An Efficient HPR Algorithm for the Wasserstein Barycenter Problem with O(Dim(P)/ε)O({Dim(P)}/\varepsilon) Computational Complexity

In this paper, we propose and analyze an efficient Halpern-Peaceman-Rachford (HPR) algorithm for solving the Wasserstein barycenter problem (WBP) with fixed supports. While the Peaceman-Rachford (PR) splitting method itself may not be convergent for solving the WBP, the HPR algorithm can achieve an $O(1/\varepsilon)$ non-ergodic iteration complexity with respect to the Karush-Kuhn-Tucker (KKT) residual. More interestingly, we propose an efficient procedure with linear time computational complexity to solve the linear systems involved in the subproblems of the HPR algorithm. As a consequence, the HPR algorithm enjoys an $O({\rm Dim(P)}/\varepsilon)$ non-ergodic computational complexity in terms of flops for obtaining an $\varepsilon$-optimal solution measured by the KKT residual for the WBP, where ${\rm Dim(P)}$ is the dimension of the variable of the WBP. This is better than the best-known complexity bound for the WBP. Moreover, the extensive numerical results on both the synthetic and real data sets demonstrate the superior performance of the HPR algorithm for solving the large-scale WBP

Real-Time Bidding by Reinforcement Learning in Display Advertising

The majority of online display ads are served through real-time bidding (RTB) --- each ad display impression is auctioned off in real-time when it is just being generated from a user visit. To place an ad automatically and optimally, it is critical for advertisers to devise a learning algorithm to cleverly bid an ad impression in real-time. Most previous works consider the bid decision as a static optimization problem of either treating the value of each impression independently or setting a bid price to each segment of ad volume. However, the bidding for a given ad campaign would repeatedly happen during its life span before the budget runs out. As such, each bid is strategically correlated by the constrained budget and the overall effectiveness of the campaign (e.g., the rewards from generated clicks), which is only observed after the campaign has completed. Thus, it is of great interest to devise an optimal bidding strategy sequentially so that the campaign budget can be dynamically allocated across all the available impressions on the basis of both the immediate and future rewards. In this paper, we formulate the bid decision process as a reinforcement learning problem, where the state space is represented by the auction information and the campaign's real-time parameters, while an action is the bid price to set. By modeling the state transition via auction competition, we build a Markov Decision Process framework for learning the optimal bidding policy to optimize the advertising performance in the dynamic real-time bidding environment. Furthermore, the scalability problem from the large real-world auction volume and campaign budget is well handled by state value approximation using neural networks.Comment: WSDM 201

The relationship between organizational commitment and turnover intention among temporary employees in the local government: Mediating role of perceived insider status and moderating role of gender

PurposeThe purpose of this study is to examine the relationships between organizational commitment and turnover intention, and to test the mediating effect of perceived insider status, and moderating effect of gender on that relationship.MethodologyData were collected using a questionnaire survey method from 820 temporary employees of government agencies working in China. The data obtained were analyzed according to the moderated mediation.FindingsAs a result of the analysis, it was determined that perceived insider status has a partial mediation effect on the relationship between organizational commitment and turnover intention. Also, the results supported the moderated mediation and showed that the indirect effect of organizational commitment and turnover intention through perceived insider status was weaker for males than females. Then, the theoretical and practical implications of the findings are discussed

Accelerating preconditioned ADMM via degenerate proximal point mappings

In this paper, we aim to accelerate a preconditioned alternating direction method of multipliers (pADMM), whose proximal terms are convex quadratic functions, for solving linearly constrained convex optimization problems. To achieve this, we first reformulate the pADMM into a form of proximal point method (PPM) with a positive semidefinite preconditioner which can be degenerate due to the lack of strong convexity of the proximal terms in the pADMM. Then we accelerate the pADMM by accelerating the reformulated degenerate PPM (dPPM). Specifically, we first propose an accelerated dPPM by integrating the Halpern iteration and the fast Krasnosel'ski\u{i}-Mann iteration into it, achieving asymptotic $o(1/k)$ and non-asymptotic $O(1/k)$ convergence rates. Subsequently, building upon the accelerated dPPM, we develop an accelerated pADMM algorithm that exhibits both asymptotic $o(1/k)$ and non-asymptotic $O(1/k)$ nonergodic convergence rates concerning the Karush-Kuhn-Tucker residual and the primal objective function value gap. Preliminary numerical experiments validate the theoretical findings, demonstrating that the accelerated pADMM outperforms the pADMM in solving convex quadratic programming problems

Treatment responses in adult depressive patients treated with dexamethasone/corticotrophin-releasing hormone

Purpose: To study the dexamethasone/corticotrophin releasing hormones (DEX/CRH) in depressed and healthy patients and to analyse the occurrence of relapse connected to hormonal dysregulation.Methods: A total of 117 depressive patients between 20 and 70 years of age were included in the study group and 40 healthy patients between 25 and 60 years of age in the control group. Group I consisted of 59 patients who received sertraline 50 - 100 mg/day for 5 weeks along with a low dose of 30 mg T3. Group II included 58 patients who received dexamethasone 1 mg orally for 5 weeks. DEX/CRH levels were analyzed. Adrenocorticotrophic hormone and cortisol levels in the blood were analysed by immuno-radiometric assay. Cortisol levels were also analysed by kinetic assay method.Results: In group I, among the 59 patients that received sertraline 50-100 mg/day for 5 weeks with a low dose of 30 mg T3, relapse was observed in 12 (20.3 %) of them. The area under the curve (AUC) was 13.9 ± 6.4 ng.min.1000/mL, which was higher than that for healthy individuals (3.8 ± 3.6 ng.min.1000/mL). Group I patients with relapse showed an adrenocorticotrophic hormone AUC of 16.9 ± 2.4 ng.min.1000/mL, while group II patients exhibited AUC of 13.9 ± 6.4 ng.min.1000/mL.Conclusion: The results emphasizes the need to test hormonal responses to different types of antidepressants.Keywords: stress, depressive patients, hormonal response, hormonal dysregulation, sertraline, dexamethasone, corticotrophin releasing hormon