Online Resource Allocation with Samples

We study an online resource allocation problem under uncertainty about demand and about the reward of each type of demand (agents) for the resource. Even though dealing with demand uncertainty in resource allocation problems has been the topic of many papers in the literature, the challenge of not knowing rewards has been barely explored. The lack of knowledge about agents' rewards is inspired by the problem of allocating units of a new resource (e.g., newly developed vaccines or drugs) with unknown effectiveness/value. For such settings, we assume that we can \emph{test} the market before the allocation period starts. During the test period, we sample each agent in the market with probability $p$. We study how to optimally exploit the \emph{sample information} in our online resource allocation problem under adversarial arrival processes. We present an asymptotically optimal algorithm that achieves $1-\Theta(1/(p\sqrt{m}))$ competitive ratio, where $m$ is the number of available units of the resource. By characterizing an upper bound on the competitive ratio of any randomized and deterministic algorithm, we show that our competitive ratio of $1-\Theta(1/(p\sqrt{m}))$ is tight for any $p =\omega(1/\sqrt{m})$. That asymptotic optimality is possible with sample information highlights the significant advantage of running a test period for new resources. We demonstrate the efficacy of our proposed algorithm using a dataset that contains the number of COVID-19 related hospitalized patients across different age groups

Near-Optimal Primal-Dual Algorithms for Quantity-Based Network Revenue Management

We study the canonical quantity-based network revenue management (NRM) problem where the decision-maker must irrevocably accept or reject each arriving customer request with the goal of maximizing the total revenue given limited resources. The exact solution to the problem by dynamic programming is computationally intractable due to the well-known curse of dimensionality. Existing works in the literature make use of the solution to the deterministic linear program (DLP) to design asymptotically optimal algorithms. Those algorithms rely on repeatedly solving DLPs to achieve near-optimal regret bounds. It is, however, time-consuming to repeatedly compute the DLP solutions in real time, especially in large-scale problems that may involve hundreds of millions of demand units. In this paper, we propose innovative algorithms for the NRM problem that are easy to implement and do not require solving any DLPs. Our algorithm achieves a regret bound of $O(\log k)$, where $k$ is the system size. To the best of our knowledge, this is the first NRM algorithm that (i) has an $o(\sqrt{k})$ asymptotic regret bound, and (ii) does not require solving any DLPs

CDR: Conservative Doubly Robust Learning for Debiased Recommendation

In recommendation systems (RS), user behavior data is observational rather than experimental, resulting in widespread bias in the data. Consequently, tackling bias has emerged as a major challenge in the field of recommendation systems. Recently, Doubly Robust Learning (DR) has gained significant attention due to its remarkable performance and robust properties. However, our experimental findings indicate that existing DR methods are severely impacted by the presence of so-called Poisonous Imputation, where the imputation significantly deviates from the truth and becomes counterproductive. To address this issue, this work proposes Conservative Doubly Robust strategy (CDR) which filters imputations by scrutinizing their mean and variance. Theoretical analyses show that CDR offers reduced variance and improved tail bounds.In addition, our experimental investigations illustrate that CDR significantly enhances performance and can indeed reduce the frequency of poisonous imputation

Tumor promoter TPA activates Wnt/β-catenin signaling in a casein kinase 1-dependent manner.

The tumor promoter 12-O-tetra-decanoylphorbol-13-acetate (TPA) has been defined by its ability to promote tumorigenesis on carcinogen-initiated mouse skin. Activation of Wnt/β-catenin signaling has a decisive role in mouse skin carcinogenesis, but it remains unclear how TPA activates Wnt/β-catenin signaling in mouse skin carcinogenesis. Here, we found that TPA could enhance Wnt/β-catenin signaling in a casein kinase 1 (CK1) ε/δ-dependent manner. TPA stabilized CK1ε and enhanced its kinase activity. TPA further induced the phosphorylation of LRP6 at Thr1479 and Ser1490 and the formation of a CK1ε-LRP6-axin1 complex, leading to an increase in cytosolic β-catenin. Moreover, TPA increased the association of β-catenin with TCF4E in a CK1ε/δ-dependent way, resulting in the activation of Wnt target genes. Consistently, treatment with a selective CK1ε/δ inhibitor SR3029 suppressed TPA-induced skin tumor formation in vivo, probably through blocking Wnt/β-catenin signaling. Taken together, our study has identified a pathway by which TPA activates Wnt/β-catenin signaling

Striking Isotopologue-Dependent Photodissociation Dynamics of Water Molecules:The Signature of an Accidental Resonance

Investigations of the photofragmentation patterns of both light and heavy water at the state-to-state level are a prerequisite for any thorough understanding of chemical processing and isotope heterogeneity in the interstellar medium. Here we reveal dynamical features of the dissociation of water molecules following excitation to the (C) over tilde (010) state using a tunable vacuum ultraviolet source in combination with the high-resolution H(D)-atom Rydberg tagging time-of-flight technique. The action spectra for forming H(D) atoms and the OH(OD) product state distributions resulting from excitation to the (C) over tilde (010) states of H2O and D2O both show striking differences, which are attributable to the effects of an isotopologue-specific accidental resonance. Such accidental-resonance-induced state mixing may contribute to the D/H isotope heterogeneity in the solar system. The present study provides an excellent example of competitive state-to-state nonadiabatic decay pathways involving at least five electronic states