Algorithmic design in neural architecture search (NAS) has received a lot of attention, aiming to improve performance and reduce computational cost. Despite the great advances made, few authors have proposed to tailor initialization techniques for NAS. However, literature shows that a good initial set of solutions facilitate finding the optima. Therefore, in this study, we propose a data-driven technique to initialize a population-based NAS algorithm. Particularly, we proposed a two-step methodology. First, we perform a calibrated clustering analysis of the search space, and second, we extract the centroids and use them to initialize a NAS algorithm. We benchmark our proposed approach against random and Latin hypercube sampling initialization using three population-based algorithms, namely a genetic algorithm, evolutionary algorithm, and aging evolution, on CIFAR-10. More specifically, we use NAS-Bench-101 to leverage the availability of NAS benchmarks. The results show that compared to random and Latin hypercube sampling, the proposed initialization technique enables achieving significant long-term improvements for two of the search baselines, and sometimes in various search scenarios (various training budgets). Moreover, we analyze the distributions of solutions obtained and find that that the population provided by the data-driven initialization technique enables retrieving local optima (maxima) of high fitness and similar configurations.

In this paper, we propose a new end-to-end methodology to optimize the energy performance as well as comfort and air quality in large buildings without any renovation work. We introduce a metamodel based on recurrent neural networks and trained to predict the behavior of a general class of buildings using a database sampled from a simulation program. This metamodel is then deployed in different frameworks and its parameters are calibrated using the specific data of two real buildings. Parameters are estimated by comparing the predictions of the metamodel with real data obtained from sensors using the CMA-ES algorithm, a derivative free optimization procedure. Then, energy consumptions are optimized while maintaining a target thermal comfort and air quality, using the NSGA-II multi-objective optimization procedure. The numerical experiments illustrate how this metamodel ensures a significant gain in energy efficiency, up to almost 10%, while being computationally much more appealing than numerical models and flexible enough to be adapted to several types of buildings.

Our lives are a succession of optimization problems. They occur when we search for the fastest route home from work or attempt to balance cost and quality on a trip to the store, or even when we decide how to spend limited free time before bed. These scenarios and many others can be represented as a mathematical optimization problem. Making the best decisions is a matter of finding their optimal solutions. And for a world steeped in optimization, two recent results provide both good and bad news.

Large-scale ride-hailing systems often combine real-time routing at the individual request level with a macroscopic Model Predictive Control (MPC) optimization for dynamic pricing and vehicle relocation. The MPC relies on a demand forecast and optimizes over a longer time horizon to compensate for the myopic nature of the routing optimization. However, the longer horizon increases computational complexity and forces the MPC to operate at coarser spatial-temporal granularity, degrading the quality of its decisions. This paper addresses these computational challenges by learning the MPC optimization. The resulting machine-learning model then serves as the optimization proxy and predicts its optimal solutions. This makes it possible to use the MPC at higher spatial-temporal fidelity, since the optimizations can be solved and learned offline. Experimental results show that the proposed approach improves quality of service on challenging instances from the New York City dataset.

We establish a broad methodological foundation for mixed-integer optimization with learned constraints. We propose an end-to-end pipeline for data-driven decision making in which constraints and objectives are directly learned from data using machine learning, and the trained models are embedded in an optimization formulation. We exploit the mixed-integer optimization-representability of many machine learning methods, including linear models, decision trees, ensembles, and multi-layer perceptrons. The consideration of multiple methods allows us to capture various underlying relationships between decisions, contextual variables, and outcomes. We also characterize a decision trust region using the convex hull of the observations, to ensure credible recommendations and avoid extrapolation. We efficiently incorporate this representation using column generation and clustering. In combination with domain-driven constraints and objective terms, the embedded models and trust region define a mixed-integer optimization problem for prescription generation. We implement this framework as a Python package (OptiCL) for practitioners. We demonstrate the method in both chemotherapy optimization and World Food Programme planning. The case studies illustrate the benefit of the framework in generating high-quality prescriptions, the value added by the trust region, the incorporation of multiple machine learning methods, and the inclusion of multiple learned constraints.

We provide new gradient-based methods for efficiently solving a broad class of ill-conditioned optimization problems. We consider the problem of minimizing a function $f : \mathbb{R}^d \rightarrow \mathbb{R}$ which is implicitly decomposable as the sum of $m$ unknown non-interacting smooth, strongly convex functions and provide a method which solves this problem with a number of gradient evaluations that scales (up to logarithmic factors) as the product of the square-root of the condition numbers of the components. This complexity bound (which we prove is nearly optimal) can improve almost exponentially on that of accelerated gradient methods, which grow as the square root of the condition number of $f$. Additionally, we provide efficient methods for solving stochastic, quadratic variants of this multiscale optimization problem. Rather than learn the decomposition of $f$ (which would be prohibitively expensive), our methods apply a clean recursive "Big-Step-Little-Step" interleaving of standard methods. The resulting algorithms use $\tilde{\mathcal{O}}(d m)$ space, are numerically stable, and open the door to a more fine-grained understanding of the complexity of convex optimization beyond condition number.

