Bayesian optimization (BO) is a sequential optimization strategy that is increasingly employed in a wide range of areas including materials design. In real world applications, acquiring high-fidelity (HF) data through physical experiments or HF simulations is the major cost component of BO. To alleviate this bottleneck, multi-fidelity (MF) methods are used to forgo the sole reliance on the expensive HF data and reduce the sampling costs by querying inexpensive low-fidelity (LF) sources whose data are correlated with HF samples. However, existing multi-fidelity BO (MFBO) methods operate under the following two assumptions that rarely hold in practical applications: (1) LF sources provide data that are well correlated with the HF data on a global scale, and (2) a single random process can model the noise in the fused data. These assumptions dramatically reduce the performance of MFBO when LF sources are only locally correlated with the HF source or when the noise variance varies across the data sources. In this paper, we dispense with these incorrect assumptions by proposing an MF emulation method that (1) learns a noise model for each data source, and (2) enables MFBO to leverage highly biased LF sources which are only locally correlated with the HF source. We illustrate the performance of our method through analytical examples and engineering problems on materials design.

In this paper we consider the problem of learning variational models in the context of supervised learning via risk minimization. Our goal is to provide a deeper understanding of the two approaches of learning of variational models via bilevel optimization and via algorithm unrolling. The former considers the variational model as a lower level optimization problem below the risk minimization problem, while the latter replaces the lower level optimization problem by an algorithm that solves said problem approximately. Both approaches are used in practice, but unrolling is much simpler from a computational point of view. To analyze and compare the two approaches, we consider a simple toy model, and compute all risks and the respective estimators explicitly. We show that unrolling can be better than the bilevel optimization approach, but also that the performance of unrolling can depend significantly on further parameters, sometimes in unexpected ways: While the stepsize of the unrolled algorithm matters a lot (and learning the stepsize gives a significant improvement), the number of unrolled iterations plays a minor role.

Partitioning Around Medoids (PAM, k-Medoids) is a popular clustering technique to use with arbitrary distance functions or similarities, where each cluster is represented by its most central object, called the medoid or the discrete median. In operations research, this family of problems is also known as facility location problem (FLP). FastPAM recently introduced a speedup for large k to make it applicable for larger problems, but the method still has a runtime quadratic in N. In this chapter, we discuss a sparse and asymmetric variant of this problem, to be used for example on graph data such as road networks. By exploiting sparsity, we can avoid the quadratic runtime and memory requirements, and make this method scalable to even larger problems, as long as we are able to build a small enough graph of sufficient connectivity to perform local optimization. Furthermore, we consider asymmetric cases, where the set of medoids is not identical to the set of points to be covered (or in the interpretation of facility location, where the possible facility locations are not identical to the consumer locations). Because of sparsity, it may be impossible to cover all points with just k medoids for too small k, which would render the problem unsolvable, and this breaks common heuristics for finding a good starting condition. We, hence, consider determining k as a part of the optimization problem and propose to first construct a greedy initial solution with a larger k, then to optimize the problem by alternating between PAM-style "swap" operations where the result is improved by replacing medoids with better alternatives and "remove" operations to reduce the number of k until neither allows further improving the result quality. We demonstrate the usefulness of this method on a problem from electrical engineering, with the input graph derived from cartographic data.

We propose and analyze exact and inexact regularized Newton-type methods for finding a global saddle point of \emph{convex-concave} unconstrained min-max optimization problems. Compared to first-order methods, our understanding of second-order methods for min-max optimization is relatively limited, as obtaining global rates of convergence with second-order information is much more involved. In this paper, we examine how second-order information can be used to speed up extra-gradient methods, even under inexactness. Specifically, we show that the proposed algorithms generate iterates that remain within a bounded set and the averaged iterates converge to an $\epsilon$-saddle point within $O(\epsilon^{-2/3})$ iterations in terms of a restricted gap function. Our algorithms match the theoretically established lower bound in this context and our analysis provides a simple and intuitive convergence analysis for second-order methods without any boundedness requirements. Finally, we present a series of numerical experiments on synthetic and real data that demonstrate the efficiency of the proposed algorithms.

