either the subset bsed on the stereotype or on the context my be performed first. Allowing Disposition to influence Phrse Selection Disposition refers to nturl tendency or predilection towrds doing something or cting in prticulr wy. We cn imbue the robot with prticulr type of disposition by hving it prefer one type of ction selection strtegy over nother. Outcome mtrices fford severl simple ction selection strtegies. The most obvious method is to choose the ction tht mximizes the robot s own outcome. This strtegy is termed mx_own. A robot s use of the mx_own strtegy over the course of mny interctions results in egoistic disposition the robot tends to do wht is best for itself without regrd to others. Alterntively, the robot my select the ction tht mximizes its prtner s outcome, strtegy termed mx_other. A robot s use of the mx_other strtegy results in n ltruistic disposition. Yet nother ction selection strtegy is for the robot to select the ction tht mximizes the sum of its nd its prtner s outcome (mx_joint). The use of this strtegy results in coopertive disposition. The min_diff ction selection strtegy, on the other hnd, selects the ction tht minimizes the difference in outcome between the robot nd the humn, resulting in fir or just disposition. Outcome mtrices fford mny other simple ction selection strtegies (see (Wgner, The Role of Trust nd Reltionships in Humn-Robot Socil Interction, 00) for other exmples). Figure depicts n exmple in which the robot is sked question. Six different phrses re vilble s response. For this exmple, the robot s disposition uniquely determines the phrse tht the robot selects. If the robot s disposition is mlevolent, then the robot chooses the min_other ction selection strtegy resulting in the selection of the phrse No, I won t let you succeed. If the robot s disposition is competitive then the robot selects the mx_diff ction selection strtegy resulting in the selection of the phrse No, but I ll help myself. Figure depicts severl other exmples.
Interdependence Spce Informtion In previous work, we presented sitution nlysis lgorithm tht clculted chrcteristics of the socil sitution or interction (such s interdependence) when presented with n outcome mtrix (Wgner & Arkin, Anlyzing Socil Situtions for Humn-Robot Interction, 008). The interdependence spce is four-dimensionl spce which mps the loction of ll interpersonl socil situtions (Kelley, Holmes, Kerr, Reis, Rusbult, & Vn Lnge, 00). A mtrix s loction in interdependence spce provides importnt informtion relting to the interction. The interdependence, correspondence, nd symmetry dimensions my be of prticulr importnce for phrse selection. The interdependence dimension mesures the extent to which ech individul s outcomes re influenced by the other individul s ctions in sitution. In low interdependence sitution, for exmple, ech individul s outcomes re reltively independent of the other individul s choice of interctive behvior (Figure left for exmple). A high interdependence sitution, on the other hnd, is sitution in which ech individul s outcomes lrgely depend on the ction of the other individul (Figure right for exmple). Correspondence describes the extent to which the outcomes of one individul in sitution re consistent with the outcomes of the other individul. If outcomes correspond then individuls tend to select interctive behviors resulting in mutully rewrding outcomes, such s temmtes in gme. If outcomes conflict then individuls tend to select interctive behviors resulting in mutully costly outcomes, such s opponents in gme. Symmetry refers to the blnce of control tht one individul hs over nother s outcomes. In symmetric sitution both individuls hve equl bility to impct the other person s outcomes. In n symmetric sitution, on the other hnd, one individul hs significntly more control over the other person s outcomes. Our results showed tht by nlyzing the interction, the robot could better select interctive ctions (Wgner & Arkin, Anlyzing Socil Situtions for Humn-Robot Interction, 008). Anlysis with respect to the interdependence spce, which we cll sitution nlysis, is nother source of potentilly vluble informtion for phrse selection. In this cse, the interction s loction in interdependence spce could serve to influence chrcteristics of the phrse, such s tone, tht is selected. For exmple, in n symmetric sitution the person in control my select more demnding stnce in the converstion. The person being controlled would likely ssume less demnding stnce. Figure 4 presents exmples of chnges in tone tht occur when the sitution is locted t different res of the interdependence