Trends in terrestrial temperature variability are perhaps more relevant for species viability than trends in mean temperature. In this paper, we develop methodology for estimating such trends using multi-resolution climate data from polar orbiting weather satellites. We derive two novel algorithms for computation that are tailored for dense, gridded observations over both space and time. We evaluate our methods with a simulation that mimics these data's features and on a large, publicly available, global temperature dataset with the eventual goal of tracking trends in cloud reflectance temperature variability.

The multi-armed bandit (MAB) model has been widely adopted for studying many practical optimization problems (network resource allocation, ad placement, crowdsourcing, etc.) with unknown parameters. The goal of the player here is to maximize the cumulative reward in the face of uncertainty. However, the basic MAB model neglects several important factors of the system in many real-world applications, where multiple arms can be simultaneously played and an arm could sometimes be "sleeping". Besides, ensuring fairness is also a key design concern in practice. To that end, we propose a new Combinatorial Sleeping MAB model with Fairness constraints, called CSMAB-F, aiming to address the aforementioned crucial modeling issues. The objective is now to maximize the reward while satisfying the fairness requirement of a minimum selection fraction for each individual arm. To tackle this new problem, we extend an online learning algorithm, UCB, to deal with a critical tradeoff between exploitation and exploration and employ the virtual queue technique to properly handle the fairness constraints. By carefully integrating these two techniques, we develop a new algorithm, called Learning with Fairness Guarantee (LFG), for the CSMAB-F problem. Further, we rigorously prove that not only LFG is feasibility-optimal, but it also has a time-average regret upper bounded by $\frac{N}{2\eta}+\frac{\beta_1\sqrt{mNT\log{T}}+\beta_2 N}{T}$, where N is the total number of arms, m is the maximum number of arms that can be simultaneously played, T is the time horizon, $\beta_1$ and $\beta_2$ are constants, and $\eta$ is a design parameter that we can tune. Finally, we perform extensive simulations to corroborate the effectiveness of the proposed algorithm. Interestingly, the simulation results reveal an important tradeoff between the regret and the speed of convergence to a point satisfying the fairness constraints.

Computing market equilibria is an important practical problem for market design (e.g. fair division, item allocation). However, computing equilibria requires large amounts of information (e.g. all valuations for all buyers for all items) and compute power. We consider ameliorating these issues by applying a method used for solving complex games: constructing a coarsened abstraction of a given market, solving for the equilibrium in the abstraction, and lifting the prices and allocations back to the original market. We show how to bound important quantities such as regret, envy, Nash social welfare, Pareto optimality, and maximin share when the abstracted prices and allocations are used in place of the real equilibrium. We then study two abstraction methods of interest for practitioners: 1) filling in unknown valuations using techniques from matrix completion, 2) reducing the problem size by aggregating groups of buyers/items into smaller numbers of representative buyers/items and solving for equilibrium in this coarsened market. We find that in real data allocations/prices that are relatively close to equilibria can be computed from even very coarse abstractions.

The problem has been excessively studied[1][2][3][4][5][6] and a vast array of methods have been introduced to either find the optimal tour or a good less time consuming approximation. This paper will concentrate onthe second path of meta-heuristics and specifically on genetic algorithms(GA) and the historical association with the TSP. GA's have been around since 1957[7], starting with simulations for biological evolution. GA's are used for optimization problems with large search spaces. The TSP as an optimization problem therefore fits the usage and an application of GA's to the TSP was conceivable. In1975 Holland [8] laid the foundation for the success and the resulting interestin GA's. With his fundamental theorem of genetic algorithms he proclaimed the efficiency of GA's for optimization problems. A generic GA starts with the generation of a population of several different tours.

Conversion optimization tools are estimated to have an average ROI of 223%. And that is totally expected as they're largely responsible for most conversions and revenue. However, CRO tools are more expensive than many other marketing tools, too (as you'll soon see in this article). And there are so many of them out there. But at the end of the day, it's not using these tools that matters but what they do for your business.

As teams apply optimization earlier and more frequently in the modeling process, they develop high-performing models at a faster pace. This virtuous cycle increases the number of models that make it into production, which amplifies the impact of these models on the business. At the Deep Learning Summit in San Francisco, SigOpt will be showcasing their model optimization software and how they automate model tuning to accelerate the model development process and amplify the impact of models in production at scale. We spoke to Nick Payton, B2B Marketing Lead at SigOpt to learn more. SigOpt's mission is to empower experts.

