A natural optimization model that formulates many online resource allocation and revenue management problems is the online linear program (LP) where the constraint matrix is revealed column by column along with the objective function. We provide a near-optimal algorithm for this surprisingly general class of online problems under the assumption of random order of arrival and some mild conditions on the size of the LP right-hand-side input. Our learning-based algorithm works by dynamically updating a threshold price vector at geometric time intervals, where the dual prices learned from revealed columns in the previous period are used to determine the sequential decisions in the current period. Our algorithm has a feature of "learning by doing", and the prices are updated at a carefully chosen pace that is neither too fast nor too slow. In particular, our algorithm doesn't assume any distribution information on the input itself, thus is robust to data uncertainty and variations due to its dynamic learning capability. Applications of our algorithm include many online multi-resource allocation and multi-product revenue management problems such as online routing and packing, online combinatorial auctions, adwords matching, inventory control and yield management.

Background: Although research on the effects of comorbidities on coronavirus disease 2019 (COVID-19) patients is increasing, the risk of cancer history has not been evaluated for the mortality of patients with COVID-19. Methods: In this retrospective study, we included 3232 patients with pathogen-confirmed COVID-19 who were hospitalized between January 18th and March 27th, 2020, at Tongji Hospital in Wuhan, China. Propensity score matching was used to minimize selection bias. Results: In total, 2665 patients with complete clinical outcomes were analyzed. The impacts of age, sex, and comorbidities were evaluated separately using binary logistic regression analysis. The results showed that age, sex, and cancer history are independent risk factors for mortality in hospitalized COVID-19 patients. COVID-19 patients with cancer exhibited a significant increase in mortality rate (29.4% vs. 10.2%, P < 0.0001). Furthermore, the clinical outcomes of patients with hematological malignancies were worse, with a mortality rate twice that of patients with solid tumors (50% vs. 26.1%). Importantly, cancer patients with complications had a significantly higher risk of poor outcomes. One hundred nine cancer patients were matched to noncancer controls in a 1:3 ratio by propensity score matching. After propensity score matching, the cancer patients still had a higher risk of mortality than the matched noncancer patients (odds ratio (OR) 2.98, 95% confidence interval (95% CI) 1.76-5.06). Additionally, elevations in ferritin, high-sensitivity C-reactive protein, erythrocyte sedimentation rate, procalcitonin, prothrombin time, interleukin-2 (IL-2) receptor, and interleukin-6 (IL-6) were observed in cancer patients.

We consider a retailer selling a single product with limited on-hand inventory over a finite selling season. Customer demand arrives according to a Poisson process, the rate of which is influenced by a single action taken by the retailer (such as price adjustment, sales commission, advertisement intensity, etc.). The relationship between the action and the demand rate is not known in advance. However, the retailer is able to learn the optimal action "on the fly" as she maximizes her total expected revenue based on the observed demand reactions.Using the pricing problem as an example, we propose a dynamic "learning-while-doing" algorithm that only involves function value estimation to achieve a near-optimal performance. Our algorithm employs a series of shrinking price intervals and iteratively tests prices within that interval using a set of carefully chosen parameters. We prove that the convergence rate of our algorithm is among the fastest of all possible algorithms in terms of asymptotic "regret" (the relative loss comparing to the full information optimal solution). Our result closes the performance gaps between parametric and non-parametric learning and between a post-price mechanism and a customer-bidding mechanism. Important managerial insight from this research is that the values of information on both the parametric form of the demand function as well as each customer's exact reservation price are less important than prior literature suggests.Our results also suggest that firms would be better off to perform dynamic learning and action concurrently rather than sequentially.

