We introduce a framework to study the transformation of problems with manifold constraints into unconstrained problems through parametrizations in terms of a Euclidean space. We call these parametrizations "trivializations". We prove conditions under which a trivialization is sound in the context of gradient-based optimization and we show how two large families of trivializations have overall favorable properties, but also suffer from a performance issue. We then introduce "dynamic trivializations", which solve this problem, and we show how these form a family of optimization methods that lie between trivializations and Riemannian gradient descent, and combine the benefits of both of them. We then show how to implement these two families of trivializations in practice for different matrix manifolds. To this end, we prove a formula for the gradient of the exponential of matrices, which can be of practical interest on its own. Finally, we show how dynamic trivializations improve the performance of existing methods on standard tasks designed to test long-term memory within neural networks.

Metaheuristic algorithms (MAs) have seen unprecedented growth thanks to their successful applications in fields including engineering and health sciences. In this work, we investigate the use of a deep learning (DL) model as an alternative tool to do so. The proposed method, called MaNet, is motivated by the fact that most of the DL models often need to solve massive nasty optimization problems consisting of millions of parameters. Feature selection is the main adopted concepts in MaNet that helps the algorithm to skip irrelevant or partially relevant evolutionary information and uses those which contribute most to the overall performance. The introduced model is applied on several unimodal and multimodal continues problems. The experiments indicate that MaNet is able to yield competitive results compared to one of the best hand-designed algorithms for the aforementioned problems, in terms of the solution accuracy and scalability.

Differentiable Architecture Search (DARTS) has attracted a lot of attention due to its simplicity and small search costs achieved by a continuous relaxation and an approximation of the resulting bi-level optimization problem. However, DARTS does not work robustly for new problems: we identify a wide range of search spaces for which DARTS yields degenerate architectures with very poor test performance. We study this failure mode and show that, while DARTS successfully minimizes validation loss, the found solutions generalize poorly when they coincide with high validation loss curvature in the space of architectures. We show that by adding one of various types of regularization we can robustify DARTS to find solutions with smaller Hessian spectrum and with better generalization properties. Based on these observations we propose several simple variations of DARTS that perform substantially more robustly in practice. Our observations are robust across five search spaces on three image classification tasks and also hold for the very different domains of disparity estimation (a dense regression task) and language modelling. We provide our implementation and scripts to facilitate reproducibility.

Bike Sharing Systems (BSSs) have been adopted in many major cities of the world due to traffic congestion and carbon emissions. Although there have been approaches to exploiting either bike trailers via crowdsourcing or carrier vehicles to reposition bikes in the "right" stations in the "right" time, they do not jointly consider the usage of both bike trailers and carrier vehicles. In this paper, we aim to take advantage of both bike trailers and carrier vehicles to reduce the loss of demand with regard to the crowdsourcing of bike trailers and the fuel cost of carrier vehicles. In the experiment, we exhibit that our approach outperforms baselines in several datasets from bike sharing companies. Introduction Bike sharing systems (BSSs) typically have a set of base stations that are strategically placed throughout a city and each station has a fixed number of docks, e.g., Capital Bike-share 1, Bluebikes 2, Mobike 3, BIXI 4, etc. At the beginning of the day, each station is stocked with a predetermined number of bikes. Customers can pick and drop bikes from any station and are charged depending on the hiring duration (Tsai, Chen, and Hong 2019; Hulot, Aloise, and Jena 2018; Lowalekar et al. 2017; Vulcano, van Ryzin, and Ratliff 2012; Schuijbroek, Hampshire, and van Hoeve 2017). Due to the individualistic and uncoordinated movements of customers, there is often starvation (empty base stations precluding bike pickup) or congestion (full base stations precluding bike return) of bikes at certain stations, which results in a significant loss of customer demand (Shu et al. 2013; Chen, Liu, and Liu 2018). To address this problem, a variety of systems (Ghosh et al. 2017; Lowalekar et al. 2017) employ the idea of repositioning idle bikes with the help of carrier vehicles during the day, by taking into account the movement of bikes by customers (Tsai, Chen, and Hong 2019; Pfrommer et al. 2014; Ghosh and V arakantham 2017).

Create optimization models using general programming language APIs or Open Programming Language (OPL) to solve the breadth of optimization models.