Neural implicit representations have recently demonstrated compelling results on dense Simultaneous Localization And Mapping (SLAM) but suffer from the accumulation of errors in camera tracking and distortion in the reconstruction. Purposely, we present GO-SLAM, a deep-learning-based dense visual SLAM framework globally optimizing poses and 3D reconstruction in real-time. Robust pose estimation is at its core, supported by efficient loop closing and online full bundle adjustment, which optimize per frame by utilizing the learned global geometry of the complete history of input frames. Simultaneously, we update the implicit and continuous surface representation on-the-fly to ensure global consistency of 3D reconstruction. Results on various synthetic and real-world datasets demonstrate that GO-SLAM outperforms state-of-the-art approaches at tracking robustness and reconstruction accuracy. Furthermore, GO-SLAM is versatile and can run with monocular, stereo, and RGB-D input.

Metasurfaces offer a flexible framework for the manipulation of light properties in the realm of thin film optics. Specifically, the polarization of light can be effectively controlled through the use of thin phase plates. This study aims to introduce a surrogate optimization framework for these devices. The framework is applied to develop two kinds of vortex phase masks (VPMs) tailored for application in astronomical high-contrast imaging. Computational intelligence techniques are exploited to optimize the geometric features of these devices. The large design space and computational limitations necessitate the use of surrogate models like partial least squares Kriging, radial basis functions, or neural networks. However, we demonstrate the inadequacy of these methods in modeling the performance of VPMs. To address the shortcomings of these methods, a data-efficient evolutionary optimization setup using a deep neural network as a highly accurate and efficient surrogate model is proposed. The optimization process in this study employs a robust particle swarm evolutionary optimization scheme, which operates on explicit geometric parameters of the photonic device. Through this approach, optimal designs are developed for two design candidates. In the most complex case, evolutionary optimization enables optimization of the design that would otherwise be impractical (requiring too much simulations). In both cases, the surrogate model improves the reliability and efficiency of the procedure, effectively reducing the required number of simulations by up to 75% compared to conventional optimization techniques.

Reinforcement learning policy evaluation problems are often modeled as finite or discounted/averaged infinite-horizon MDPs. In this paper, we study undiscounted off-policy policy evaluation for absorbing MDPs. Given the dataset consisting of the i.i.d episodes with a given truncation level, we propose a so-called MWLA algorithm to directly estimate the expected return via the importance ratio of the state-action occupancy measure. The Mean Square Error (MSE) bound for the MWLA method is investigated and the dependence of statistical errors on the data size and the truncation level are analyzed. With an episodic taxi environment, computational experiments illustrate the performance of the MWLA algorithm.

This paper proposes a combined optimization and learning method for impact-friendly, non-prehensile catching of objects at non-zero velocity. Through a constrained Quadratic Programming problem, the method generates optimal trajectories up to the contact point between the robot and the object to minimize their relative velocity and reduce the impact forces. Next, the generated trajectories are updated by Kernelized Movement Primitives, which are based on human catching demonstrations to ensure a smooth transition around the catching point. In addition, the learned human variable stiffness (HVS) is sent to the robot's Cartesian impedance controller to absorb the post-impact forces and stabilize the catching position. Three experiments are conducted to compare our method with and without HVS against a fixed-position impedance controller (FP-IC). The results showed that the proposed methods outperform the FP-IC while adding HVS yields better results for absorbing the post-impact forces.

We consider network-based decentralized optimization problems, where each node in the network possesses a local function and the objective is to collectively attain a consensus solution that minimizes the sum of all the local functions. A major challenge in decentralized optimization is the reliance on communication which remains a considerable bottleneck in many applications. To address this challenge, we propose an adaptive randomized communication-efficient algorithmic framework that reduces the volume of communication by periodically tracking the disagreement error and judiciously selecting the most influential and effective edges at each node for communication. Within this framework, we present two algorithms: Adaptive Consensus (AC) to solve the consensus problem and Adaptive Consensus based Gradient Tracking (AC-GT) to solve smooth strongly convex decentralized optimization problems. We establish strong theoretical convergence guarantees for the proposed algorithms and quantify their performance in terms of various algorithmic parameters under standard assumptions. Finally, numerical experiments showcase the effectiveness of the framework in significantly reducing the information exchange required to achieve a consensus solution.

Stochastic optimization methods have been hugely successful in making large-scale optimization problems feasible when computing the full gradient is computationally prohibitive. Using the theory of modified equations for numerical integrators, we propose a class of stochastic differential equations that approximate the dynamics of general stochastic optimization methods more closely than the original gradient flow. Analyzing a modified stochastic differential equation can reveal qualitative insights about the associated optimization method. Here, we study mean-square stability of the modified equation in the case of stochastic coordinate descent.