title: Applying Mathematical Optimization Methods to an ACT-R Instance-Based Learning Model.
abstract: Computational models of cognition provide an interface to connect advanced mathematical tools and methods to empirically supported theories of behavior in psychology, cognitive science, and neuroscience. In this article, we consider a computational model of instance-based learning, implemented in the ACT-R cognitive architecture. We propose an approach for obtaining mathematical reformulations of such cognitive models that improve their computational tractability. For the well-established Sugar Factory dynamic decision making task, we conduct a simulation study to analyze central model parameters. We show how mathematical optimization techniques can be applied to efficiently identify optimal parameter values with respect to different optimization goals. Beyond these methodological contributions, our analysis reveals the sensitivity of this particular task with respect to initial settings and yields new insights into how average human performance deviates from potential optimal performance. We conclude by discussing possible extensions of our approach as well as future steps towards applying more powerful derivative-based optimization methods.
authors.affiliation: Institute of Psychology, Heidelberg University, Hauptstr. 47-51, 69117 Heidelberg, Germany.|Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany.
authors.forename: Nadia
authors.initials: N
authors.lastname: Said
authors.affiliation: Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany.
authors.forename: Michael
authors.initials: M
authors.lastname: Engelhart
authors.affiliation: Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany.
authors.forename: Christian
authors.initials: C
authors.lastname: Kirches
authors.affiliation: Interdisciplinary Center for Scientific Computing (IWR), Heidelberg University, Im Neuenheimer Feld 205, 69120 Heidelberg, Germany.
authors.forename: Stefan
authors.initials: S
authors.lastname: Körkel
authors.affiliation: Institute of Psychology, Heidelberg University, Hauptstr. 47-51, 69117 Heidelberg, Germany.
authors.forename: Daniel V
authors.initials: DV
authors.lastname: Holt
mesh_terms: D000465:Algorithms; D003071:Cognition; D019336:Cognitive Science / Q000379:methods*; D003198:Computer Simulation; D003657:Decision Making; D006801:Humans; D007858:Learning; D008433:Mathematics; D009488:Neurosciences