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We propose a new learning framework that captures the tiered structure of many real-world user-interaction applications, where the users can be divided into two groups based on their different tolerance on exploration risks and should be treated separately. In this setting, we simultaneously maintain two policies π^O and πE: π^O ("O" for "online") interacts with more risk-tolerant users from the first tier and minimizes regret by balancing exploration and exploitation as usual, while π^E ("E" for "exploit") exclusively focuses on exploitation for risk-averse users from the second tier utilizing the data collected so far. An important question is whether such a separation yields advantages over the standard online setting (i.e., π^E=π^O) for the risk-averse users. We individually consider the gap-independent vs. gap-dependent settings. For the former, we prove that the separation is indeed not beneficial from a minimax perspective. For the latter, we show that if choosing Pessimistic Value Iteration as the exploitation algorithm to produce π^E, we can achieve a constant regret for risk-averse users independent of the number of episodes K, which is in sharp contrast to the Ω(logK) regret for any online RL algorithms in the same setting, while the regret of π^O (almost) maintains its online regret optimality and does not need to compromise for the success of π^E. 

Abstract One of the most poorly understood aspects of low-mass star formation is how multiple-star systems are formed. Here we present the results of Atacama Large Millimeter/submillimeter Array (ALMA) Band 6 observations toward a forming quadruple protostellar system, G206.93-16.61E2, in the Orion B molecular cloud. ALMA 1.3 mm continuum emission reveals four compact objects, of which two are Class I young stellar objects and the other two are likely in prestellar phase. The 1.3 mm continuum emission also shows three asymmetric ribbon-like structures that are connected to the four objects, with lengths ranging from ∼500 to ∼2200 au. By comparing our data with magnetohydrodynamic simulations, we suggest that these ribbons trace accretion flows and also function as gas bridges connecting the member protostars. Additionally, ALMA CO J = 2−1 line emission reveals a complicated molecular outflow associated with G206.93-16.61E2, with arc-like structures suggestive of an outflow cavity viewed pole-on. 

We report results of a project to map HCN and HCO+ J=1→0 emission toward a sample of molecular clouds in the inner Galaxy, all containing dense clumps that are actively engaged in star formation. We compare these two molecular line tracers with millimeter continuum emission and extinction, as inferred from 13CO, as tracers of dense gas in molecular clouds. The fraction of the line luminosity from each tracer that comes from the dense gas, as measured by AV>8 mag, varies substantially from cloud to cloud. In all cases, a substantial fraction (in most cases, the majority) of the total luminosity arises in gas below the AV>8 mag threshold and outside the region of strong millimeter continuum emission. Measurements of L(HCN) toward other galaxies will likely be dominated by such gas at lower surface densities. Substantial, even dominant, contributions to the total line luminosity can arise in gas with densities typical of the cloud as a whole (n ∼ 100 cm-3). Defining the dense clump from the HCN or HCO+ emission itself, similarly to previous studies, leads to a wide range of clump properties, with some being considerably larger and less dense than in previous studies. HCN and HCO+ have a similar ability to trace dense gas for the clouds in this sample. For the two clouds with low virial parameters, 13CO is definitely a worse tracer of the dense gas, but for the other four, it is equally good (or bad) at tracing dense gas.