The Traveling-Salesperson-Problem (TSP) is arguably one of the best-known NP-hard combinatorial optimization problems. The two sophisticated heuristic solvers LKH and EAX and respective (restart) variants manage to calculate close-to optimal or even optimal solutions, also for large instances with several thousand nodes in reasonable time. In this work we extend existing benchmarking studies by addressing anytime behaviour of inexact TSP solvers based on empirical runtime distributions leading to an increased understanding of solver behaviour and the respective relation to problem hardness. It turns out that performance ranking of solvers is highly dependent on the focused approximation quality. Insights on intersection points of performances offer huge potential for the construction of hybridized solvers depending on instance features. Moreover, instance features tailored to anytime performance and corresponding performance indicators will highly improve automated algorithm selection models by including comprehensive information on solver quality.

The increasing demand for democratizing machine learning algorithms for general software developers calls for hyperparameter optimization (HPO) solutions at low cost. Many machine learning algorithms have hyperparameters, which can cause a large variation in the training cost. But this effect is largely ignored in existing HPO methods, which are incapable to properly control cost during the optimization process. To address this problem, we develop a cost effective HPO solution. The core of our solution is a new randomized direct-search method. We prove a convergence rate of $O(\frac{\sqrt{d}}{\sqrt{K}})$ and provide an analysis on how it can be used to control evaluation cost under reasonable assumptions. Extensive evaluation using a latest AutoML benchmark shows a strong any time performance of the proposed HPO method when tuning cost-related hyperparameters.

This work proposes an iterative sparse-regularized regression method to recover governing equations of nonlinear dynamical systems from noisy state measurements. The method is inspired by the Sparse Identification of Nonlinear Dynamics (SINDy) approach of {\it [Brunton et al., PNAS, 113 (15) (2016) 3932-3937]}, which relies on two main assumptions: the state variables are known {\it a priori} and the governing equations lend themselves to sparse, linear expansions in a (nonlinear) basis of the state variables. The aim of this work is to improve the accuracy and robustness of SINDy in the presence of state measurement noise. To this end, a reweighted $\ell_1$-regularized least squares solver is developed, wherein the regularization parameter is selected from the corner point of a Pareto curve. The idea behind using weighted $\ell_1$-norm for regularization -- instead of the standard $\ell_1$-norm -- is to better promote sparsity in the recovery of the governing equations and, in turn, mitigate the effect of noise in the state variables. We also present a method to recover single physical constraints from state measurements. Through several examples of well-known nonlinear dynamical systems, we demonstrate empirically the accuracy and robustness of the reweighted $\ell_1$-regularized least squares strategy with respect to state measurement noise, thus illustrating its viability for a wide range of potential applications.

This paper studies the problem of globally optimizing a variable of interest that is part of a causal model in which a sequence of interventions can be performed. This problem arises in biology, operational research, communications and, more generally, in all fields where the goal is to optimize an output metric of a system of interconnected nodes. Our approach combines ideas from causal inference, uncertainty quantification and sequential decision making. In particular, it generalizes Bayesian optimization, which treats the input variables of the objective function as independent, to scenarios where causal information is available. We show how knowing the causal graph significantly improves the ability to reason about optimal decision making strategies decreasing the optimization cost while avoiding suboptimal solutions. We propose a new algorithm called Causal Bayesian Optimization (CBO). CBO automatically balances two trade-offs: the classical exploration-exploitation and the new observation-intervention, which emerges when combining real interventional data with the estimated intervention effects computed via do-calculus. We demonstrate the practical benefits of this method in a synthetic setting and in two real-world applications.

We consider the matrix completion problem of recovering a structured low rank matrix with partially observed entries with mixed data types. Vast majority of the solutions have proposed computationally feasible estimators with strong statistical guarantees for the case where the underlying distribution of data in the matrix is continuous. A few recent approaches have extended using similar ideas these estimators to the case where the underlying distributions belongs to the exponential family. Most of these approaches assume that there is only one underlying distribution and the low rank constraint is regularized by the matrix Schatten Norm. We propose a computationally feasible statistical approach with strong recovery guarantees along with an algorithmic framework suited for parallelization to recover a low rank matrix with partially observed entries for mixed data types in one step. We also provide extensive simulation evidence that corroborate our theoretical results.

