Analyzing Abstraction and Hierarchical Decision-Making in Absolute Identification by Information-Theoretic Bounded Rationality

Abstract

In the face of limited computational resources, bounded rational decision theory predicts that information-processing should be concentrated on actions that make a significant contribution in terms of the utility achieved. Accordingly, information-processing can be simplified by choosing stereotypic actions that lead to satisfactory performance over a range of different inputs rather than choosing a specific action for each input. Such a set of similar inputs with similar action responses would then correspond to an abstraction that can be harnessed with possibly negligible loss in utility, but with potentially considerable savings in information-processing effort. Here we test this prediction in an identification task, where human subjects were asked to estimate the roundness of ellipses varying from a straight line to a perfect circle. Crucially, when reporting their estimates, subjects could choose between three different levels of precision corresponding to three levels of abstraction in a decision-making hierarchy. To induce changes in level selection, we manipulated the information-processing resources available at the perceptual and action stages by varying the difficulty of identifying the stimulus and by enforcing different response times in the action stage. In line with theoretical predictions, we find that subjects adapt their abstraction level depending on the available resources. We compare subjects' behavior to the maximum efficiency predicated by the bounded rational decision-making model and investigate possible sources of inefficiency.

The two kinds of free energy and the Bayesian revolution

“…While the reference function in (25) is already completely specified, we still need to know how to determine the value function Q in the case of (24). For the partial mean-field assumption (23) it is defined in the literature [99,100] as QðaÞ ≔ hUðX 0 ; S 0 Þi qðX 0 ;S 0 jA ¼ aÞ þ HðqðX 0 jA ¼ aÞÞ;…”

“…Once the form of the trial distributions q-e.g., by a partial mean-field assumption (23) or a Bethe approximation (see S1 Appendix)-and the reference ϕ are defined, the variational free energy is simply determined by F(qkϕ). In the case of a meanfield assumption, the resulting free energy minimization problem is solved approximately by performing an alternating optimization scheme, in which the variational free energy is minimized separately with respect to each of the variable factors in a factorization of q, for example by alternating between min q(S) F, min q(S 0 |A) F, and min q(A) F in the case of the partial meanfield assumption (23), where in each step the factors that are not optimized are kept fixed (cf. Fig 7).…”

“…Moreover, the free energy trade-off can also be used to describe networks of agents, where each agent is limited in its ability, but the system as a whole has a higher information processing capacity—for example, neurons in a brain or humans in a group. In such systems different levels of abstraction arise depending on the different positions of decision-makers in the network [ 23 , 71 , 85 ]. As we have discussed in Section 4.3, just like coding and rate-distortion theory, utility theory with information costs can only provide optimality bounds but does not specify any particular mechanism of how to achieve optimality.…”

“…In the economic literature, for example, trade-offs between utility and entropic uncertainty measures that take the form of free energies have been proposed to describe decisionmakers with stochastic choice behavior due to limited resources [10][11][12][13][14] or robust decisionmakers with limited precision in their models [15,16]. The free energy trade-off between entropy and reward can also be found in information-theoretic models of biological perception-action systems [17][18][19], some of which have been subjected to experimental testing [20][21][22][23][24][25]. Finally, in the neuroscience literature the notion of free energy has risen to recent fame as the central puzzle piece in the Free Energy Principle [26] that has been used to explain a cornucopia of experimental findings including neural prediction error signals [27], synaptic plasticity rules [28], neural effects of biased competition and attention [29,30], visual exploration in humans [31], and more-see the references in [32].…”

Nash equilibria in human sensorimotor interactions explained by Q-Learning

“…Such an implicit information penalization of action policies can be regarded as a form of bounded rational decision-making, where decision-makers trade off between utility and information costs that are required to achieve a certain level of precision [45][46][47] . Such information costs have been previously suggested to model costs of motor planning and abstraction 48,49 . Another form of limited information-processing capability is subjects' limited sensory precision regarding the perception of force, that we have modeled by assuming Gaussian sensory noise corresponding ten percent of the workspace 50,51 .…”