In this work, we study probability functions associated with Gaussian mixture models. Our primary focus is on extending the use of spherical radial decomposition for multivariate Gaussian random vectors to the context of Gaussian mixture models, which are not inherently spherical but only conditionally so. Specifically, the conditional probability distribution, given a random parameter of the random vector, follows a Gaussian distribution, allowing us to apply Bayesian analysis tools to the probability function. This assumption, together with spherical radial decomposition for Gaussian random vectors, enables us to represent the probability function as an integral over the Euclidean sphere. Using this representation, we establish sufficient conditions to ensure the differentiability of the probability function and provide and integral representation of its gradient. Furthermore, leveraging the Bayesian decomposition, we approximate the probability function using random sampling over the parameter space and the Euclidean sphere. Finally, we present numerical examples that illustrate the advantages of this approach over classical approximations based on random vector sampling.

The non-convex nature of trained neural networks has created significant obstacles in their incorporation into optimization models. Considering the wide array of applications that this embedding has, the optimization and deep learning communities have dedicated significant efforts to the convexification of trained neural networks. Many approaches to date have considered obtaining convex relaxations for each non-linear activation in isolation, which poses limitations in the tightness of the relaxations. Anderson et al. (2020) strengthened these relaxations and provided a framework to obtain the convex hull of the graph of a piecewise linear convex activation composed with an affine function; this effectively convexifies activations such as the ReLU together with the affine transformation that precedes it. In this article, we contribute to this line of work by developing a recursive formula that yields a tight convexification for the composition of an activation with an affine function for a wide scope of activation functions, namely, convex or ``S-shaped". Our approach can be used to efficiently compute separating hyperplanes or determine that none exists in various settings, including non-polyhedral cases. We provide computational experiments to test the empirical benefits of these convex approximations.

The use of Mixed-Integer Linear Programming (MILP) models to represent neural networks with Rectified Linear Unit (ReLU) activations has become increasingly widespread in the last decade. This has enabled the use of MILP technology to test--or stress--their behavior, to adversarially improve their training, and to embed them in optimization models leveraging their predictive power. Many of these MILP models rely on activation bounds. That is, bounds on the input values of each neuron. In this work, we explore the tradeoff between the tightness of these bounds and the computational effort of solving the resulting MILP models. We provide guidelines for implementing these models based on the impact of network structure, regularization, and rounding.

Dealing with uncertainty in optimization parameters is an important and longstanding challenge. Typically, uncertain parameters are predicted accurately, and then a deterministic optimization problem is solved. However, the decisions produced by this so-called \emph{predict-then-optimize} procedure can be highly sensitive to uncertain parameters. In this work, we contribute to recent efforts in producing \emph{decision-focused} predictions, i.e., to build predictive models that are constructed with the goal of minimizing a \emph{regret} measure on the decisions taken with them. We formulate the exact expected regret minimization as a pessimistic bilevel optimization model. Then, using duality arguments, we reformulate it as a non-convex quadratic optimization problem. Finally, we show various computational techniques to achieve tractability. We report extensive computational results on shortest-path instances with uncertain cost vectors. Our results indicate that our approach can improve training performance over the approach of Elmachtoub and Grigas (2022), a state-of-the-art method for decision-focused learning.

We address the challenge of reliable and accurate proprioception in soft robots, specifically those with tight packaging constraints and relying only on internally embedded sensors. While various sensing approaches with single sensors have been tried, often with a constant curvature assumption, we look into sensing local deformations at multiple locations of the sensor. In our approach, we multi-tap an off-the-shelf resistive sensor by creating multiple electrical connections onto the resistive layer of the sensor and we insert the sensor into a soft body. This modification allows us to measure changes in resistance at multiple segments throughout the length of the sensor, providing improved resolution of local deformations in the soft body. These measurements inform a model based on a finite element method (FEM) that estimates the shape of the soft body and the magnitude of an external force acting at a known arbitrary location. Our model-based approach estimates soft body deformation with approximately 3% average relative error while taking into account internal fluidic actuation. Our estimate of external force disturbance has an 11% relative error within a range of 0 to 5 N. The combined sensing and modeling approach can be integrated, for instance, into soft manipulation platforms to enable features such as identifying the shape and material properties of an object being grasped. Such manipulators can benefit from the inherent softness and compliance while being fully proprioceptive, relying only on embedded sensing and not on external systems such as motion capture. Such proprioception is essential for the deployment of soft robots in real-world scenarios.

