A Class of Mean-field LQG Games with Partial Information

The large-population system consists of considerable small agents whose individual behavior and mass effect are interrelated via their state-average. The mean-field game provides an efficient way to get the decentralized strategies of large-population system when studying its dynamic optimizations. Unlike other large-population literature, this current paper possesses the following distinctive features. First, our setting includes the partial information structure of large-population system which is practical from real application standpoint. Specially, two cases of partial information structure are considered here: the partial filtration case (see Section 2, 3) where the available information to agents is the filtration generated by an observable component of underlying Brownian motion; the noisy observation case (Section 4) where the individual agent can access an additive white-noise observation on its own state. Also, it is new in filtering modeling that our sensor function may depend on the state-average. Second, in both cases, the limiting state-averages become random and the filtering equations to individual state should be formalized to get the decentralized strategies. Moreover, it is also new that the limit average of state filters should be analyzed here. This makes our analysis very different to the full information arguments of large-population system. Third, the consistency conditions are equivalent to the wellposedness of some Riccati equations, and do not involve the fixed-point analysis as in other mean-field games. The $\epsilon$-Nash equilibrium properties are also presented.Comment: 19 page

Research on Technology Spillover Effects on Agricultural Productivity in China

Technology contributes to the modern economic development directly and indirectly, and it changes the operating system and working method during the economic transformation. Along with institutional reform and modern economic structural transformation of China, agriculture still plays an ineradicable role in the development of Chinese economy, and it is the cornerstone for countries with large population. In this paper, the main purpose is to study how technology spillover effects work on agricultural productivity. In order to solve this question, I focus on two aspects, the one is from R&D perspective， and the other is the improvement of actual agricultural production techniques. This paper investigates the question by empirical analysis, and I collect panel data from three statistical yearbooks of China. The datasets consist of annul data from 1992 to 2013 and cross-sectional data of 30 regions of China, the statistical package Eviews will be employed to generate empirical results. There are four models in my paper, the first three models are set to study the puzzle directly based on the hypotheses, and the last one is a modified model after some necessary tests. The results show that technology has different spillover effects on agricultural productivity in different aspects, even though some variables are insignificant in explaining the model

Mean Field Linear-Quadratic-Gaussian (LQG) Games of Forward-Backward Stochastic Differential Equations

This paper studies a new class of dynamic optimization problems of large-population (LP) system which consists of a large number of negligible and coupled agents. The most significant feature in our setup is the dynamics of individual agents follow the forward-backward stochastic differential equations (FBSDEs) in which the forward and backward states are coupled at the terminal time. This current paper is hence different to most existing large-population literature where the individual states are typically modeled by the SDEs including the forward state only. The associated mean-field linear-quadratic-Gaussian (LQG) game, in its forward-backward sense, is also formulated to seek the decentralized strategies. Unlike the forward case, the consistency conditions of our forward-backward mean-field games involve six Riccati and force rate equations. Moreover, their initial and terminal conditions are mixed thus some special decoupling technique is applied here. We also verify the $\epsilon$-Nash equilibrium property of the derived decentralized strategies. To this end, some estimates to backward stochastic system are employed. In addition, due to the adaptiveness requirement to forward-backward system, our arguments here are not parallel to those in its forward case.Comment: 21 page

Reduce API Debugging Overhead via Knowledge Prepositioning

OpenAPI indicates a behavior where producers offer Application Programming Interfaces (APIs) to help end-users access their data, resources, and services. Generally, API has many parameters that need to be entered. However, it is challenging for users to understand and document these parameters correctly. This paper develops an API workbench to help users learn and debug APIs. Based on this workbench, much exploratory work has been proposed to reduce the overhead of learning and debugging APIs. We explore the knowledge, such as parameter characteristics (e.g., enumerability) and constraints (e.g., maximum/minimum value), from the massive API call logs to narrow the range of parameter values. Then, we propose a fine-grained approach to enrich the API documentation by extracting dependency knowledge between APIs. Finally, we present a learning-based prediction method to predict API execution results before the API is called, significantly reducing user debugging cycles. The experiments evaluated on the online system show that this work's approach substantially improves the user experience of debugging OpenAPIs.Comment: arXiv admin note: text overlap with arXiv:1509.01626, arXiv:1502.01710 by other author

Frustratingly Easy Model Generalization by Dummy Risk Minimization

Empirical risk minimization (ERM) is a fundamental machine learning paradigm. However, its generalization ability is limited in various tasks. In this paper, we devise Dummy Risk Minimization (DuRM), a frustratingly easy and general technique to improve the generalization of ERM. DuRM is extremely simple to implement: just enlarging the dimension of the output logits and then optimizing using standard gradient descent. Moreover, we validate the efficacy of DuRM on both theoretical and empirical analysis. Theoretically, we show that DuRM derives greater variance of the gradient, which facilitates model generalization by observing better flat local minima. Empirically, we conduct evaluations of DuRM across different datasets, modalities, and network architectures on diverse tasks, including conventional classification, semantic segmentation, out-of-distribution generalization, adverserial training, and long-tailed recognition. Results demonstrate that DuRM could consistently improve the performance under all tasks with an almost free lunch manner. Furthermore, we show that DuRM is compatible with existing generalization techniques and we discuss possible limitations. We hope that DuRM could trigger new interest in the fundamental research on risk minimization.Comment: Technical report; 22 page