Decentralized Cooperative Stochastic Bandits

We study a decentralized cooperative stochastic multi-armed bandit problem with $K$ arms on a network of $N$ agents. In our model, the reward distribution of each arm is the same for each agent and rewards are drawn independently across agents and time steps. In each round, each agent chooses an arm to play and subsequently sends a message to her neighbors. The goal is to minimize the overall regret of the entire network. We design a fully decentralized algorithm that uses an accelerated consensus procedure to compute (delayed) estimates of the average of rewards obtained by all the agents for each arm, and then uses an upper confidence bound (UCB) algorithm that accounts for the delay and error of the estimates. We analyze the regret of our algorithm and also provide a lower bound. The regret is bounded by the optimal centralized regret plus a natural and simple term depending on the spectral gap of the communication matrix. Our algorithm is simpler to analyze than those proposed in prior work and it achieves better regret bounds, while requiring less information about the underlying network. It also performs better empirically

Estimating adaptive setpoint temperatures using weather stations

Reducing both the energy consumption and CO 2 emissions of buildings is nowadays one of the main objectives of society. The use of heating and cooling equipment is among the main causes of energy consumption. Therefore, reducing their consumption guarantees such a goal. In this context, the use of adaptive setpoint temperatures allows such energy consumption to be significantly decreased. However, having reliable data from an external temperature probe is not always possible due to various factors. This research studies the estimation of such temperatures without using external temperature probes. For this purpose, a methodology which consists of collecting data from 10 weather stations of Galicia is carried out, and prediction models (multivariable linear regression (MLR) and multilayer perceptron (MLP)) are applied based on two approaches: (1) using both the setpoint temperature and the mean daily external temperature from the previous day; and (2) using the mean daily external temperature from the previous 7 days. Both prediction models provide adequate performances for approach 1, obtaining accurate results between 1 month (MLR) and 5 months (MLP). However, for approach 2, only the MLP obtained accurate results from the 6th month. This research ensures the continuity of using adaptive setpoint temperatures even in case of possible measurement errors or failures of the external temperature probes.Spanish Ministry of Science, Innovation and Universities 00064742/ITC-20133094Spanish Ministry of Economy, Industry and Competitiveness BIA 2017-85657-

Open Problem: Polynomial linearly-convergent method for geodesically convex optimization?

Let $f \colon \mathcal{M} \to \mathbb{R}$ be a Lipschitz and geodesically convex function defined on a $d$-dimensional Riemannian manifold $\mathcal{M}$. Does there exist a first-order deterministic algorithm which (a) uses at most $O(\mathrm{poly}(d) \log(\epsilon^{-1}))$ subgradient queries to find a point with target accuracy $\epsilon$, and (b) requires only $O(\mathrm{poly}(d))$ arithmetic operations per query? In convex optimization, the classical ellipsoid method achieves this. After detailing related work, we provide an ellipsoid-like algorithm with query complexity $O(d^2 \log^2(\epsilon^{-1}))$ and per-query complexity $O(d^2)$ for the limited case where $\mathcal{M}$ has constant curvature (hemisphere or hyperbolic space). We then detail possible approaches and corresponding obstacles for designing an ellipsoid-like method for general Riemannian manifolds

Convergence and Trade-Offs in Riemannian Gradient Descent and Riemannian Proximal Point

In this work, we analyze two of the most fundamental algorithms in geodesically convex optimization: Riemannian gradient descent and (possibly inexact) Riemannian proximal point. We quantify their rates of convergence and produce different variants with several trade-offs. Crucially, we show the iterates naturally stay in a ball around an optimizer, of radius depending on the initial distance and, in some cases, on the curvature. In contrast, except for limited cases, previous works bounded the maximum distance between iterates and an optimizer only by assumption, leading to incomplete analyses and unquantified rates. We also provide an implementable inexact proximal point algorithm yielding new results on minmax problems, and we prove several new useful properties of Riemannian proximal methods: they work when positive curvature is present, the proximal operator does not move points away from any optimizer, and we quantify the smoothness of its induced Moreau envelope. Further, we explore beyond our theory with empirical tests

Violencia psicológica en el trabajo: Métodos de evaluación y variables sociodemográficas relevantes

