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In this paper, the problem of maximizing a black-box function f:→ℝ is studied in the Bayesian framework with a Gaussian Process prior. In particular, a new algorithm for this problem is proposed, and high probability bounds on its simple and cumulative regret are established. The query point selection rule in most existing methods involves an exhaustive search over an increasingly fine sequence of uniform discretizations of . The proposed algorithm, in contrast, adaptively refines  which leads to a lower computational complexity, particularly when  is a subset of a high dimensional Euclidean space. In addition to the computational gains, sufficient conditions are identified under which the regret bounds of the new algorithm improve upon the known results. Finally, an extension of the algorithm to the case of contextual bandits is proposed, and high probability bounds on the contextual regret are presented. 

We analyze the drivers, distribution, and properties of the relativistic electron precipitation (REP) detected near midnight by the Polar Orbiting Environmental Satellites (POES) and Meteorological Operational (MetOp) satellites, critical for understanding radiation belt losses and nightside atmospheric energy input. REP is either driven by wave‐particle interactions (isolated precipitation within the outer radiation belt), or current sheet scattering (CSS; precipitation with energy dispersion), or a combination of the two. We evaluate the L‐MLT distribution for the identified REP events in which only one process evidently drove the precipitation (∼10% of the REP near midnight). We show that the two mechanisms coexist and drive precipitation in a broadL‐shell range (4–7). However, wave‐driven REP was also observed atL < 4, whereas CSS‐driven REP was also detected atL > 7. Moreover, we estimate the magnetotail stretching during each REP event using the magnetic field observations from the Geostationary Operational Environmental Satellite (GOES). Both wave‐particle interactions and CSS drive REP in association with a stretched magnetotail, although CSS‐driven REP potentially shows more pronounced stretching. Wave‐driven REP events are localized inLshell and often occur on spatial scales of <0.3 L. Using either proton precipitation (observed by POES/MetOp during wave‐driven REP) as a proxy for electromagnetic ion cyclotron (EMIC) wave activity or wave observations (from GOES and the Van Allen Probes) at the conjugate event location, we find that ∼73% wave‐driven REP events are associated with EMIC waves.