Control Engineering Methods for the Design of Robust Behavioral Treatments

Abstract

In this paper, a robust control approach is used to address the problem of adaptive behavioral treatment design. Human behavior (e.g., smoking and exercise) and reactions to treatment are complex and depend on many unmeasurable external stimuli, some of which are unknown. Thus, it is crucial to model human behavior over many subject responses. We propose a simple (low order) uncertain affine model subject to uncertainties whose response covers the most probable behavioral responses. The proposed model contains two different types of uncertainties: uncertainty of the dynamics and external perturbations that patients face in their daily life. Once the uncertain model is defined, we demonstrate how least absolute shrinkage and selection operator (lasso) can be used as an identification tool. The lasso algorithm provides a way to directly estimate a model subject to sparse perturbations. With this estimated model, a robust control algorithm is developed, where one relies on the special structure of the uncertainty to develop efficient optimization algorithms. This paper concludes by using the proposed algorithm in a numerical experiment that simulates treatment for the urge to smoke.

System Identification Algorithm for Non-Uniformly Sampled Data

“…However, dynamical modeling allows researchers to inform development of a person-based intervention instead of finding a generalized treatment. Clinicians could design a personalized treatment for each patient (e.g., using model predictive control, as in Bekiroglu et al (2016)) if its dynamical model is known. On the other hand, as mentioned in the introduction, most behavioral data have some remarkable challenges for system identification.…”

“…One of the major problems in the modeling of behavioral processes is defining the inputs and outputs. In the literature, treatments are usually assumed to be an input, and then the effects of this input can be measured with different outcomes (i.e., Bekiroglu et al (2016) and references therein). Therefore, in this paper we assumed that the treatment is given constantly (step) as an input for this specific patient and the effects of the treatment is measured on craving with a single item on an 11-point response scale (e.g.…”

“…Moreover some more recent applications, such as the design of medical/behavioral treatment Bekiroglu et al (2016); Lagoa et al (2014), have significant challenges that can only be effectively addressed by using continuous time models. For instance, the behavioral process data sets (e.g.…”

“…For instance, the behavioral process data sets (e.g. Bekiroglu et al (2016); Lagoa et al (2014)), measured with ecological momentary assessment (EMA), contain a significant amount of noise and non-uniform samples. Since, to develop efficient personalized treatments, one needs a model that approximates subject behavior, there is a need for the development of system identification algorithms that can accommodate noisy, sparse, non-uniform measurements.…”

“…The second assumption is only needed for developing efficient closed form expressions of some quantities used in the algorithm. Note that the second assumption is not restrictive since in many settings (including, for example, medical/behavioral treatment studies) the inputs are low complex ones such as combinations of steps and/ or impulses; e.g., see Bekiroglu et al (2016); Lagoa et al (2014). Finally, we propose a randomized Frank-Wolfe algorithm to efficiently solve the resulting optimizations problems.…”