Online Ranking: Discrete Choice, Spearman Correlation and Other Feedback

Given a set $V$ of $n$ objects, an online ranking system outputs at each time step a full ranking of the set, observes a feedback of some form and suffers a loss. We study the setting in which the (adversarial) feedback is an element in $V$, and the loss is the position (0th, 1st, 2nd...) of the item in the outputted ranking. More generally, we study a setting in which the feedback is a subset $U$ of at most $k$ elements in $V$, and the loss is the sum of the positions of those elements. We present an algorithm of expected regret $O(n^{3/2}\sqrt{Tk})$ over a time horizon of $T$ steps with respect to the best single ranking in hindsight. This improves previous algorithms and analyses either by a factor of either $\Omega(\sqrt{k})$, a factor of $\Omega(\sqrt{\log n})$ or by improving running time from quadratic to $O(n\log n)$ per round. We also prove a matching lower bound. Our techniques also imply an improved regret bound for online rank aggregation over the Spearman correlation measure, and to other more complex ranking loss functions

Rank aggregation in cyclic sequences

In this paper we propose the problem of finding the cyclic sequence which best represents a set of cyclic sequences. Given a set of elements and a precedence cost matrix we look for the cyclic sequence of the elements which is at minimum distance from all the ranks when the permutation metric distance is the Kendall Tau distance. In other words, the problem consists of finding a robust cyclic rank with respect to a set of elements. This problem originates from the Rank Aggregation Problem for combining different linear ranks of elements. Later we define a probability measure based on dissimilarity between cyclic sequences based on the Kendall Tau distance. Next, we also introduce the problem of finding the cyclic sequence with minimum expected cost with respect to that probability measure. Finally, we establish certain relationships among some classical problems and the new problems that we have proposed.Ministerio de Economía y CompetitividadJunta de AndalucíaFondo Europeo de Desarrollo Regiona

Online Combinatorial Linear Optimization via a Frank-Wolfe-based Metarounding Algorithm

Metarounding is an approach to convert an approximation algorithm for linear optimization over some combinatorial classes to an online linear optimization algorithm for the same class. We propose a new metarounding algorithm under a natural assumption that a relax-based approximation algorithm exists for the combinatorial class. Our algorithm is much more efficient in both theoretical and practical aspects

Rank Aggregation for Non-stationary Data Streams

The problem of learning over non-stationary ranking streams arises naturally, particularly in recommender systems. The rankings represent the preferences of a population, and the non-stationarity means that the distribution of preferences changes over time. We propose an algorithm that learns the current distribution of ranking in an online manner. The bottleneck of this process is a rank aggregation problem. We propose a generalization of the Borda algorithm for non-stationary ranking streams. As a main result, we bound the minimum number of samples required to output the ground truth with high probability. Besides, we show how the optimal parameters are set. Then, we generalize the whole family of weighted voting rules (the family to which Borda belongs) to situations in which some rankings are more reliable than others. We show that, under mild assumptions, this generalization can solve the problem of rank aggregation over non-stationary data streams.This work is partially funded by the Industrial Chair “Data science & Artificial Intelligence for Digitalized Industry & Services” from Telecom Paris (France), the Basque Government through the BERC 2018–2021 and the Elkartek program (KK-2018/00096, KK-2020/00049), and by the Spanish Government excellence accreditation Severo Ochoa SEV-2013-0323 (MICIU) and the project TIN2017-82626-R (MINECO). J. Del Ser also acknowledges funding support from the Basque Government (Consolidated Research Gr. MATHMODE, IT1294-19)

Synergistic and combinatorial optimization of finite element models for monitored buildings

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Hybrid simulation techniques in the structural analysis and testing of architectural heritage

L'abstract è presente nell'allegato / the abstract is in the attachmen

Approaching rank aggregation problems by using evolution strategies: The case of the optimal bucket order problem

The optimal bucket order problem consists in obtaining a complete consensus ranking (ties are allowed) from a matrix of preferences (possibly obtained from a database of rankings). In this paper, we tackle this problem by using evolution strategies. We designed specific mutation operators which are able to modify the inner structure of the buckets, which introduces more diversity into the search process. We also study different initialization methods and strategies for the generation of the population of descendants. The proposed evolution strategies are tested using a benchmark of 52 databases and compared with the current state-of-the-art algorithm LIA. We carry out a standard machine learning statistical analysis procedure to identify a subset of outstanding configurations of the proposed evolution strategies. The study shows that the best evolution strategy improves upon the accuracy obtained by the standard greedy method (BPA) by 35%, and that of LIA by 12.5%