spce. Interdependence Spce Informtion for Phrse Selection High Interdependence Concerned tone Csul tone Low Interdependence Asymmetric Symmetric Figure 4 Exmples of how the tone of phrse might be influenced by chnges in interdependence spce dimension. For exmple, s the interdependence spce dimension goes to symmetric the tone of the phrse could become more demnding. Summry nd Conclusions Demnding tone Friendly tone This rticle hs presented method for using outcome mtrices for socil phrse selection. Typiclly outcome mtrices represent socil decision problem in which both individuls select mong different socil ctions. In the work presented here these socil ctions re replced with phrses. Ech phrse in the mtrix includes outcome vlues indicting the chnge in influence tht speking the phrse would hve on both gents. A method by which universl set of phrses cn be reduced to subset pproprite for the context nd the interctive prtner hs lso been outlined. We hve discussed technique for using stereotypes to select phrses bsed on ctegories of individuls, the inclusion of disposition in phrse selection, nd the use of interdependence spce informtion. Mny of the methods tht hve been presented re preliminry in the sense tht they hve yet to be fully tested on n implemented system. Additionlly, it is uncler if nd how well this pproch would scle to more dynmic nd complex socil systems. The described system, for instnce, relies on predetermined set of phrses. Lerning of new phrses might be ccomplished by directly copying sttements mde by the humn nd incorporting these sttements into the robot s universl set of phrses. Instntneous phrse construction is not ddressed nd would likely be n importnt nd necessry prt of system tsked with mnging open ended dilog. Still, it is potentilly interesting question, how fr the described system would go towrds relistic dilog with
humn. Even prtil system my llow the robot to interct in more relistic mnner. Potentil pplictions of the system might include socil robot tht ugments its existing socil behvior with occsionl phrses. Future work will focus on sclbility nd the development of pplictions bsed on limited set of phrses. Interctive Computing, Georgi Institute of Technology, Atlnt, GA. Wgner, A. R., & Arkin, R. C. (008). Anlyzing Socil Situtions for Humn-Robot Interction. Interction Studies, 0 (). References Cho, C., & Thomz, A. L. (00). Turn Tking for Humn- Robot Interction. AAAI 00 Fll Symposium Workshop. Arlington, VA. Chuhn, A., & Lopes, L. S. (00). Acquiring Vocbulry through Humn Robot Interction: A Lerning Architecture for Grounding Words with Multiple Menings. AAAI 00 Fll Symposium Workshop. Arlington, VA. Gibbons, R. (). Gme Theory for Applied Economists. Princeton, NJ: Princeton University Press. Iwhshi, N., Sugiur, K., Tguchi, R., Ngl, T., & Tniguchi, T. (00). Robots tht Lern to Communicte: A Developmentl Approch to Personlity nd Physiclly Situted Humn-Robot Converstions. AAAI 00 Fll Symposium Workshop. Arlington, VA. Kelley, H. H., Holmes, J. G., Kerr, J. G., Reis, H. T., Rusbult, C. E., & Vn Lnge, P. A. (00). An Atls of Interpersonl Situtions. New York, NY: Cmbridge University Press. Kelly, H. H., & Thibut, J. W. (8). Interpersonl Reltions: A Theory of Interdependence. New York, NY: John Wiley & Sons. Osborne, M. J., & Rubinstein, A. (4). A Course in Gme Theory. Cmbridge, MA: MIT Press. Petrosino, A., & Gold, K. (00). Towrd Fst Mpping for Robot Adjective Lerning. AAAI 00 Fll Symposium Workshop. Arlington, VA. Rusbult, C. E., & Vn Lnge, P. A. (00). Interdependence, Interction, nd Reltionships. Annul Review of Psychology, 54, 5-5. Scheutz, M., Schermerhorn, P., & Krmer, J. (006). First Steps towrd Nturl Humn-Like HRI. Humn-Robot Interction (HRI 006). Slt Lke City, Uth. Sers, D. O., Peplu, L. A., & Tylor, S. E. (). Socil Psychology. Englewood Cliffs, New Jersey: Prentice Hll. Skubic, M., Perznowski, D., Schultz, A., & Adms, W. (00). Using Sptil Lnguge in Humn-Robot Dilog. Proceedings of the Interntionl Conference on Robotics nd Automtion (ICRA 00). Wshington, DC. Spiliotopoulos, D., & etl. (00). Humn robot interction bsed on spoken nturl lnguge dilogue. Proceedings of the Europen Workshop on Service nd Humnoid Robots. Wgner, A. R. (00). Creting nd Using Mtrix Representtions of Socil Interction. Humn-Robot Interction (HRI). Sn Diego, CA. Wgner, A. R. (00). Extended Abstrct: Using Stereotypes to Understnd One's Interctive Prtner. Interntionl Conference on Autonomous Agents nd Multigent Systems (AAMAS 00). Toronto, Cnd. Wgner, A. R. (00). The Role of Trust nd Reltionships in Humn-Robot Socil Interction. Ph.D. diss., School of