Improving predictive understanding of Earth system variability and change requires data-model integration. Efficient data-model integration for complex models requires surrogate modeling to reduce model evaluation time. However, building a surrogate of a large-scale Earth system model (ESM) with many output variables is computationally intensive because it involves a large number of expensive ESM simulations. In this effort, we propose an efficient surrogate method capable of using a few ESM runs to build an accurate and fast-to-evaluate surrogate system of model outputs over large spatial and temporal domains. We first use singular value decomposition to reduce the output dimensions, and then use Bayesian optimization techniques to generate an accurate neural network surrogate model based on limited ESM simulation samples. Our machine learning based surrogate methods can build and evaluate a large surrogate system of many variables quickly. Thus, whenever the quantities of interest change such as a different objective function, a new site, and a longer simulation time, we can simply extract the information of interest from the surrogate system without rebuilding new surrogates, which significantly saves computational efforts. We apply the proposed method to a regional ecosystem model to approximate the relationship between 8 model parameters and 42660 carbon flux outputs. Results indicate that using only 20 model simulations, we can build an accurate surrogate system of the 42660 variables, where the consistency between the surrogate prediction and actual model simulation is 0.93 and the mean squared error is 0.02. This highly-accurate and fast-to-evaluate surrogate system will greatly enhance the computational efficiency in data-model integration to improve predictions and advance our understanding of the Earth system.

Bayesian optimal design of experiments (BODE) has been successful in acquiring information about a quantity of interest (QoI) which depends on a black-box function. BODE is characterized by sequentially querying the function at specific designs selected by an infill-sampling criterion. However, most current BODE methods operate in specific contexts like optimization, or learning a universal representation of the black-box function. The objective of this paper is to design a BODE for estimating the statistical expectation of a physical response surface. This QoI is omnipresent in uncertainty propagation and design under uncertainty problems. Our hypothesis is that an optimal BODE should be maximizing the expected information gain in the QoI. We represent the information gain from a hypothetical experiment as the Kullback-Liebler (KL) divergence between the prior and the posterior probability distributions of the QoI. The prior distribution of the QoI is conditioned on the observed data and the posterior distribution of the QoI is conditioned on the observed data and a hypothetical experiment. The main contribution of this paper is the derivation of a semi-analytic mathematical formula for the expected information gain about the statistical expectation of a physical response. The developed BODE is validated on synthetic functions with varying number of input-dimensions. We demonstrate the performance of the methodology on a steel wire manufacturing problem.

Topology design optimization offers a tremendous opportunity in design and manufacturing freedoms by designing and producing a part from the ground-up without a meaningful initial design as required by conventional shape design optimization approaches. Ideally, with adequate problem statements, to formulate and solve the topology design problem using a standard topology optimization process, such as SIMP (Simplified Isotropic Material with Penalization) is possible. However, in reality, an estimated over thousands of design iterations is often required for just a few design variables, the conventional optimization approach is, in general, impractical or computationally unachievable for real-world applications significantly diluting the development of the topology optimization technology. There is, therefore, a need for a different approach that will be able to optimize the initial design topology effectively and rapidly. In this study, a novel topology optimization approach based on conditional Wasserstein generative adversarial networks (CWGAN) is developed to replicate the conventional topology optimization algorithms in an extremely computationally inexpensive way. CWGAN consists of a generator and a discriminator, both of which are deep convolutional neural networks (CNN). The limited samples of data, quasi-optimal planar structures, needed for training purposes are generated using the conventional topology optimization algorithms. With CWGANs, the topology optimization conditions can be set to a required value before generating samples.

Several problems in modeling and control of stochastically-driven dynamical systems can be cast as regularized semi-definite programs. We examine two such representative problems and show that they can be formulated in a similar manner. The first, in statistical modeling, seeks to reconcile observed statistics by suitably and minimally perturbing prior dynamics. The second seeks to optimally select a subset of available sensors and actuators for control purposes. To address modeling and control of large-scale systems we develop a unified algorithmic framework using proximal methods. Our customized algorithms exploit problem structure and allow handling statistical modeling, as well as sensor and actuator selection, for substantially larger scales than what is amenable to current general-purpose solvers. We establish linear convergence of the proximal gradient algorithm, draw contrast between the proposed proximal algorithms and alternating direction method of multipliers, and provide examples that illustrate the merits and effectiveness of our framework. Index Terms Actuator selection, sensor selection, sparsity-promoting estimation and control, method of multipliers, nonsmooth convex optimization, proximal algorithms, regularization for design, semi-definite programming, structured covariances. I. INTRODUCTION Convex optimization has had tremendous impact on many disciplines, including system identification and control design [1]-[7]. The present paper focuses on two representative control problems, statistical control-oriented modeling and sensor/actuator selection, that are cast as convex programs.