En esta Tesis Doctoral se analiza la presencia de acoso psicológico (mobbing), acoso sexual (sexual harrasment) y burnout en una muestra de 1730 trabajadores de la Comunidad Valenciana. En la investigación se han empleado métodos diferentes en la evaluación de la violencia y del burnout. Se contrastan los resultados obtenidos con los diferentes métodos a la vez que se ponen en relación con una serie de características sociolaborales de interés tales como el tamaño de la empresa, la edad, el tipo de empresa, el género del acosador y el género de la víctima o el estatus ocupado en la escala laboral por el agresor. Los resultados muestran que el tipo de empresa (pública versus privada) y el género de la víctima (hombre versus mujer) no se relacionan con la mayor o menor presencia de acoso psicológico, mientras que la edad y el tamaño de la empresa (grande versus pequeña) de los trabajadores que informan de haber sido víctimas de acoso si que se relacionan, de esta forma, hallamos mayor tasa de acosados en el grupo de personas mayores y en las empresas más pequeñas. En cuanto al estatus ocupado por el agresor, éste siempre ocupa una posición jerárquica superior en la escala laboral y cuando no tenemos en cuenta el género de la víctima los hombres aparecen como los principales agresores. Por lo que se refiere al acoso sexual y las variables sociolaborales, no hemos encontramos diferencias en cuanto al tipo de empresa, la edad, ni en el tamaño de la empresa en el que trabajan las víctimas, pero sí en el género de las víctimas, así, las mujeres informan haber sido víctimas de acoso sexual en mayor medida que los hombres. Estos resultados (mayor acoso sexual en mujeres que en hombres), los encontramos tanto en las empresas privadas como públicas, en el grupo de mayores y en las empresas grandes. Cuando nos referimos al estatus del perpetrador y el género de la víctima los hombres son acosados por personas que ocupan una posición similar a la suya en la jerarquía laboral mientras que cuando la víctima es una mujer el acoso proviene la mayoría de las veces de personas que ocupan una posición jerárquica superior. Finalmente las mujeres son acosadas principalmente por hombres y los hombres por mujeres. Respecto al burnout, los resultados muestran al igual que sucedía con el acoso psicológico, que el tipo de empresa y el género de la víctima no se relacionan con la mayor o menor presencia de burnout, ocurre por igual en los dos tipos de empresa y tanto en hombres como en mujeres. Por lo que se refiere a la edad y el tamaño de la empresa en la que trabaja la víctima, las personas mayores informan haber experimentado más desgaste profesional y encontramos mayor presencia de este síndrome en las empresas pequeñas.This doctoral thesis examines the presence of psychological harassment (mobbing), sexual harassment and burnout in a sample of 1730 workers of the Valecian Community. In the research different methods have been used for the assessment of violence and burnout. We contrasted the results obtained with the different methods and we put them into relation with a number of social-labour characteristics of interest such as firm size, age, type of company, gender of the harasser and gender of the victim or the status held in the company by the harasser. Results show that the type of company (public versus private) and victim's gender (male versus female) are not related to the same degree of psychological harassment, while the age and company size (large versus small) of the workers who reported having been victims of harassment were related. With respect to sexual harassment and social-labour variables, we only found differences in the gender of the victims, thus women reported themselves to be victims of sexual harassment to a greater extend than men. When we refer to the status of the perpetrator and the victim's gender, men are harassed by people who occupy a similar to their position in the occupational hierarchy while when the victim is a woman, harassment comes most often from people who occupy a higher hierarchical position. With regard to burnout, we found the type of company and the victim's gender not to be related to the greater or lesser presence of burnout. Finally, with respect to age, we found that older people reported having experienced more burnout, and, with regard to the size of company in which the victim works, we found this syndrome to be the more common presented in small firms. This study also provides interesting information about the social variables mentioned, as well as the gender and status of the harasser

Accelerated Methods for Riemannian Min-Max Optimization Ensuring Bounded Geometric Penalties

In this work, we study optimization problems of the form $\min_x \max_y f(x, y)$, where $f(x, y)$ is defined on a product Riemannian manifold $\mathcal{M} \times \mathcal{N}$ and is $\mu_x$-strongly geodesically convex (g-convex) in $x$ and $\mu_y$-strongly g-concave in $y$, for $\mu_x, \mu_y \geq 0$. We design accelerated methods when $f$ is $(L_x, L_y, L_{xy})$-smooth and $\mathcal{M}$, $\mathcal{N}$ are Hadamard. To that aim we introduce new g-convex optimization results, of independent interest: we show global linear convergence for metric-projected Riemannian gradient descent and improve existing accelerated methods by reducing geometric constants. Additionally, we complete the analysis of two previous works applying to the Riemannian min-max case by removing an assumption about iterates staying in a pre-specified compact set.Comment: added weakly-convex analysis, and some remark

Time series ordinal classification via shapelets

Nominal time series classification has been widely developed over the last years. However, to the best of our knowledge, ordinal classification of time series is an unexplored field, and this paper proposes a first approach in the context of the shapelet transform (ST). For those time series dataset where there is a natural order between the labels and the number of classes is higher than 2, nominal classifiers are not capable of achieving the best results, because the models impose the same cost of misclassification to all the errors, regardless the difference between the predicted and the ground-truth. In this sense, we consider four different evaluation metrics to do so, three of them of an ordinal nature. The first one is the widely known Information Gain (IG), proved to be very competitive for ST methods, whereas the remaining three measures try to boost the order information by refining the quality measure. These three measures are a reformulation of the Fisher score, the Spearman's correlation coefficient (ρ), and finally, the Pearson's correlation coefficient (R 2 ). An empirical evaluation is carried out, considering 7 ordinal datasets from the UEA & UCR time series classification repository, 4 classifiers (2 of them of nominal nature, whereas the other 2 are of ordinal nature) and 2 performance measures (correct classification rate, CCR, and average mean absolute error, AMAE). The results show that, for both performance metrics, the ST quality metric based on R 2 is able to obtain the best results, specially for AMAE, for which the differences are statistically significant in favour of R 2