One of the major concerns of targeting interventions on individuals in social welfare programs is discrimination: individualized treatments may induce disparities on sensitive attributes such as age, gender, or race. This paper addresses the question of the design of fair and efficient treatment allocation rules. We adopt the non-maleficence perspective of "first do no harm": we propose to select the fairest allocation within the Pareto frontier. We provide envy-freeness justifications to novel counterfactual notions of fairness. We discuss easy-to-implement estimators of the policy function, by casting the optimization into a mixed-integer linear program formulation. We derive regret bounds on the unfairness of the estimated policy function, and small sample guarantees on the Pareto frontier. Finally, we illustrate our method using an application from education economics.

In simulation-based optimization, the optimal setting of the input parameters of the objective function can be determined by heuristic optimization techniques. However, when simulators model the stochasticity of real-world problems, their output is a random variable and multiple evaluations of the objective function are necessary to properly compare the expected performance of different parameter settings. This paper presents a novel reactive sample size algorithm based on parametric tests and indifference-zone selection, which can be used for improving the efficiency and robustness of heuristic optimization methods. The algorithm reactively decides, in an online manner, the sample size to be used for each comparison during the optimization according to observed statistical evidence. Tests employ benchmark functions extended with artificial levels of noise and a simulation-based optimization tool for hotel revenue management. Experimental results show that the reactive method can improve the efficiency and robustness of simulation-based optimization techniques.

Modeling and simulation is certainly a vast discipline with a broad and complex body of knowledge having, beyond the surface, a large technical and theoretical background (Minsky, 1965) (Banks et al., 2009) (Zeigler et al., 2000) (Boccara, 2003) which consequently, is hard of being completely mastered from modelers coming from disperse domains like biology, ecology or even computer science. Among the existing formalisms, the agent-based or individual-based is increasing gradually the number of adepts in the recent years. The Individual-based modeling is a powerful methodology which is having more and more acceptance between researchers and practitioners of distinct branches from social to biological sciences, including specifically the modeling of ecological processes and microbial consortia studies. Certainly, one of the main reasons for the success of this approach is the relative simplicity for capturing micro-level properties, stochasticity and spatially complex phenomena without the requirement of a high level of mathematical background (Grimm and Railsback, 2005). But the counterpart of the ease for building complex and feature rich models, is the lack of a closed formal mathematical form of the model which implies that the study of these models cannot be attacked analytically.

This paper examines the relationship between user pageview (PV) histories and their item-choice behavior on an e-commerce website. We focus on PV sequences, which represent time series of the number of PVs for each user--item pair. We propose a shape-restricted optimization model that accurately estimates item-choice probabilities for all possible PV sequences. This model imposes monotonicity constraints on item-choice probabilities by exploiting partial orders for PV sequences, according to the recency and frequency of a user's previous PVs. To improve the computational efficiency of our optimization model, we devise efficient algorithms for eliminating all redundant constraints according to the transitivity of the partial orders. Experimental results using real-world clickstream data demonstrate that our method achieves higher prediction performance than that of a state-of-the-art optimization model and common machine learning methods.

In this paper, we design and analyze a new family of adaptive subgradient methods for solving an important class of weakly convex (possibly nonsmooth) stochastic optimization problems. Adaptive methods that use exponential moving averages of past gradients to update search directions and learning rates have recently attracted a lot of attention for solving optimization problems that arise in machine learning. Nevertheless, their convergence analysis almost exclusively requires smoothness and/or convexity of the objective function. In contrast, we establish non-asymptotic rates of convergence of first and zeroth-order adaptive methods and their proximal variants for a reasonably broad class of nonsmooth \& nonconvex optimization problems. Experimental results indicate how the proposed algorithms empirically outperform stochastic gradient descent and its zeroth-order variant for solving such optimization problems.