We consider Online Convex Optimization (OCO) in the setting where the costs are $m$-strongly convex and the online learner pays a switching cost for changing decisions between rounds. We show that the recently proposed Online Balanced Descent (OBD) algorithm is constant competitive in this setting, with competitive ratio $3 + O(1/m)$, irrespective of the ambient dimension. Additionally, we show that when the sequence of cost functions is $\epsilon$-smooth, OBD has near-optimal dynamic regret and maintains strong per-round accuracy. We demonstrate the generality of our approach by showing that the OBD framework can be used to construct competitive algorithms for a variety of online problems across learning and control, including online variants of ridge regression, logistic regression, maximum likelihood estimation, and LQR control.

Propositional model counting (MC), or #SAT, is the task of counting the number of satisfying assignments for a given propositional formula [14]. Weighted model counting (WMC), or weighted #SAT, additionally incorporates a weight function over the set of all possible assignments. Offering an elegant formalism for encoding various probabilistic inference problems, WMC is a unifying approach for probabilistic inference. In particular, probabilistic graphical models [20], probabilistic planning [10], probabilistic logic programming [25], probabilistic databases [30] and probabilistic ontologies [2] can greatly benefit from advances in WMC. Two important special cases of WMC are weighted #CNF and weighted #DNF, where the former requires the input formula to be in CNF, and the latter to be in DNF. Both of these problems have a wide variety of applications. Inference in probabilistic graphical models typically reduces to solving weighted #CNF instances, while query evaluation in probabilistic databases reduces to solving weighted #DNF instances. The major bottleneck in WMC is its inherent computational complexity.

Traditional cognitive theories systematically apply classical set-theoretic structures to model human judgements and decisions under uncertainty. This is particularly evident in theories of rational decision-making, like expected utility theory, where Bayesian, or Kolmogorovian [1], models of probability directly follow from axioms on agents' preferences [2, 3]. However, several cognitive puzzles have been discovered in empirical tests, which provide evidence of systematic deviations from Kolmogorovian probability structures (see, e.g., [4]). For example, Kahneman and Tversky identified a conjunction fallacy in human probability judgements, namely, the law of monotonicity of Kolmogorovian probability does not generally hold in this kind of judgements [5]. Also, in human decision-making, Tversky and Shafir proved that the law of total Kolmogorovian probability does not hold in the disjunction effect [6], while Allais and Ellsberg indicated that people do not always choose by maximizing an expected utility with respect to a Kolmogorovian probability measure [7]. As a consequence of the puzzles above, traditional theories using Kolmogorovian structures, though normatively compelling, are descriptively flawed, which led several authors to elaborate alternative proposals able to more efficiently and realistically represent human behaviour. This was the starting point of the bounded rationality research programme, initially proposed by Herbert Simon [8] and systematically applied by Kahneman and Tversky [5, 6] to describe concrete judgements and decisions. Bounded rationality models give good predictions in a variety of circumstances.

This paper reviews recent advances in the field of optimization under uncertainty via a modern data lens, highlights key research challenges and promise of data-driven optimization that organically integrates machine learning and mathematical programming for decision-making under uncertainty, and identifies potential research opportunities. A brief review of classical mathematical programming techniques for hedging against uncertainty is first presented, along with their wide spectrum of applications in Process Systems Engineering. A comprehensive review and classification of the relevant publications on data-driven distributionally robust optimization, data-driven chance constrained program, data-driven robust optimization, and data-driven scenario-based optimization is then presented. This paper also identifies fertile avenues for future research that focuses on a closed-loop data-driven optimization framework, which allows the feedback from mathematical programming to machine learning, as well as scenario-based optimization leveraging the power of deep learning techniques. Perspectives on online learning-based data-driven multistage optimization with a learning-while-optimizing scheme is presented.