In this work, we address the scenario in which the target domain is continually, albeit slowly, evolving, and in which, at different time frames, we are given a batch of test data to classify. We exploit the geometry-awareness that optimal transport offers for the resolution of continuous domain adaptation problems. We propose a regularized optimal transport model that takes into account the transportation cost, the entropy of the probabilistic coupling, the labels of the source domain, and the similarity between successive target domains. The resulting optimization problem is efficiently solved with a forward-backward splitting algorithm based on Bregman distances. Experiments show that the proposed approach leads to a significant improvement in terms of speed and performance with respect to the state of the art.

We consider learning problems of an intuitive and concise preference model, called lexicographic preference lists (LP-lists). Given a set of examples that are pairwise ordinal preferences over a universe of objects built of attributes of discrete values, we want to learn (1) an optimal LP-list that decides the maximum number of these examples, or (2) a near-optimal LP-list that decides as many examples as it can. To this end, we introduce a dynamic programming based algorithm and a genetic algorithm for these two learning problems, respectively. Furthermore, we empirically demonstrate that the sub-optimal models computed by the genetic algorithm very well approximate the de facto optimal models computed by our dynamic programming based algorithm, and that the genetic algorithm outperforms the baseline greedy heuristic with higher accuracy predicting new preferences.

A lot of real-world applications could be modeled as the Mixed-Integer Non-Linear Programming (MINLP) problems, and some prominent examples include portfolio optimization, resource allocation, image classification, as well as path planning. Actually, most of the models for these applications are non-convex and always involve some conflicting objectives. Hence, the Multi-Objective Evolutionary Algorithm (MOEA), which does not require the gradient information and is efficient at dealing with the multi-objective optimization problems, is adopted frequently for these problems. In this work, we discuss the coding scheme for MOEA in MINLP, and the major discussion focuses on the constrained portfolio optimization problem, which is a classic financial problem and could be naturally modeled as MINLP. As a result, the challenge, faced by a direct coding scheme for MOEA in MINLP, is pointed out that the searching in multiple search spaces is very complicated. Thus, a Compressed Coding Scheme (CCS), which converts an MINLP problem into a continuous problem, is proposed to address this challenge. The analyses and experiments on 20 portfolio benchmark instances, of which the number of available assets ranging from 31 to 2235, consistently indicate that CCS is not only efficient but also robust for dealing with the constrained multi-objective portfolio optimization.

In medical decision making, we have to choose among several expensive diagnostic tests such that the certainty about a patient's health is maximized while remaining within the bounds of resources like time and money. The expected increase in certainty in the patient's condition due to performing a test is called the value of information (VoI) for that test. In general, VoI relates to acquiring additional information to improve decision-making based on probabilistic reasoning in an uncertain system. This paper presents a framework for acquiring information based on VoI in uncertain systems modeled as Probabilistic Logic Programs (PLPs). Optimal decision-making in uncertain systems modeled as PLPs have already been studied before. But, acquiring additional information to further improve the results of making the optimal decision has remained open in this context. We model decision-making in an uncertain system with a PLP and a set of top-level queries, with a set of utility measures over the distributions of these queries. The PLP is annotated with a set of atoms labeled as "observable"; in the medical diagnosis example, the observable atoms will be results of diagnostic tests. Each observable atom has an associated cost. This setting of optimally selecting observations based on VoI is more general than that considered by any prior work. Given a limited budget, optimally choosing observable atoms based on VoI is intractable in general. We give a greedy algorithm for constructing a "conditional plan" of observations: a schedule where the selection of what atom to observe next depends on earlier observations. We show that, preempting the algorithm anytime before completion provides a usable result, the result improves over time, and, in the absence of a well-defined budget, converges to the optimal solution.

Often, when modeling human decision-making behaviors in th e context of human-robot teaming, the emotion aspect of human is ignored. Nevertheless, the influence of em otion, in some cases, is not only undeniable but beneficial. This work studies the humanlike characteristics brought b y regret emotion in one-human-multi-robot teaming for the application of domain search. In such application, the task management load is outsourced to the robots to reduce the human's workload, freeing the human to do more important work. The regret decision model is first used by each robot for deciding whether to request human service, th en is extended for optimally queuing the requests from multiple robots. For the movement of the robots in the domain search, we designed a path planning algorithm based on dynamic programming for each robot. The simulation shows that the humanlike characteristics, namely, risk-seeking and risk-aversion, indeed bring some appealing eff ects for balancing the workload and performance in the human-multi-robot team.