We consider black-box optimization in which only an extremely limited number of function evaluations, on the order of around 100, are affordable and the function evaluations must be performed in even fewer batches of a limited number of parallel trials. This is a typical scenario when optimizing variable settings that are very costly to evaluate, for example in the context of simulation-based optimization or machine learning hyperparameterization. We propose an original method that uses established approaches to propose a set of points for each batch and then down-selects from these candidate points to the number of trials that can be run in parallel. The key novelty of our approach lies in the introduction of a hyperparameterized method for down-selecting the number of candidates to the allowed batch-size, which is optimized offline using automated algorithm configuration. We tune this method for black box optimization and then evaluate on classical black box optimization benchmarks. Our results show that it is possible to learn how to combine evaluation points suggested by highly diverse black box optimization methods conditioned on the progress of the optimization. Compared with the state of the art in black box minimization and various other methods specifically geared towards few-shot minimization, we achieve an average reduction of 50\% of normalized cost, which is a highly significant improvement in performance.

Since its introduction a decade ago, \emph{relative entropy policy search} (REPS) has demonstrated successful policy learning on a number of simulated and real-world robotic domains, not to mention providing algorithmic components used by many recently proposed reinforcement learning (RL) algorithms. While REPS is commonly known in the community, there exist no guarantees on its performance when using stochastic and gradient-based solvers. In this paper we aim to fill this gap by providing guarantees and convergence rates for the sub-optimality of a policy learned using first-order optimization methods applied to the REPS objective. We first consider the setting in which we are given access to exact gradients and demonstrate how near-optimality of the objective translates to near-optimality of the policy. We then consider the practical setting of stochastic gradients, and introduce a technique that uses \emph{generative} access to the underlying Markov decision process to compute parameter updates that maintain favorable convergence to the optimal regularized policy.

In the family of Intelligent Transportation Systems (ITS), Multimodal Transport Systems (MMTS) have placed themselves as a mainstream transportation mean of our time as a feasible integrative transportation process. The Global Economy progressed with the help of transportation. The volume of goods and distances covered have doubled in the last ten years, so there is a high demand of an optimized transportation, fast but with low costs, saving resources but also safe, with low or zero emissions. Thus, it is important to have an overview of existing research in this field, to know what was already done and what is to be studied next. The main objective is to explore a beneficent selection of the existing research, methods and information in the field of multimodal transportation research, to identify industry needs and gaps in research and provide context for future research. The selective survey covers multimodal transport design and optimization in terms of: cost, time, and network topology. The multimodal transport theoretical aspects, context and resources are also covering various aspects. The survey's selection includes nowadays best methods and solvers for Intelligent Transportation Systems (ITS). The gap between theory and real-world applications should be further solved in order to optimize the global multimodal transportation system.

Given an optimization problem, the Hessian matrix and its eigenspectrum can be used in many ways, ranging from designing more efficient second-order algorithms to performing model analysis and regression diagnostics. When nonlinear models and non-convex problems are considered, strong simplifying assumptions are often made to make Hessian spectral analysis more tractable. This leads to the question of how relevant the conclusions of such analyses are for more realistic nonlinear models. In this paper, we exploit deterministic equivalent techniques from random matrix theory to make a \emph{precise} characterization of the Hessian eigenspectra for a broad family of nonlinear models, including models that generalize the classical generalized linear models, without relying on strong simplifying assumptions used previously. We show that, depending on the data properties, the nonlinear response model, and the loss function, the Hessian can have \emph{qualitatively} different spectral behaviors: of bounded or unbounded support, with single- or multi-bulk, and with isolated eigenvalues on the left- or right-hand side of the bulk. By focusing on such a simple but nontrivial nonlinear model, our analysis takes a step forward to unveil the theoretical origin of many visually striking features observed in more complex machine learning models.