Due to their capacity to condense the spatiotemporal structure of a data set in a format amenable for human interpretation, forecasting, and anomaly detection, causality graphs are routinely estimated in social sciences, natural sciences, and engineering. A popular approach to mathematically formalize causality is based on vector autoregressive (VAR) models, which constitutes an alternative to the well-known but usually intractable Granger causality. Relying on such a VAR causality notion, this paper develops two algorithms with complementary benefits to track time-varying causality graphs in an online fashion. Despite using data in a sequential fashion, both algorithms are shown to asymptotically attain the same average performance as a batch estimator with all data available at once. Moreover, their constant complexity per update renders these algorithms appealing for big-data scenarios. Theoretical and experimental performance analysis support the merits of the proposed algorithms. Remarkably, no probabilistic models or stationarity assumptions need to be introduced, which endows the developed algorithms with considerable generality

This report provides an in-depth overview over the implications and novelty Generalized Variational Inference (GVI) (Knoblauch et al., 2019) brings to Deep Gaussian Processes (DGPs) (Damianou & Lawrence, 2013). Specifically, robustness to model misspecification as well as principled alternatives for uncertainty quantification are motivated with an information-geometric view. These modifications have clear interpretations and can be implemented in less than 100 lines of Python code. Most importantly, the corresponding empirical results show that DGPs can greatly benefit from the presented enhancements.

In a nutshell, the (µ / λ) CMA-ES is an iterative black box optimization algorithm, that, in each of its iterations, samples λ candidate This paper introduces a novel theoretically sound approach for solutions from a multivariate normal distribution, evaluates the celebrated CMA-ES algorithm. Assuming the parameters of these solutions (sequentially or in parallel) retains µ candidates the multi variate normal distribution for the minimum follow a and adjusts the sampling distribution used for the next iteration conjugate prior distribution, we derive their optimal update at to give higher probability to good samples. Each iteration can be each iteration step. Not only provides this Bayesian framework a individually seen as taking an initial guess or prior for the multi justification for the update of the CMA-ES algorithm but it also gives variate parameters, namely the mean and the covariance, and after two new versions of CMA-ES either assuming normal-Wishart or making an experiment by evaluating these sample points with the normal-Inverse Wishart priors, depending whether we parametrize fit function updating the initial parameters accordingly.

Exact structured inference with neural network scoring functions is computationally challenging but several methods have been proposed for approximating inference. One approach is to perform gradient descent with respect to the output structure directly (Belanger and McCallum, 2016). Another approach, proposed recently, is to train a neural network (an "inference network") to perform inference (Tu and Gimpel, 2018). In this paper, we compare these two families of inference methods on three sequence labeling datasets. We choose sequence labeling because it permits us to use exact inference as a benchmark in terms of speed, accuracy, and search error. Across datasets, we demonstrate that inference networks achieve a better speed/accuracy/search error trade-off than gradient descent, while also being faster than exact inference at similar accuracy levels. We find further benefit by combining inference networks and gradient descent, using the former to provide a warm start for the latter.

The problem of combined state and input estimation of linear structural systems based on measured responses and a priori knowledge of structural model is considered. A novel methodology using Gaussian process latent force models is proposed to tackle the problem in a stochastic setting. Gaussian process latent force models (GPLFMs) are hybrid models that combine differential equations representing a physical system with data-driven non-parametric Gaussian process models. In this work, the unknown input forces acting on a structure are modelled as Gaussian processes with some chosen covariance functions which are combined with the mechanistic differential equation representing the structure to construct a GPLFM. The GPLFM is then conveniently formulated as an augmented stochastic state-space model with additional states representing the latent force components, and the joint input and state inference of the resulting model is implemented using Kalman filter. The augmented state-space model of GPLFM is shown as a generalization of the class of input-augmented state-space models, is proven observable, and is robust compared to conventional augmented formulations in terms of numerical stability. The hyperparameters governing the covariance functions are estimated using maximum likelihood optimization based on the observed data, thus overcoming the need for manual tuning of the hyperparameters by trial-and-error. To assess the performance of the proposed GPLFM method, several cases of state and input estimation are demonstrated using numerical simulations on a 10-dof shear building and a 76-storey ASCE benchmark office tower. Results obtained indicate the superior performance of the proposed approach over conventional Kalman filter based approaches.

Future buildings will offer new convenience, comfort, and efficiency possibilities to their residents. Changes will occur to the way people live as technology involves into people's lives and information processing is fully integrated into their daily living activities and objects. The future expectation of smart buildings includes making the residents' experience as easy and comfortable as possible. The massive streaming data generated and captured by smart building appliances and devices contains valuable information that needs to be mined to facilitate timely actions and better decision making. Machine learning and big data analytics will undoubtedly play a critical role to enable the delivery of such smart services. In this paper, we survey the area of smart building with a special focus on the role of techniques from machine learning and big data analytics. This survey also reviews the current trends and challenges faced in the development of smart building services.