arXiv subjects
Publications and source records attributed to Zhengning Hu.
We provide a systematic method to classify all smooth weak Fano toric varieties of Picard rank $3$ in any dimension using Macaulay2, and describe the classification explicitly in dimensions $3$ and $4$. There are $28$ and $114$ isomorphism classes of rank $3$ weak Fano toric threefolds and fourfolds, respectively.
The Hurwitz space $\overline{\mathscr{H}}_{k,g}$ is a compactification of the space of smooth genus-$g$ curves with a simply-branched degree-$k$ map to $\mathbb{P}^1$. In this paper, we initiate a study of the Chow rings of these spaces, proving in particular that when $k=3$ (which is the first case in which the Chow ring is not already known), the codimension-2 Chow group is generated by the fundamental classes of codimension-2 boundary strata. The key tool is to realize the codimension-1 boundary strata of $\overline{\mathscr{H}}_{3,g}$ as the images of gluing maps whose domains are products of Hurwitz spaces $\mathscr{H}_{k',g'}(μ)$ with a single marked fiber of prescribed (not necessarily simple) ramification profile $μ$, and to prove that the spaces $\mathscr{H}_{k',g'}(μ)$ with $k'=2,3$ have trivial Chow ring.
We compute the integral Chow rings of the stacks ${\mathcal H}_{g,n}^w$ parametrizing hyperelliptic curves with $n$ marked Weierstrass points. We prove that the integral Chow rings of each of these stacks is generated as an algebra by any of the $Ψ$-classes and that all relations live in degree one.
We compute the integral Grothendieck rings of the moduli stacks, $\mathcal{M}_2$, $\overline{\mathcal{M}}_2$ of smooth and stable curves of genus two respectively. We compute $K_0(\mathcal{M}_2)$ by using the presentation of $\mathcal{M}_2$ as a global quotient stack given by Vistoli. To compute the Grothendieck ring $K_0(\overline{\mathcal{M}}_2)$ we decompose $\overline{\mathcal{M}}_2$ as $Δ_1$ and its complement $\overline{\mathcal{M}}_2 \setminus Δ_1$ and use their presentations as quotient stacks given by Larson to compute their Grothendieck rings. We show that they are torsion-free and this, together with the Riemann-Roch isomorphism allows to ultimately give a presentation for the integral Grothendieck ring $K_0(\overline{\mathcal{M}}_2)$.
Bidding strategies that help advertisers determine bidding prices are receiving increasing attention as more and more ad impressions are sold through real-time bidding systems. This paper first describes the problem and challenges of optimizing bidding strategies for individual advertisers in real-time bidding display advertising. Then, several representative bidding strategies are introduced, especially the research advances and challenges of reinforcement learning-based bidding strategies. Further, we quantitatively evaluate the performance of several representative bidding strategies on the iPinYou dataset. Specifically, we examine the effects of state, action, and reward function on the performance of reinforcement learning-based bidding strategies. Finally, we summarize the general steps for optimizing bidding strategies using reinforcement learning algorithms and present our suggestions.
We calculate the classes of the universal hyperelliptic Weierstrass divisor $\bar{\mathcal H}_{g,w}$ and the universal $g^1_2$ divisor $\bar{\mathcal H}_{g,g^1_2}$. Our results are expressed in terms of a basis for $Cl(\bar{\mathcal H}_{g,1})$ and $Cl(\bar{\mathcal H}_{g,2})$ computed by Scavia.
Real-time bidding (RTB) has become a critical way of online advertising. In RTB, an advertiser can participate in bidding ad impressions to display its advertisements. The advertiser determines every impression's bidding price according to its bidding strategy. Therefore, a good bidding strategy can help advertisers improve cost efficiency. This paper focuses on optimizing a single advertiser's bidding strategy using reinforcement learning (RL) in RTB. Unfortunately, it is challenging to optimize the bidding strategy through RL at the granularity of impression due to the highly dynamic nature of the RTB environment. In this paper, we first utilize a widely accepted linear bidding function to compute every impression's base price and optimize it by a mutable adjustment factor derived from the RTB auction environment, to avoid optimizing every impression's bidding price directly. Specifically, we use the maximum entropy RL algorithm (Soft Actor-Critic) to optimize the adjustment factor generation policy at the impression-grained level. Finally, the empirical study on a public dataset demonstrates that the proposed bidding strategy has superior performance compared with the baselines.