Decentralized Exploration in Multi-Armed Bandits

We consider the decentralized exploration problem: a set of players collaborate to identify the best arm by asynchronously interacting with the same stochastic environment. The objective is to insure privacy in the best arm identification problem between asynchronous, collaborative, and thrifty players. In the context of a digital service, we advocate that this decentralized approach allows a good balance between the interests of users and those of service providers: the providers optimize their services, while protecting the privacy of the users and saving resources. We define the privacy level as the amount of information an adversary could infer by intercepting the messages concerning a single user. We provide a generic algorithm Decentralized Elimination, which uses any best arm identification algorithm as a subroutine. We prove that this algorithm insures privacy, with a low communication cost, and that in comparison to the lower bound of the best arm identification problem, its sample complexity suffers from a penalty depending on the inverse of the probability of the most frequent players. Then, thanks to the genericity of the approach, we extend the proposed algorithm to the non-stationary bandits. Finally, experiments illustrate and complete the analysis

Supervised Feature Space Reduction for Multi-Label Nearest Neighbors

International audienceWith the ability to process many real-world problems, multi-label classification has received a large attention in recent years and the instance-based ML-kNN classifier is today considered as one of the most efficient. But it is sensitive to noisy and redundant features and its performances decrease with increasing data dimensionality. To overcome these problems, dimensionality reduction is an alternative but current methods optimize reduction objectives which ignore the impact on the ML-kNN classification. We here propose ML-ARP, a novel dimensionality reduction algorithm which, using a variable neighborhood search meta-heuristic, learns a linear projection of the feature space which specifically optimizes the ML-kNN classification loss. Numerical comparisons have confirmed that ML-ARP outperforms ML-kNN without data processing and four standard multi-label dimensionality reduction algorithms

Toward An Uncertainty Principle For Weighted Graphs

International audienceThe uncertainty principle states that a signal cannot be localized both in time and frequency. With the aim of extending this result to signals on graphs, Agaskar & Lu introduce notions of graph and spectral spreads. They show that a graph uncertainty principle holds for some families of unweighted graphs. This principle states that a signal cannot be simultaneously localized both in graph and spectral domains. In this paper, we aim to extend their work to weighted graphs. We show that a naive extension of their definitions leads to inconsistent results such as discontinuity of the graph spread when regarded as a function of the graph structure. To circumvent this problem, we propose another definition of graph spread that relies on an inverse similarity matrix. We also discuss the choice of the distance function that appears in this definition. Finally, we compute and plot uncertainty curves for families of weighted graphs

Memory Bandits: a Bayesian approach for the Switching Bandit Problem

International audienceThe Thompson Sampling exhibits excellent results in practice and it has been shown to be asymptotically optimal. The extension of Thompson Sampling algorithm to the Switching Multi-Armed Bandit problem, proposed in [13], is a Thompson Sampling equiped with a Bayesian online change point detector [1]. In this paper, we propose another extension of this approach based on a Bayesian aggregation framework. Experiments provide some evidences that in practice, the proposed algorithm compares favorably with the previous version of Thompson Sampling for the Switching Multi-Armed Bandit Problem, while it outperforms clearly other algorithms of the state-of-the-art

Restarted Bayesian Online Change-point Detector achieves Optimal Detection Delay

International audienceIn this paper, we consider the problem of sequential change-point detection where both the changepoints and the distributions before and after the change are assumed to be unknown. For this problem of primary importance in statistical and sequential learning theory, we derive a variant of the Bayesian Online Change Point Detector proposed by (Fearnhead & Liu, 2007) which is easier to analyze than the original version while keeping its powerful message-passing algorithm. We provide a non-asymptotic analysis of the false-alarm rate and the detection delay that matches the existing lower-bound. We further provide the first explicit high-probability control of the detection delay for such approach. Experiments on synthetic and realworld data show that this proposal outperforms the state-of-art change-point detection strategy, namely the Improved Generalized Likelihood Ratio (Improved GLR) while compares favorably with the original Bayesian Online Change Point Detection strategy

Fat Embolism Syndrome, a Diagnostic Dilemma: Case Report and Review of the Literature

Fat embolism syndrome (FES) remains a diagnostic dilemma on a world scale. It has a variable degree of presentation, which makes the diagnostic confirmation hard to obtain. FES is a life-threatening condition which is usually associated with orthopedic trauma, particularly long bones fractures whose early fixation helps in preventing it. It requires supportive care, and no specific treatment is needed. Here, we report the case of a FES in a 20 year-old male patient with right femoral shaft fracture following a motorbike accident, which is diagnosed by Gurd’s criteria and confirmed after exclusion of other diagnosis with similar clinical presentation

Memory Bandits: a Bayesian approach for the Switching Bandit Problem

International audienceThe Thompson Sampling exhibits excellent results in practice and it has been shown to be asymptotically optimal. The extension of Thompson Sampling algorithm to the Switching Multi-Armed Bandit problem, proposed in [13], is a Thompson Sampling equiped with a Bayesian online change point detector [1]. In this paper, we propose another extension of this approach based on a Bayesian aggregation framework. Experiments provide some evidences that in practice, the proposed algorithm compares favorably with the previous version of Thompson Sampling for the Switching Multi-Armed Bandit Problem, while it outperforms clearly other algorithms of the state-of-the-art

Memory Bandits: a Bayesian approach for the Switching Bandit Problem

International audienceThe Thompson Sampling exhibits excellent results in practice and it has been shown to be asymptotically optimal. The extension of Thompson Sampling algorithm to the Switching Multi-Armed Bandit problem, proposed in [13], is a Thompson Sampling equiped with a Bayesian online change point detector [1]. In this paper, we propose another extension of this approach based on a Bayesian aggregation framework. Experiments provide some evidences that in practice, the proposed algorithm compares favorably with the previous version of Thompson Sampling for the Switching Multi-Armed Bandit Problem, while it outperforms clearly other algorithms of the state-of-the-art

Memory Bandits: Towards the Switching Bandit Problem Best Resolution

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Uncertainty principle on graphs

International audienceGraph Signal Processing (GSP) is a mathematical framework that aims at extending classical Fourier harmonic analysis to irregular domains described using graphs. Within this framework, authors have proposed to define operators (e.g. translations, convolutions) and processes (e.g. filtering, sampling). A very important and fundamental result in classical harmonic analysis is the uncertainty principle, which states that a signal cannot be localized both in time and in frequency domains. In this chapter, we explore the uncertainty principle in the context of GSP. More precisely, we present notions of graph and spectral spreads, and show that the existence of signals that are both localized in the graph domain and in the spectrum domain depends on the graph