Solving Constraint Optimization Problems (COPs) can be dramatically simplified by boundary estimation, that is, providing tight boundaries of cost functions. By feeding a supervised Machine Learning (ML) model with data composed of known boundaries and extracted features of COPs, it is possible to train the model to estimate boundaries of a new COP instance. In this paper, we first give an overview of the existing body of knowledge on ML for Constraint Programming (CP) which learns from problem instances. Second, we introduce a boundary estimation framework that is applied as a tool to support a CP solver. Within this framework, different ML models are discussed and evaluated regarding their suitability for boundary estimation, and countermeasures to avoid unfeasible estimations that avoid the solver to find an optimal solution are shown. Third, we present an experimental study with distinct CP solvers on seven COPs. Our results show that near-optimal boundaries can be learned for these COPs with only little overhead. These estimated boundaries reduce the objective domain size by 60-88% and can help the solver to find near-optimal solutions early during search.

Energy systems optimization problems are complex due to strongly non-linear system behavior and multiple competing objectives, e.g. economic gain vs. environmental impact. Moreover, a large number of input variables and different variable types, e.g. continuous and categorical, are challenges commonly present in real-world applications. In some cases, proposed optimal solutions need to obey explicit input constraints related to physical properties or safety-critical operating conditions. This paper proposes a novel data-driven strategy using tree ensembles for constrained multi-objective optimization of black-box problems with heterogeneous variable spaces for which underlying system dynamics are either too complex to model or unknown. In an extensive case study comprised of synthetic benchmarks and relevant energy applications we demonstrate the competitive performance and sampling efficiency of the proposed algorithm compared to other state-of-the-art tools, making it a useful all-in-one solution for real-world applications with limited evaluation budgets.

Even skilled fantasy football managers can be disappointed by their mid-season rosters as some players inevitably fall short of draft day expectations. Team managers can quickly discover that their team has a low score ceiling even if they start their best active players. A novel and diverse combinatorial optimization system proposes high volume and unique player trades between complementary teams to balance trade fairness. Several algorithms create the valuation of each fantasy football player with an ensemble of computing models such as Quantum Support Vector Classifier with Permutation Importance (QSVC-PI), Quantum Support Vector Classifier with Accumulated Local Effects (QSVC-ALE), Variational Quantum Circuit with Permutation Importance (VQC-PI), Hybrid Quantum Neural Network with Permutation Importance (HQNN-PI), eXtreme Gradient Boosting Classifier (XGB), and Subject Matter Expert (SME) rules. The valuation of each player is personalized based on league rules, roster, and selections. Similarly, the cost of trading away a player is related to a team's roster, such as the depth at a position, slot count, position importance, etc. Teams are paired together for trading based on a cosine dissimilarity score so that teams can offset their respective strengths and weaknesses. A knapsack 0-1 algorithm computes outgoing players for each team. Postprocessors apply analytics and deep learning models to measure 6 different objective measures about each trade, such as parity, pain, and fairness. Over the 2020 and 2021 National Football League (NFL) seasons, a group of 24 experts from IBM and ESPN evaluated trade quality through 10 Football Error Analysis Tool (FEAT) sessions. Our system started with 76.9% of high-quality trades and was deployed for the 2021 season with 97.3% of high-quality trades. To increase trade quantity, our quantum, classical, and rules-based computing have 100% trade uniqueness. This paper will discuss our diverse computing paradigms that value players, cost determinations, personalization experience, knapsack 0-1 algorithm and our experimental results. Throughout the 2020 season, we served over 239 million trade proposals and insights with over 55 million user interactions. In 2021, we introduced trade personalization so that the trade proposals were created around user preferences.

Reinforcement learning (RL) for continuous control typically employs distributions whose support covers the entire action space. In this work, we investigate the colloquially known phenomenon that trained agents often prefer actions at the boundaries of that space. We draw theoretical connections to the emergence of bang-bang behavior in optimal control, and provide extensive empirical evaluation across a variety of recent RL algorithms. We replace the normal Gaussian by a Bernoulli distribution that solely considers the extremes along each action dimension - a bang-bang controller. Surprisingly, this achieves state-of-the-art performance on several continuous control benchmarks - in contrast to robotic hardware, where energy and maintenance cost affect controller choices. Since exploration, learning,and the final solution are entangled in RL, we provide additional imitation learning experiments to reduce the impact of exploration on our analysis. Finally, we show that our observations generalize to environments that aim to model real-world challenges and evaluate factors to mitigate the emergence of bang-bang solutions. Our findings emphasize challenges for benchmarking continuous control algorithms, particularly in light of potential real-world applications.