Searcharxiv⌕ Search

arXiv subjects

Haomin Wen

Publications and source records attributed to Haomin Wen.

42 records · Page 3Linked to original sources

DRL4Route: A Deep Reinforcement Learning Framework for Pick-up and Delivery Route Prediction

Pick-up and Delivery Route Prediction (PDRP), which aims to estimate the future service route of a worker given his current task pool, has received rising attention in recent years. Deep neural networks based on supervised learning have emerged as the dominant model for the task because of their powerful ability to capture workers' behavior patterns from massive historical data. Though promising, they fail to introduce the non-differentiable test criteria into the training process, leading to a mismatch in training and test criteria. Which considerably trims down their performance when applied in practical systems. To tackle the above issue, we present the first attempt to generalize Reinforcement Learning (RL) to the route prediction task, leading to a novel RL-based framework called DRL4Route. It combines the behavior-learning abilities of previous deep learning models with the non-differentiable objective optimization ability of reinforcement learning. DRL4Route can serve as a plug-and-play component to boost the existing deep learning models. Based on the framework, we further implement a model named DRL4Route-GAE for PDRP in logistic service. It follows the actor-critic architecture which is equipped with a Generalized Advantage Estimator that can balance the bias and variance of the policy gradient estimates, thus achieving a more optimal policy. Extensive offline experiments and the online deployment show that DRL4Route-GAE improves Location Square Deviation (LSD) by 0.9%-2.7%, and Accuracy@3 (ACC@3) by 2.4%-3.2% over existing methods on the real-world dataset.

cs.LG↗

Area of convex disks

This paper considers metric balls $B(p,R)$ in two dimensional Riemannian manifolds when $R$ is less than half the convexity radius. We prove that $Area(B(p,R)) \geq \frac{8}πR^2$. This inequality has long been conjectured for $R$ less than half the injectivity radius. This result also yields the upper bound $μ_2(B(p,R)) \leq 2(\fracπ{2 R})^2$ on the first nonzero Neumann eigenvalue $μ_2$ of the Laplacian in terms only of the radius. This has also been conjectured for $R$ up to half the injectivity radius.

math.DG↗

Scattering data versus lens data on surfaces

The scattering data of a Riemannian manifold with boundary record the incoming and outgoing directions of each geodesic passing through. We show that the scattering data of a generic Riemannian surface with no trapped geodesics and no conjugate points determine the lengths of geodesics. Counterexamples exists when trapped geodesics are allowed.

math.DG↗

On monotonicity of some combinatorial sequences

We confirm Sun's conjecture that $(\root{n+1}\of{F_{n+1}}/\root{n}\of{F_n})_{n\ge 4}$ is strictly decreasing to the limit 1, where $(F_n)_{n\ge0}$ is the Fibonacci sequence. We also prove that the sequence $(\root{n+1}\of{D_{n+1}}/\root{n}\of{D_n})_{n\ge3}$ is strictly decreasing with limit $1$, where $D_n$ is the $n$-th derangement number. For $m$-th order harmonic numbers $H_n^{(m)}=\sum_{k=1}^n 1/k^m\ (n=1,2,3,\ldots)$, we show that $(\root{n+1}\of{H^{(m)}_{n+1}}/\root{n}\of{H^{(m)}_n})_{n\ge3}$ is strictly increasing.

math.CO↗

Simple Riemannian surfaces are scattering rigid

Scattering rigidity of a Riemannian manifold allows one to tell the metric of a manifold with boundary by looking at the directions of geodesics at the boundary. Lens rigidity allows one to tell the metric of a manifold with boundary from the same information plus the length of geodesics. There are a variety of results about lens rigidity but very little is known for scattering rigidity. We will discuss the subtle difference between these two types of rigidities and prove that they are equivalent for two-dimensional simple manifolds with boundaries. In particular, this implies that two-dimensional simple manifolds (such as the flat disk) are scattering rigid since they are lens/boundary rigid (Pestov--Uhlmann, 2005).

math.DG↗

Lipschitz minimality of the multiplication maps of unit complex, quaternion and octonion numbers

We prove that the multiplication maps $\mathbb{s}^n \times \mathbb{s}^n \rightarrow \mathbb{s}^n$ ($n = 1, 3, 7$) for unit complex, quaternion and octonion numbers are, up to isometries of domain and range, the unique Lipschitz constant minimizers in their homotopy classes. Other geometrically natural maps, such as projections of Hopf fibrations, have already been shown to be, up to isometries, the unique Lipschitz constant minimizers in their homotopy classes, and it is suspected that this may hold true for all Riemannian submersions of compact homogeneous spaces.

math.GT↗