Conic optimization has recently emerged as a powerful tool for designing tractable and guaranteed algorithms for non-convex polynomial optimization problems. On the one hand, tractability is crucial for efficiently solving large-scale problems and, on the other hand, strong bounds are needed to ensure high quality solutions. In this research, we investigate the strengthening of RLT relaxations of polynomial optimization problems through the addition of nine different types of constraints that are based on linear, second-order cone, and semidefinite programming to solve to optimality the instances of well established test sets of polynomial optimization problems. We describe how to design these conic constraints and their performance with respect to each other and with respect to the standard RLT relaxations. Our first finding is that the different variants of nonlinear constraints (second-order cone and semidefinite) are the best performing ones in around $50\%$ of the instances. Additionally, we present a machine learning approach to decide on the most suitable constraints to add for a given instance. The computational results show that the machine learning approach significantly outperforms each and every one of the nine individual approaches.

This is one of the most applied courses on Genetic Algorithms (GA), which presents an integrated framework to solve real-world optimization problems in the most simple way. For the first time, we have presented a practical course in the domain of metaheuristics algorithms required for students, researchers and practitioners. Firstly, we will introduce the basic theory of GA, then implement the simplest version of GA, namely Binary GA, into Matlab, and then present the continuous version, real GA, of it. Therefore, the main focus will be on the Genetic Algorithm as the most well-regarded optimization algorithm in the literature. In the following sections, we will introduce some well-known operation research problems, including transportation problems, hub location problems (HLP), quadratic assignment problems and travelling salesman problems (TSP) and try to solve them via GA.

Approximating the Koopman operator from data is numerically challenging when many lifting functions are considered. Even low-dimensional systems can yield unstable or ill-conditioned results in a high-dimensional lifted space. In this paper, Extended Dynamic Mode Decomposition (DMD) and DMD with control, two methods for approximating the Koopman operator, are reformulated as convex optimization problems with linear matrix inequality constraints. Asymptotic stability constraints and system norm regularizers are then incorporated as methods to improve the numerical conditioning of the Koopman operator. Specifically, the H-infinity norm is used to penalize the input-output gain of the Koopman system. Weighting functions are then applied to penalize the system gain at specific frequencies. These constraints and regularizers introduce bilinear matrix inequality constraints to the regression problem, which are handled by solving a sequence of convex optimization problems. Experimental results using data from an aircraft fatigue structural test rig and a soft robot arm highlight the advantages of the proposed regression methods.

The discovery of drug-target interactions (DTIs) is a very promising area of research with great potential. The accurate identification of reliable interactions among drugs and proteins via computational methods, which typically leverage heterogeneous information retrieved from diverse data sources, can boost the development of effective pharmaceuticals. Although random walk and matrix factorization techniques are widely used in DTI prediction, they have several limitations. Random walk-based embedding generation is usually conducted in an unsupervised manner, while the linear similarity combination in matrix factorization distorts individual insights offered by different views. To tackle these issues, we take a multi-layered network approach to handle diverse drug and target similarities, and propose a novel optimization framework, called Multiple similarity DeepWalk-based Matrix Factorization (MDMF), for DTI prediction. The framework unifies embedding generation and interaction prediction, learning vector representations of drugs and targets that not only retain higher-order proximity across all hyper-layers and layer-specific local invariance, but also approximate the interactions with their inner product. Furthermore, we develop an ensemble method (MDMF2A) that integrates two instantiations of the MDMF model, optimizing the area under the precision-recall curve (AUPR) and the area under the receiver operating characteristic curve (AUC) respectively. The empirical study on real-world DTI datasets shows that our method achieves statistically significant improvement over current state-of-the-art approaches in four different settings. Moreover, the validation of highly ranked non-interacting pairs also demonstrates the potential of MDMF2A to discover novel DTIs.

This paper develops the method of Continuous Pontryagin Differentiable Programming (Continuous PDP), which enables a robot to learn an objective function from a few sparsely demonstrated keyframes. The keyframes, labeled with some time stamps, are the desired task-space outputs, which a robot is expected to follow sequentially. The time stamps of the keyframes can be different from the time of the robot's actual execution. The method jointly finds an objective function and a time-warping function such that the robot's resulting trajectory sequentially follows the keyframes with minimal discrepancy loss. The Continuous PDP minimizes the discrepancy loss using projected gradient descent, by efficiently solving the gradient of the robot trajectory with respect to the unknown parameters. The method is first evaluated on a simulated robot arm and then applied to a 6-DoF quadrotor to learn an objective function for motion planning in unmodeled environments. The results show the efficiency of the method, its ability to handle time misalignment between keyframes and robot execution, and the generalization of objective learning into unseen motion conditions.

