A/B Testing and Best-arm Identification for Linear Bandits with Robustness to Non-stationarity

We investigate the fixed-budget best-arm identification (BAI) problem for linear bandits in a potentially non-stationary environment. Given a finite arm set $\mathcal{X}\subset\mathbb{R}^d$, a fixed budget $T$, and an unpredictable sequence of parameters $\left\lbrace\theta_t\right\rbrace_{t=1}^{T}$, an algorithm will aim to correctly identify the best arm $x^* := \arg\max_{x\in\mathcal{X}}x^\top\sum_{t=1}^{T}\theta_t$ with probability as high as possible. Prior work has addressed the stationary setting where $\theta_t = \theta_1$ for all $t$ and demonstrated that the error probability decreases as $\exp(-T /\rho^*)$ for a problem-dependent constant $\rho^*$. But in many real-world $A/B/n$ multivariate testing scenarios that motivate our work, the environment is non-stationary and an algorithm expecting a stationary setting can easily fail. For robust identification, it is well-known that if arms are chosen randomly and non-adaptively from a G-optimal design over $\mathcal{X}$ at each time then the error probability decreases as $\exp(-T\Delta^2_{(1)}/d)$, where $\Delta_{(1)} = \min_{x \neq x^*} (x^* - x)^\top \frac{1}{T}\sum_{t=1}^T \theta_t$. As there exist environments where $\Delta_{(1)}^2/ d \ll 1/ \rho^*$, we are motivated to propose a novel algorithm $\mathsf{P1}$-$\mathsf{RAGE}$ that aims to obtain the best of both worlds: robustness to non-stationarity and fast rates of identification in benign settings. We characterize the error probability of $\mathsf{P1}$-$\mathsf{RAGE}$ and demonstrate empirically that the algorithm indeed never performs worse than G-optimal design but compares favorably to the best algorithms in the stationary setting.Comment: 25 pages, 6 figure

Spatial assessment of fishing effort around European marine reserves: Implications for successful fisheries management

9 pages, 3 figures, 4 tablesWe examined the spatial dynamic of artisanal fishing fleets around five European marine protected areas (MPAs) to derive general implications for the evaluation of MPAs as fisheries management tools. The coastal MPAs studied were located off France, Malta and Spain and presented a variety of spatial designs and processes of establishment. We developed a standardized methodology to define factors influencing effort allocation and to produce fishing effort maps by merging GIS with geostatistical modelling techniques. Results revealed that in most cases the factors “distance to the no-take”, “water depth”, and “distance to the port” had a significant influence on effort allocation by the fishing fleets. Overall, we found local concentration of fishing effort around the MPA borders. Thus, neglecting the pattern of fishing effort distribution in evaluating MPA benefits, such as spillover of biomass, could hamper sound interpretation of MPAs as fisheries management toolsThis manuscript is a product of the fisheries working package (WP2) of the European Commission project “Marine Protected Areas as Tools for Fisheries Management and Conservation” (EMPAFISH; Contract No. 006539). Part of the data collected for this study was also funded by the European project BIOMEX (Contract No. QLRT-2001-00891). The first author was sponsored by a research fellowship of the German Research Foundation (DFG)Peer reviewe

Approche en chimie environnementale : de la quantification ciblée de contaminnats à l'évaluation de la contamination du milieu aquatique par une approche non ciblée.

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Cytonuclear interactions affect adaptive traits of the annual plant Arabidopsis thaliana in the field

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