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作者：Koessler, Frederic; Scarsini, Marco; Tomala, Tristan
作者单位：Luiss Guido Carli University
摘要：We consider multipopulation Bayesian games with a large number of players. Each player aims at minimizing a cost function that depends on this player's own action, the distribution of players' actions in all populations, and an unknown state parameter. We study the nonatomic limit versions of these games and introduce the concept of Bayes correlated Wardrop equilibrium, which extends the concept of Bayes correlated equilibrium to nonatomic games. We prove that Bayes correlated Wardrop equilibr...
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作者：Bogomolnaia, Anna; Moulin, Herve
作者单位：University of Glasgow; Centre National de la Recherche Scientifique (CNRS)
摘要：We must assign n agents to m posts subject to negative congestion; what assignment is fair and efficient? If congestion is anonymous (each agent adds one unit), it is always possible to assign each agent to one of the agent's top n out of the n x m feasible allocations. This ordinal interpretation of ex ante fairness can be adjusted if congestion is weighted (agent-specific). An assignment is competitive if I don't want to move to an empty post or to an occupied one at its current congestion l...
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作者：Yang, Lei; Toh, Kim-Chuan
作者单位：Sun Yat Sen University; National University of Singapore
摘要：The Bregman proximal gradient method (BPGM), which uses the Bregman distance as a proximity measure in the iterative scheme, has recently been redeveloped for minimizing convex composite problems without the global Lipschitz gradient continuity assumption. This makes the BPGM appealing for a wide range of applications, and hence, it has received growing attention in recent years. However, most existing convergence results are obtained only under the assumption that the involved subproblems are...
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作者：Hang, Nguyen Thi Van; Sarabi, Ebrahim
作者单位：Nanyang Technological University; Vietnam Academy of Science & Technology (VAST); University System of Ohio; Miami University
摘要：Local convergence analysis of the augmented Lagrangian method (ALM) is established for a large class of composite optimization problems with nonunique Lagrange multipliers under a second-order sufficient condition. We present a new second-order variational property called the semistability of second subderivatives and demonstrate that it is widely satisfied for numerous classes of functions, which is important for applications in constrained and composite optimization problems. Using the latte...
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作者：Caragiannis, Ioannis; Kanellopoulos, Panagiotis; Kyropoulou, Maria
作者单位：Aarhus University; University of Essex
摘要：With very few exceptions, recent research in fair division has mostly focused on deterministic allocations. Deviating from this trend, we study the fairness notion of interim envy-freeness (iEF) for lotteries over allocations, which serves as a sweet spot between the too-stringent notion of ex post envy-freeness and the very weak notion of ex ante envy freeness. Our analysis relates iEF to other fairness notions as well and reveals trade-offs between iEF and efficiency. Even though several of ...
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作者：Royset, Johannes O.; Chen, Louis L.; Eckstrand, Eric
作者单位：University of Southern California; United States Department of Defense; United States Navy; Naval Postgraduate School
摘要：In practice, optimization models are often prone to unavoidable inaccuracies because of dubious assumptions and corrupted data. Traditionally, this placed special emphasis on risk-based and robust formulations, and their focus on conservative decisions. We develop, in contrast, an optimistic framework based on Rockafellian relaxations in which optimization is conducted not only over the original decision space but also jointly with a choice of model perturbation. The framework enables us to ad...
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作者：Lambers, Roel; Pendavingh, Rudi; Spieksma, Frits
作者单位：Eindhoven University of Technology
摘要：We investigate a new tournament format that consists of a series of individual knockout tournaments; we call this new format a serial knockout competition (SKC). This format has recently been adopted by the Professional Darts Corporation. Depending on the seedings of the players used for each of the knockout tournaments, players can meet in the various rounds (e.g., first round, second round ... semifinal, final) of the knockout tournaments. Following a fairness principle of treating all playe...
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作者：Possamai, Dylan; Touzi, Nizar
作者单位：New York University; New York University Tandon School of Engineering
摘要：This paper provides a complete review of the continuous-time optimal contracting problem introduced by Sannikov in the extended context allowing for possibly different discount rates for both parties. The agent's problem is to seek for optimal effort given the compensation scheme proposed by the principal over a random horizon. Then, given the optimal agent's response, the principal determines the best compensation scheme in terms of running payment, retirement, and lump-sum payment at retirem...
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作者：Gamarnik, David; Kizildag, Eren C.; Zadik, Ilias
作者单位：Massachusetts Institute of Technology (MIT); Columbia University; Yale University
摘要：We consider the problem of training a shallow neural network with quadratic activation functions and the generalization power of such trained networks. Assuming that the samples are generated by a full rank matrix W* of the hidden network node weights, we obtain the following results. We establish that all full -rank approximately stationary solutions of the risk minimization problem are also approximate global optimums of the risk (in -sample and population). As a consequence, we establish th...
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作者：Hu, Xiaomeng; Klep, Igor; Nie, Tiawang
作者单位：University of California System; University of California San Diego; University of Ljubljana; University of Primorska
摘要：This paper studies Positivstellensatze and moment problems for sets K that are given by universal quantifiers. Let Q be the closed set of universal quantifiers. Fix a finite nonnegative Borel measure whose support is Q and assume it satisfies the multivariate Carleman condition. First, we prove a Positivstellensatz with universal quantifiers: if a polynomialf is positive on K, then f belongs to the associated quadratic module, under the archimedeanness assumption. Second, we prove some necessa...