In this chapter, an integer linear programming formulation for the problem of obtaining task-relevant, multi-resolution, environment abstractions for resource-constrained autonomous agents is presented. The formulation leverages concepts from information-theoretic signal compression, specifically, the information bottleneck (IB) method, to pose an abstraction problem as an optimal encoder search over the space of multi-resolution trees. The abstractions emerge in a task-relevant manner as a function of agent information-processing constraints. We detail our formulation, and show how hierarchical tree structures, signal encoders, and information-theoretic methods for signal compression can be unified under a common theme. A discussion delineating the benefits and drawbacks of our formulation is presented, as well as a detailed explanation how our approach can be interpreted within the context of generating abstractions for resource-constrained autonomous systems. It is shown that the resulting information-theoretic abstraction problem over the space of multi-resolution trees can be formulated as a integer linear programming (ILP) problem. We demonstrate the approach on a number of examples, and provide a discussion detailing the differences of the proposed framework compared to existing methods. Lastly, we consider a linear program relaxation of the ILP problem, thereby demonstrating that multi-resolution information-theoretic tree abstractions can be obtained by solving a convex program.

The online assignment problem plays an important role in operational research and computer science which is why immense attention has been given to improving its solution quality. Due to the incomplete information about the input, it is difficult for online algorithms to produce the optimal solution. The quality of the solution of an online algorithm is measured using a competitive ratio. No online deterministic algorithm can achieve a competitive ratio better than (2n-1). It has been shown that advice in online computation improves the lower bound of the competitive ratio of online problems. Advice in online computation can be interpreted as additional information for the online algorithm to compensate for the lack of information about the whole input sequence. In this study, we investigate how introducing machine-learned advice could improve the competitive ratio for this problem. We provide an online algorithm for the online assignment problem by simulating a machine learning algorithm that predicts the whole input in advance. We utilize an optimal offline algorithm to provide a matching solution from the predicted input. Furthermore, we investigate how the prediction error of machine learning affects the competitive ratio of the online algorithm. We utilize a benchmark data set to perform our empirical analysis. We show that as the Machine Learning prediction error increases, the solution quality decreases. Moreover, the magnitude of error is directly proportional to the size of the input. This result is analogous to the competitive ratio of the best deterministic algorithm for the online assignment problem which is dependent also on the parameter n.

In human-robot interactions, eye movements play an important role in non-verbal communication. However, controlling the motions of a robotic eye that display similar performance as the human oculomotor system is still a major challenge. In this paper, we study how to control a realistic model of the human eye with a cable-driven actuation system that mimics the six degrees of freedom of the extra-ocular muscles. The biomimetic design introduces novel challenges to address, most notably the need to control the pretension on each individual muscle to prevent the loss of tension during motion, that would lead to cable slack and lack of control. We built a robotic prototype and developed a nonlinear simulator and two controllers. In the first approach, we linearized the nonlinear model, using a local derivative technique, and designed linear-quadratic optimal controllers to optimize a cost function that accounts for accuracy, energy expenditure, and movement duration. The second method uses a recurrent neural network that learns the nonlinear system dynamics from sample trajectories of the system, and a non-linear trajectory optimization solver that minimizes a similar cost function. We focused on the generation of rapid saccadic eye movements with fully unconstrained kinematics, and the generation of control signals for the six cables that simultaneously satisfied several dynamic optimization criteria. The model faithfully mimics the three-dimensional rotational kinematics and dynamics observed for human saccades. Our experimental results indicate that while both methods yielded similar results, the nonlinear method is more flexible for future improvements to the model, for which the calculations of the linearized model's position-dependent pretensions and local derivatives become particularly tedious.

Biclustering algorithms partition data and covariates simultaneously, providing new insights in several domains, such as analyzing gene expression to discover new biological functions. This paper develops a new model-free biclustering algorithm in abstract spaces using the notions of energy distance (ED) and the maximum mean discrepancy (MMD) -- two distances between probability distributions capable of handling complex data such as curves or graphs. The proposed method can learn more general and complex cluster shapes than most existing literature approaches, which usually focus on detecting mean and variance differences. Although the biclustering configurations of our approach are constrained to create disjoint structures at the datum and covariate levels, the results are competitive. Our results are similar to state-of-the-art methods in their optimal scenarios, assuming a proper kernel choice, outperforming them when cluster differences are concentrated in higher-order moments. The model's performance has been tested in several situations that involve simulated and real-world datasets. Finally, new theoretical consistency results are established using some tools of the theory of optimal transport.

In recent years, the dramatic progress in machine learning has begun to impact many areas of science and technology significantly. In the present perspective article, we explore how quantum technologies are benefiting from this revolution. We showcase in illustrative examples how scientists in the past few years have started to use machine learning and more broadly methods of artificial intelligence to analyze quantum measurements, estimate the parameters of quantum devices, discover new quantum experimental setups, protocols, and feedback strategies, and generally improve aspects of quantum computing, quantum communication, and quantum simulation. We highlight open challenges and future possibilities and conclude with some speculative visions for the next decade.