2 research outputs found
You Are What You Eat: A Preference-Aware Inverse Optimization Approach
A key challenge in the emerging field of precision nutrition entails
providing diet recommendations that reflect both the (often unknown) dietary
preferences of different patient groups and known dietary constraints specified
by human experts. Motivated by this challenge, we develop a preference-aware
constrained-inference approach in which the objective function of an
optimization problem is not pre-specified and can differ across various
segments. Among existing methods, clustering models from machine learning are
not naturally suited for recovering the constrained optimization problems,
whereas constrained inference models such as inverse optimization do not
explicitly address non-homogeneity in given datasets. By harnessing the
strengths of both clustering and inverse optimization techniques, we develop a
novel approach that recovers the utility functions of a constrained
optimization process across clusters while providing optimal diet
recommendations as cluster representatives. Using a dataset of patients' daily
food intakes, we show how our approach generalizes stand-alone clustering and
inverse optimization approaches in terms of adherence to dietary guidelines and
partitioning observations, respectively. The approach makes diet
recommendations by incorporating both patient preferences and expert
recommendations for healthier diets, leading to structural improvements in both
patient partitioning and nutritional recommendations for each cluster. An
appealing feature of our method is its ability to consider infeasible but
informative observations for a given set of dietary constraints. The resulting
recommendations correspond to a broader range of dietary options, even when
they limit unhealthy choices
Inverse Learning: A Data-driven Framework to Infer Optimizations Models
We consider the problem of inferring optimal solutions and unknown parameters
of a partially-known constrained problem using a set of past decisions. We
assume that the constraints of the original optimization problem are known
while optimal decisions and the objective are to be inferred. In such
situations, the quality of the optimal solution is evaluated in relation to the
existing observations and the known parameters of the constrained problem. A
method previously used in such settings is inverse optimization. This method
can be used to infer the utility functions of a decision-maker and to find
optimal solutions based on these inferred parameters indirectly. However,
little effort has been made to generalize the inverse optimization methodology
to data-driven settings to address the quality of the inferred optimal
solutions. In this work, we present a data-driven inverse linear optimization
framework (Inverse Learning) that aims to infer the optimal solution to an
optimization problem directly based on the observed data and the existing known
parameters of the problem. We validate our model on a dataset in the diet
recommendation problem setting to find personalized diets for prediabetic
patients with hypertension. Our results show that our model obtains optimal
personalized daily food intakes that preserve the original data trends while
providing a range of options to patients and providers. The results show that
our proposed model is able to both capture optimal solutions with minimal
perturbation from the given observations and, at the same time, achieve the
inherent objectives of the original problem. We show an inherent trade-off in
the quality of the inferred solutions with different metrics and provide
insights into how a range of optimal solutions can be inferred in constrained
environments