A Bellman equation, named after Richard E. Bellman, is a necessary condition for optimality associated with the mathematical optimization method known as dynamic programming.[1] It writes the "value" of a decision problem at a certain point in time in terms of the payoff from some initial choices and the "value" of the remaining decision problem that results from those initial choices.[citation The Bellman equation was first applied to engineering control theory and to other topics in applied mathematics, and subsequently became an important tool in economic theory; though the basic concepts of dynamic programming are prefigured in John von Neumann and Oskar Morgenstern's Theory of Games and Economic Behavior and Abraham Wald's sequential analysis.[citation In continuous-time optimization problems, the analogous equation is a partial differential equation that is called the Hamilton–Jacobi–Bellman equation.[4][5] In discrete time any multi-stage optimization problem can be solved by analyzing the appropriate Bellman equation.

Many of the commodities that affect our everyday lives are processed by smelters and fumer-furnace operations. These include products made from copper, nickel, and zinc, such as electrical wiring, kitchen appliances, and some types of batteries. Smelters are also used to produce precious metals, such as gold or silver, and animal feed, and to provide heat for dryers and roasters, which must be operated in concert for efficient production. Despite the importance of smelters, operations are becoming increasingly challenging. Most smelters globally have been in operation for at least 20 years, resulting in higher maintenance requirements. Second, feed quality is declining.

Robots performing tasks in warehouses provide the first example of wide-spread adoption of autonomous vehicles in transportation and logistics. The efficiency of these operations, which can vary widely in practice, are a key factor in the success of supply chains. In this work we consider the problem of coordinating a fleet of robots performing picking operations in a warehouse so as to maximize the net profit achieved within a time period while respecting problem- and robot-specific constraints. We formulate the problem as a weighted set packing problem where the elements in consideration are items on the warehouse floor that can be picked up and delivered within specified time windows. We enforce the constraint that robots must not collide, that each item is picked up and delivered by at most one robot, and that the number of robots active at any time does not exceed the total number available. Since the set of routes is exponential in the size of the input, we attack optimization of the resulting integer linear program using column generation, where pricing amounts to solving an elementary resource-constrained shortest-path problem. We propose an efficient optimization scheme that avoids consideration of every increment within the time windows. We also propose a heuristic pricing algorithm that can efficiently solve the pricing subproblem. While this itself is an important problem, the insights gained from solving these problems effectively can lead to new advances in other time-widow constrained vehicle routing problems.

Bayesian experimental design (BED) is to answer the question that how to choose designs that maximize the information gathering. For implicit models, where the likelihood is intractable but sampling is possible, conventional BED methods have difficulties in efficiently estimating the posterior distribution and maximizing the mutual information (MI) between data and parameters. Recent work proposed the use of gradient ascent to maximize a lower bound on MI to deal with these issues. However, the approach requires a sampling path to compute the pathwise gradient of the MI lower bound with respect to the design variables, and such a pathwise gradient is usually inaccessible for implicit models. In this paper, we propose a novel approach that leverages recent advances in stochastic approximate gradient ascent incorporated with a smoothed variational MI estimator for efficient and robust BED. Without the necessity of pathwise gradients, our approach allows the design process to be achieved through a unified procedure with an approximate gradient for implicit models. Several experiments show that our approach outperforms baseline methods, and significantly improves the scalability of BED in high-dimensional problems.

Optimizing the hyperparameters and architecture of a neural network is a long yet necessary phase in the development of any new application. This consuming process can benefit from the elaboration of strategies designed to quickly discard low quality configurations and focus on more promising candidates. This work aims at enhancing HyperNOMAD, a library that adapts a direct search derivative-free optimization algorithm to tune both the architecture and the training of a neural network simultaneously, by targeting two keys steps of its execution and exploiting cheap approximations in the form of static surrogates to trigger the early stopping of the evaluation of a configuration and the ranking of pools of candidates. These additions to HyperNOMAD are shown to improve on its resources consumption without harming the quality of the proposed solutions.

We review our recent work in the area of autonomous materials research, highlighting the coupling of machine learning methods and models and more problem-aware modeling. We review the general Bayesian framework for closed-loop design employed by many autonomous materials platforms. We then provide examples of our work on such platforms. We finally review our approaches to extend current statistical and ML models to better reflect problem-specific structure including the use of physics-based models and incorporation of operational considerations into the decision-making procedure.