A Monomial-Oriented GVW for Computing Gr\"obner Bases

The GVW algorithm, presented by Gao et al., is a signature-based algorithm for computing Gr\"obner bases. In this paper, a variant of GVW is presented. This new algorithm is called a monomial-oriented GVW algorithm or mo-GVW algorithm for short. The mo-GVW algorithm presents a new frame of GVW and regards {\em labeled monomials} instead of {\em labeled polynomials} as basic elements of the algorithm. Being different from the original GVW algorithm, for each labeled monomial, the mo-GVW makes efforts to find the smallest signature that can generate this monomial. The mo-GVW algorithm also avoids generating J-pairs, and uses efficient methods of searching reducers and checking criteria. Thus, the mo-GVW algorithm has a better performance during practical implementations

Mean field error estimate of the random batch method for large interacting particle system

The random batch method (RBM) proposed in [Jin et al., J. Comput. Phys., 400(2020), 108877] for large interacting particle systems is an efficient with linear complexity in particle numbers and highly scalable algorithm for $N$-particle interacting systems and their mean-field limits when $N$ is large. We consider in this work the quantitative error estimate of RBM toward its mean-field limit, the Fokker-Planck equation. Under mild assumptions, we obtain a uniform-in-time $O(\tau^2 + 1/N)$ bound on the scaled relative entropy between the joint law of the random batch particles and the tensorized law at the mean-field limit, where $\tau$ is the time step size and $N$ is the number of particles. Therefore, we improve the existing rate in discretization step size from $O(\sqrt{\tau})$ to $O(\tau)$ in terms of the Wasserstein distance

OBTAINING INTEREST GROUP IDENTIFIERS FROM URL ADDRESS BAR

API scripts can be used to send information identifying user’s interests from their devices to entities, e.g., content publishers for use in customizing content for the users. However, in some situations, e.g., when a user enters a search query in an address bar of a web browser, the scripts may not be executed. Other techniques can be used to send the information identifying user’s interests, such as macros, HTTP headers, and/or cookies

Automatic Curriculum Learning With Over-repetition Penalty for Dialogue Policy Learning

Dialogue policy learning based on reinforcement learning is difficult to be applied to real users to train dialogue agents from scratch because of the high cost. User simulators, which choose random user goals for the dialogue agent to train on, have been considered as an affordable substitute for real users. However, this random sampling method ignores the law of human learning, making the learned dialogue policy inefficient and unstable. We propose a novel framework, Automatic Curriculum Learning-based Deep Q-Network (ACL-DQN), which replaces the traditional random sampling method with a teacher policy model to realize the dialogue policy for automatic curriculum learning. The teacher model arranges a meaningful ordered curriculum and automatically adjusts it by monitoring the learning progress of the dialogue agent and the over-repetition penalty without any requirement of prior knowledge. The learning progress of the dialogue agent reflects the relationship between the dialogue agent's ability and the sampled goals' difficulty for sample efficiency. The over-repetition penalty guarantees the sampled diversity. Experiments show that the ACL-DQN significantly improves the effectiveness and stability of dialogue tasks with a statistically significant margin. Furthermore, the framework can be further improved by equipping with different curriculum schedules, which demonstrates that the framework has strong generalizability