No-Regret Learning in Dynamic Competition with Reference Effects Under Logit Demand

This work is dedicated to the algorithm design in a competitive framework, with the primary goal of learning a stable equilibrium. We consider the dynamic price competition between two firms operating within an opaque marketplace, where each firm lacks information about its competitor. The demand follows the multinomial logit (MNL) choice model, which depends on the consumers' observed price and their reference price, and consecutive periods in the repeated games are connected by reference price updates. We use the notion of stationary Nash equilibrium (SNE), defined as the fixed point of the equilibrium pricing policy for the single-period game, to simultaneously capture the long-run market equilibrium and stability. We propose the online projected gradient ascent algorithm (OPGA), where the firms adjust prices using the first-order derivatives of their log-revenues that can be obtained from the market feedback mechanism. Despite the absence of typical properties required for the convergence of online games, such as strong monotonicity and variational stability, we demonstrate that under diminishing step-sizes, the price and reference price paths generated by OPGA converge to the unique SNE, thereby achieving the no-regret learning and a stable market. Moreover, with appropriate step-sizes, we prove that this convergence exhibits a rate of $\mathcal{O}(1/t)$

Analysis of the current status and influencing factors of cross-regional hospitalization services utilization by basic medical insurance participants in China − taking a central province as an example

BackgroundThe geographically uneven distribution of healthcare resources has resulted in a dramatic increase of cross-regional hospitalization services in China. The over-use of cross-regional hospitalization services may hinder the utilization and improvement of local hospitalization services. It is of great practical significance to study the utilization of cross-regional hospitalization services and its influencing factors in order to effectively allocate medical resources and guide patients to seek medical treatment rationally. Therefore, this study aims to analyze the current situation and influencing factors of the utilization of cross-regional hospitalization services by patients insured by basic medical insurance in China.MethodsA total of 3,291 cross-provincial inpatients were randomly selected in a central province of China in 2020. The level of medical institutions, hospitalization expenses and actual reimbursement rate were selected as indicators of hospitalization service utilization. Exploratory factor analysis was used to assess the dimensionality of influencing factors and reduce the number of variables, and binomial logistic regression analysis and multiple linear regression analysis to explore the influencing factors of the utilization of cross-regional hospitalization services.ResultsThe proportion of cross-provincial inpatients choosing tertiary hospitals was the highest with average hospitalization expenses of 24,662 yuan and an actual reimbursement rate of 51.0% on average. Patients insured by Urban Employees’ Basic Medical Insurance (UEBMI) were more frequently (92.9% vs. 88.5%) to choose tertiary hospitals than those insured by Urban and Rural Residents’ Basic Medical Insurance (URRBMI), and their average hospitalization expenses (30,727 yuan) and actual reimbursement rate (68.2%) were relatively higher (p < 0.001). The factor “income and security,” “convenience of medical treatment” and “disease severity” had significant effects on inpatients’ selection of medical institution level, hospitalization expenses and actual reimbursement rate, while the factor “demographic characteristics” only had significant effects on hospitalization expenses and actual reimbursement rate.ConclusionCross-provincial inpatients choose tertiary hospitals more frequently, and their financial burdens of medical treatment are heavy. A variety of factors jointly affect the utilization of cross-provincial hospitalization services for insured patients. It is necessary to narrow down the gap of medical treatment between UEBMI and URRBMI patients, and make full use of high-quality medical resources across regions

Policy-based Primal-Dual Methods for Convex Constrained Markov Decision Processes

We study convex Constrained Markov Decision Processes (CMDPs) in which the objective is concave and the constraints are convex in the state-action visitation distribution. We propose a policy-based primal-dual algorithm that updates the primal variable via policy gradient ascent and updates the dual variable via projected sub-gradient descent. Despite the loss of additivity structure and the nonconvex nature, we establish the global convergence of the proposed algorithm by leveraging a hidden convexity in the problem under the general soft-max parameterization, and prove the $\mathcal{O}\left(T^{-1/3}\right)$ convergence rate in terms of both optimality gap and constraint violation. When the objective is strongly concave in the visitation distribution, we prove an improved convergence rate of $\mathcal{O}\left(T^{-1/2}\right)$. By introducing a pessimistic term to the constraint, we further show that a zero constraint violation can be achieved while preserving the same convergence rate for the optimality gap. This work is the first one in the literature that establishes non-asymptotic convergence guarantees for policy-based primal-dual methods for solving infinite-horizon discounted convex CMDPs.Comment: 31 page