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We consider optimal decision-making problems in an uncertain environment. In particular, we consider the case in which the distribution of the input is unknown, yet there is abundant historical data drawn from the distribution. In this paper, we propose a new type of distributionally robust optimization model called the likelihood robust optimization (LRO) model for this class of problems. In contrast to previous work on distributionally robust optimization that focuses on certain parameters (e.g., mean, variance, etc.) of the input distribution, we exploit the historical data and define the accessible distribution set to contain only those distributions that make the observed data achieve a certain level of likelihood. Then we formulate the targeting problem as one of optimizing the expected value of the objective function under the worst-case distribution in that set. Our model avoids the over-conservativeness of some prior robust approaches by ruling out unrealistic distributions while maintaining robustness of the solution for any statistically likely outcomes. We present statistical analyses of our model using Bayesian statistics and empirical likelihood theory. Specifically, we prove the asymptotic behavior of our distribution set and establish the relationship between our model and other distributionally robust models. To test the performance of our model, we apply it to the newsvendor problem and the portfolio selection problem. The test results show that the solutions of our model indeed have desirable performance.

We present a probabilistic forecasting framework based on convolutional neural network for multiple related time series forecasting. The framework can be applied to estimate probability density under both parametric and non-parametric settings. More specifically, stacked residual blocks based on dilated causal convolutional nets are constructed to capture the temporal dependencies of the series. Combined with representation learning, our approach is able to learn complex patterns such as seasonality, holiday effects within and across series, and to leverage those patterns for more accurate forecasts, especially when historical data is sparse or unavailable. Extensive empirical studies are performed on several real-world datasets, including datasets from JD.com, China's largest online retailer. The results show that our framework outperforms other state-of-the-art methods in both accuracy and efficiency.In such circumstances, instead of predicting individual or a small number of time series, one needs to predict thousands or millions of related series. Real-world applications are far more complicated. For instance, new products emerge weekly on retail platforms. Forecasting the demand of products without historical shopping festival data (e.g., Black Friday in North America, "11.11" shopping festival in China) is another challenge. Furthermore, forecasting often requires the consideration of exogenous variables that have significant influence on future demand (e.g., promotion plans provided by operations teams, accurate weather forecasts for brick and mortar retailers). Such forecasting problems can be extended to a variety of domains.Examples include forecasting the web traffic for internet companies kaggle (2017), the energy consumption for individual households, the load for servers in a data center Flunkert et al. (2017) and traffic flows in transportation domain Lv et al. (2015). Classical forecasting methods, such as ARIMA Box et al. (2015) and exponential smoothing Hyndman et al. (2008), are widely employed for univariate base-level forecasting. To incorporate exogenous covariates, several extensions of these methods have been proposed, such as ARIMAX and dynamic regression models Hyndman and Athanasopoulos (2018). These models are well-suited for applications in which the structure of the data is well understood and there is sufficient historical data. However, working with thousands or millions of series requires prohibitive labor and computing resources for parameter estimation. Moreover, they are not applicable in situations where historical data is sparse or unavailable. Recurrent neural network (RNN) Graves (2013) and the sequence to sequence (Seq2Seq) framework Cho et al. (2014); Sutskever et al. (2014) have achieved great success in many different sequential tasks such as machine translation Sutskever et al. (2014), language modeling Mikolov et al. (2010) and recently found applications in the field of time series forecasting Laptev et al.

Knowledge is limited about the patterns of viral persistence and host response in patients with COVID-19. This large study from Wuhan, China, reports longitudinal data on viral positivity as well the patterns of antibody and inflammatory response during the course of COVID-19. These data would be valuable for developing effective preventive and treatment strategies against COVID-19.

The characteristics of COVID-19 patients with persistent SARS-CoV-2 infection are not yet well described. Here, we compare the clinical and molecular features of patients with long duration of viral shedding (LDs) with those from patients with short duration patients (SDs), and healthy donors (HDs). We find that several cytokines and chemokines, such as interleukin (IL)-2, tumor necrosis factor (TNF) and lymphotoxin α (LT-α) are present at lower levels in LDs than SDs. Single-cell RNA sequencing shows that natural killer (NK) cells and CD14+ monocytes are reduced, while regulatory T cells are increased in LDs; moreover, T and NK cells in LDs are less activated than in SDs. Importantly, most cells in LDs show reduced expression of ribosomal protein (RP) genes and related pathways, with this inversed correlation between RP levels and infection duration further validated in 103 independent patients. Our results thus indicate that immunosuppression and low RP expression may be related to the persistence of the viral infection in COVID-19 patients.