Optimization and ML are increasingly intersecting. Occasionally overlapping, sometimes complementary and most often best used in combination. Data Scientists should be interested in Operations Research, and Operations Researcher's are increasingly using Machine Learning. This presentation will provide a structure for understanding and applying these two techniques. It describes when Optimization techniques originating from operations research are the better solution and when it is beneficial to apply ML. More importantly, we describe how complex, high-value business problems can be solved with better by combining the techniques, rather than by using only one of them.

The computational effort for the evaluation of numerical simulations based on e.g. the finite-element method is high. Metamodels can be utilized to create a low-cost alternative. However the number of required samples for the creation of a sufficient metamodel should be kept low, which can be achieved by using adaptive sampling techniques. In this Master thesis adaptive sampling techniques are investigated for their use in creating metamodels with the Kriging technique, which interpolates values by a Gaussian process governed by prior covariances. The Kriging framework with extension to multifidelity problems is presented and utilized to compare adaptive sampling techniques found in the literature for benchmark problems as well as applications for contact mechanics. This thesis offers the first comprehensive comparison of a large spectrum of adaptive techniques for the Kriging framework. Furthermore a multitude of adaptive techniques is introduced to multifidelity Kriging as well as well as to a Kriging model with reduced hyperparameter dimension called partial least squares Kriging. In addition, an innovative adaptive scheme for binary classification is presented and tested for identifying chaotic motion of a Duffing's type oscillator.

Value iteration is a fixed point iteration technique utilized to obtain the optimal value function and policy in a discounted reward Markov Decision Process (MDP). Here, a contraction operator is constructed and applied repeatedly to arrive at the optimal solution. Value iteration is a first order method and therefore it may take a large number of iterations to converge to the optimal solution. In this work, we propose a novel second order value iteration procedure based on the Newton-Raphson method. We first construct a modified contraction operator and then apply Newton-Raphson method to arrive at our algorithm. We prove the global convergence of our algorithm to the optimal solution and show the second order convergence. Through experiments, we demonstrate the effectiveness of our proposed approach.

Object shape provides important information for robotic manipulation; for instance, selecting an effective grasp depends on both the global and local shape of the object of interest, while reaching into clutter requires accurate surface geometry to avoid unintended contact with the environment. Model-based 3D object manipulation is a widely studied problem; however, obtaining the accurate 3D object models for multiple objects often requires tedious work. In this letter, we exploit Gaussian process implicit surfaces (GPIS) extracted from RGB-D sensor data to grasp an unknown object. We propose a reconstruction-aware trajectory optimization that makes use of the extracted GPIS model plan a motion to improve the ability to estimate the object's 3D geometry, while performing a pick-and-place action. We present a probabilistic approach for a robot to autonomously learn and track the object, while achieve the manipulation task. We use a sampling-based trajectory generation method to explore the unseen parts of the object using the estimated conditional entropy of the GPIS model. We validate our method with physical robot experiments across eleven different objects of varying shape from the YCB object dataset. Our experiments show that our reconstruction-aware trajectory optimization provides higher-quality 3D object reconstruction when compared with directly solving the manipulation task or using a heuristic to view unseen portions of the object.

Adversarial training shows promise as an approach for training models that are robust towards adversarial perturbation. In this paper, we explore some of the practical challenges of adversarial training. We present a sensitivity analysis that illustrates that the effectiveness of adversarial training hinges on the settings of a few salient hyperparameters. We show that the robustness surface that emerges across these salient parameters can be surprisingly complex and that therefore no effective one-size-fits-all parameter settings exist. We then demonstrate that we can use the same salient hyperparameters as tuning knob to navigate the tension that can arise between robustness and accuracy. Based on these findings, we present a practical approach that leverages hyperparameter optimization techniques for tuning adversarial training to maximize robustness while keeping the loss in accuracy within a defined budget.

In this article we are going to discuss training neural networks using particle swarm optimization (PSO). Training a neural network is an optimization problem so the optimization algorithm is of primary importance. When training MLPs we are adjusting weights between neurons using an error function as our optimization objective. PNNs and GRNNs use a smoothing factor, σ to define the network. The objective is to find sigmas that minimize error.

In this paper, we propose an interior-point method for linearly constrained optimization problems (possibly nonconvex). The method - which we call the Hessian barrier algorithm (HBA) - combines a forward Euler discretization of Hessian Riemannian gradient flows with an Armijo backtracking step-size policy. In this way, HBA can be seen as an alternative to mirror descent (MD), and contains as special cases the affine scaling algorithm, regularized Newton processes, and several other iterative solution methods. Our main result is that, modulo a non-degeneracy condition, the algorithm converges to the problem's set of critical points; hence, in the convex case, the algorithm converges globally to the problem's minimum set. In the case of linearly constrained quadratic programs (not necessarily convex), we also show that the method's convergence rate is $\mathcal{O}(1/k^\rho)$ for some $\rho\in(0,1]$ that depends only on the choice of kernel function (i.e., not on the problem's primitives). These theoretical results are validated by numerical experiments in standard non-convex test functions and large-scale traffic assignment problems.

Evolution and learning are two of the fundamental mechanisms by which life adapts in order to survive and to transcend limitations. These biological phenomena inspired successful computational methods such as evolutionary algorithms and deep learning. Evolution relies on random mutations and on random genetic recombination. Here we show that learning to evolve, i.e. learning to mutate and recombine better than at random, improves the result of evolution in terms of fitness increase per generation and even in terms of attainable fitness. We use deep reinforcement learning to learn to dynamically adjust the strategy of evolutionary algorithms to varying circumstances. Our methods outperform classical evolutionary algorithms on combinatorial and continuous optimization problems.

Policy gradient algorithms are among the best candidates for the much anticipated application of reinforcement learning to real-world control tasks, such as the ones arising in robotics. However, the trial-and-error nature of these methods introduces safety issues whenever the learning phase itself must be performed on a physical system. In this paper, we address a specific safety formulation, where danger is encoded in the reward signal and the learning agent is constrained to never worsen its performance. By studying actor-only policy gradient from a stochastic optimization perspective, we establish improvement guarantees for a wide class of parametric policies, generalizing existing results on Gaussian policies. This, together with novel upper bounds on the variance of policy gradient estimators, allows to identify those meta-parameter schedules that guarantee monotonic improvement with high probability. The two key meta-parameters are the step size of the parameter updates and the batch size of the gradient estimators. By a joint, adaptive selection of these meta-parameters, we obtain a safe policy gradient algorithm.

In this report we review memory-based meta-learning as a tool for building sample-efficient strategies that learn from past experience to adapt to any task within a target class. Our goal is to equip the reader with the conceptual foundations of this tool for building new, scalable agents that operate on broad domains. To do so, we present basic algorithmic templates for building near-optimal predictors and reinforcement learners which behave as if they had a probabilistic model that allowed them to efficiently exploit task structure. Furthermore, we recast memory-based meta-learning within a Bayesian framework, showing that the meta-learned strategies are near-optimal because they amortize Bayes-filtered data, where the adaptation is implemented in the memory dynamics as a state-machine of sufficient statistics. Essentially, memory-based meta-learning translates the hard problem of probabilistic sequential inference into a regression problem.