Frequency Disentanglement Distillation Image Deblurring Network

Due to the blur information and content information entanglement in the blind deblurring task, it is very challenging to directly recover the sharp latent image from the blurred image. Considering that in the high-dimensional feature map, blur information mainly exists in the low-frequency region, and content information exists in the high-frequency region. In this paper, we propose a encoder–decoder model to realize disentanglement from the perspective of frequency, and we named it as frequency disentanglement distillation image deblurring network (FDDN). First, we modified the traditional distillation block by embedding the frequency split block (FSB) in the distillation block to separate the low-frequency and high-frequency region. Second, the modified distillation block, we named frequency distillation block (FDB), can recursively distill the low-frequency feature to disentangle the blurry information from the content information, so as to improve the restored image quality. Furthermore, to reduce the complexity of the network and ensure the high-dimension of the feature map, the frequency distillation block (FDB) is placed on the end of encoder to edit the feature map on the latent space. Quantitative and qualitative experimental evaluations indicate that the FDDN can remove the blur effect and improve the image quality of actual and simulated images

Cognitive Impairment Mediates the Association between Dietary Inflammation and Depressive Symptoms in the Elderly

The underlying mechanism in both cognitive impairment and depression was chronic inflammation, which could be reflected by the dietary inflammatory index (DII). However, the effect of cognitive impairment on the association between DII and depression was not clear. Therefore, in this study, we hypothesized that cognitive impairment could mediate the association between dietary inflammation and depressive symptoms. A total of 2550 participants aged ≥60 from the National Health and Nutrition Examination Survey (NHANES) in 2011–2014 were involved in the serial, cross-sectional study. Proinflammatory and anti-inflammatory diets were measured by DII. Cognitive impairment was measured by four dimensions, CERAD-immediate, CERAN-delayed, animal fluency test, and DSST. Depressive symptoms were measured by PHQ-9 scores. We found that a proinflammatory diet and cognitive impairment were both risk factors for depressive symptoms. An interaction between an inflammatory diet and cognitive impairment was detected (P-interaction = 0.060). In addition, all four dimensions of cognition mediated the association between DII and depressive symptom scores. Part of the association between DII and depressive symptoms scores could be explained by different dimensions of cognitive function, and the proportion of mediation ranged from 10.0% to 36.7%. In conclusion, cognitive impairment levels partly mediated the association between DII and depressive symptoms

The Mediating Role of Dietary Inflammatory Index in the Association between Eating Breakfast and Obesity: A Cross-Sectional Study

Obesity is closely related with diet, including the regularity of meals and inflammation in the diet. No previous study focused on the associations among eating breakfast, which is regarded the most important meal, dietary inflammation, and obesity. This study analyzed data from the National Health and Nutrition Examination Survey (NHANES) from 2007 to 2018, with 23,758 participants involved. Obesity and dietary inflammation were measured by body mass index (BMI) and dietary inflammatory index (DII), respectively. Eating breakfast was defined by two days of dietary recalls based on NHANES dietary data. Pro-inflammatory diet and skipping breakfast were positively associated with obesity in the whole population. Compared with eating breakfast in both recalls, skipping breakfast had the higher OR of obesity, especially for individuals who reported no recall. Participants with diabetes were the sensitive population of these associations. Compared with participants who reported breakfast in both recalls, the mediated proportion of participants reported breakfast in one recall and in no recall were 24.71% and 27.34%, respectively. The association between eating breakfast and obesity was partly mediated by DII. We recommended eating breakfast regularly to reduce dietary inflammation, as well as further obesity, especially for diabetic populations

Additional file 1 of Ideal cardiovascular health metrics have better identification of arthritis

Supplementary Material