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.

Parameter Inference for Computational Cognitive Models with Approximate Bayesian Computation

“…Said et al. () optimized the performance of an ACT‐R model with different methods, and Nelder–Mead was one of the best‐performing methods. Logačev and Vasishth () optimized the parameters of a sentence parsing model using Nelder–Mead.…”

“…Vandekerckhove and Tuerlinckx (2007) optimized the parameters of the Ratcliff diffusion model using Nelder-Mead. Said et al (2016) optimized the performance of an ACT-R model with different methods, and Nelder-Mead was one of the best-performing methods. Loga cev and Vasishth (2016) optimized the parameters of a sentence parsing model using Nelder-Mead.…”

“…For example, Anderson, Reder, and Lebiere (1996) investigated the effect of various parameter values on the overall model fit by performing sensitivity analysis, where they manipulated the model parameters one by one and demonstrated how the model fit changes. There is also a recent line of research focused on constructing fully analytic ACT-R models (Said et al, 2016), which could allow more efficient parameter inference using, for example, gradient-based methods. Some recent ACT-R studies have also used neuroimaging data to isolate active mental stages during task completion and used these measurements to infer specific model parameters (Anderson & Fincham, 2014a;Zhang, Walsh, & Anderson, 2016).…”

“…Papers have pointed out different issues with the parameter inference methods used with cognitive models. One issue that has been raised is the fact that manual parameter tuning is still commonly used instead of automatic parameter inference methods (Lane & Gobet, 2013;Raymond, Fornberg, Buck-Gengler, Healy, & Bourne, 2008;Said, Engelhart, Kirches, K€ orkel, & Holt, 2016). Another issue has been the fact that the most basic automatic inference methods might either not be efficient enough or be unable to visualize the model fit over the parameter space (Gluck, Stanley, Moore, Reitter, & Halbr€ ugge, 2010;Moore, 2011).…”

“…In general, it would be preferable to use principled approaches that are well motivated from a theoretical standpoint, and even offer general performance guarantees. Also, some of these approaches, such as mathematical programming (Said et al., ), require altering or rewriting the model to match the assumptions of the inference method. It would be preferable to have approaches that are generally applicable for any computational cognitive model, such that the inference procedure does not force limitations to the model structure, and that alterations to the model do not necessitate alterations to the inference procedures as well.…”