We study the problem of learning the preferences of drivers and planners in the context of last mile delivery. Given a data set containing historical decisions and delivery locations, the goal is to capture the implicit preferences of the decision-makers. We consider two ways to use the historical data: one is through a probability estimation method that learns transition probabilities between stops (or zones). This is a fast and accurate method, recently studied in a VRP setting. Furthermore, we explore the use of machine learning to infer how to best balance multiple objectives such as distance, probability and penalties. Specifically, we cast the learning problem as a structured output prediction problem, where training is done by repeatedly calling the TSP solver. Another important aspect we consider is that for last-mile delivery, every address is a potential client and hence the data is very sparse. Hence, we propose a two-stage approach that first learns preferences at the zone level in order to compute a zone routing; after which a penalty-based TSP computes the stop routing. Results show that the zone transition probability estimation performs well, and that the structured output prediction learning can improve the results further. We hence showcase a successful combination of both probability estimation and machine learning, all the while using standard TSP solvers, both during learning and to compute the final solution; this means the methodology is applicable to other, real-life, TSP variants, or proprietary solvers.

The graph represents a network of 1,263 Twitter users whose tweets in the requested range contained "#cloudcomputing", or who were replied to or mentioned in those tweets. The network was obtained from the NodeXL Graph Server on Monday, 11 October 2021 at 14:39 UTC. The requested start date was Monday, 11 October 2021 at 00:01 UTC and the maximum number of days (going backward) was 14. The maximum number of tweets collected was 7,500. The tweets in the network were tweeted over the 2-day, 23-hour, 26-minute period from Friday, 08 October 2021 at 00:29 UTC to Sunday, 10 October 2021 at 23:56 UTC.

But more often, the objective involves multiple criteria including not only the total distance of the tour but also other factors such as travel costs, travel time, and fuel consumption. Moreover, in reality, there are numerous implicit preferences ingrained in the minds of the route planners and the drivers. Drivers, for instance, have familiarity with certain neighborhoods and knowledge of the state of roads, and often consider the best places for rest and lunch breaks. This knowledge is difficult to formulate and balance when operational routing decisions have to be made. This motivates us to learn the implicit preferences from past solutions and to incorporate these learned preferences in the optimization process. These preferences are in the form of arc probabilities, i.e., the more preferred a route is, the higher is the joint probability. The novelty of this work is the use of a neural network model to estimate the arc probabilities, which allows for additional features and automatic parameter estimation. This first requires identifying suitable features, neural architectures and loss functions, taking into account that there is typically few data available. We investigate the difference with a prior weighted Markov counting approach, and study the applicability of neural networks in this setting.

Theoretical computer science is everywhere, for TCS is concerned with the foundations of computing and computing is everywhere! In the last three decades, a vibrant Latin American TCS community has emerged: here, we describe and celebrate some of its many noteworthy achievements. Computer science became a distinct academic discipline in the 1950s and early 1960s. The first CS department in the U.S. was formed in 1962, and by the 1970s virtually every university in the U.S. had one. In contrast, by the late 1970s, just a handful of Latin American universities were actively conducting research in the area. Several CS departments were eventually established during the late 1980s. Often, theoreticians played a decisive role in the foundation of these departments. One key catalyst in articulating collaborations among the few but growing number of enthusiastic theoreticians who were active in the international academic arena was the foundation of regional conferences.

Just getting workers to the office can be a challenge, amid ongoing travel restrictions aimed at containing the pandemic, said Gaston Silva Maldonado, project and systems analyst at Chilean food processor giant Agrosuper SA. "Our employees have been prevented from moving from one city to another, or even from one point of the city to another," Mr. Maldonado said, citing local lockdown rules. Based in Rancagua, Agrosuper employs about 3,500 office workers, in addition to thousands more in its production plants. So far, he said, only administrative staff and production plant workers deemed essential have returned to the workplace. With the Chilean government in July announcing a five-week plan to gradually ease travel restrictions within the country, the company is hoping to bring back more in the weeks ahead. To do that, Agrosuper has started using robotic process automation to scan and relay employment data on its more than 12,000 workers to a government website that issues emergency travel passes required at health checkpoints scattered throughout the country.