Variance Reduction on Adaptive Stochastic Mirror Descent

We study the idea of variance reduction applied to adaptive stochastic mirror descent algorithms in nonsmooth nonconvex finite-sum optimization problems. We propose a simple yet generalized adaptive mirror descent algorithm with variance reduction named SVRAMD and provide its convergence analysis in different settings. We prove that variance reduction reduces the gradient complexity of most adaptive mirror descent algorithms and boost their convergence. In particular, our general theory implies variance reduction can be applied to algorithms using time-varying step sizes and self-adaptive algorithms such as AdaGrad and RMSProp. Moreover, our convergence rates recover the best existing rates of non-adaptive algorithms. We check the validity of our claims using experiments in deep learning.Comment: NeurIPS 2020 OPT worksho

Efficient Non-Learning Similar Subtrajectory Search

Similar subtrajectory search is a finer-grained operator that can better capture the similarities between one query trajectory and a portion of a data trajectory than the traditional similar trajectory search, which requires the two checked trajectories are similar to each other in whole. Many real applications (e.g., trajectory clustering and trajectory join) utilize similar subtrajectory search as a basic operator. It is considered that the time complexity is O(mn^2) for exact algorithms to solve the similar subtrajectory search problem under most trajectory distance functions in the existing studies, where m is the length of the query trajectory and n is the length of the data trajectory. In this paper, to the best of our knowledge, we are the first to propose an exact algorithm to solve the similar subtrajectory search problem in O(mn) time for most of widely used trajectory distance functions (e.g., WED, DTW, ERP, EDR and Frechet distance). Through extensive experiments on three real datasets, we demonstrate the efficiency and effectiveness of our proposed algorithms.Comment: VLDB 202

Online Ridesharing with Meeting Points [Technical Report]

Nowadays, ridesharing becomes a popular commuting mode. Dynamically arriving riders post their origins and destinations, then the platform assigns drivers to serve them. In ridesharing, different groups of riders can be served by one driver if their trips can share common routes. Recently, many ridesharing companies (e.g., Didi and Uber) further propose a new mode, namely "ridesharing with meeting points". Specifically, with a short walking distance but less payment, riders can be picked up and dropped off around their origins and destinations, respectively. In addition, meeting points enables more flexible routing for drivers, which can potentially improve the global profit of the system. In this paper, we first formally define the Meeting-Point-based Online Ridesharing Problem (MORP). We prove that MORP is NP-hard and there is no polynomial-time deterministic algorithm with a constant competitive ratio for it. We notice that a structure of vertex set, $k$-skip cover, fits well to the MORP. $k$-skip cover tends to find the vertices (meeting points) that are convenient for riders and drivers to come and go. With meeting points, MORP tends to serve more riders with these convenient vertices. Based on the idea, we introduce a convenience-based meeting point candidates selection algorithm. We further propose a hierarchical meeting-point oriented graph (HMPO graph), which ranks vertices for assignment effectiveness and constructs $k$-skip cover to accelerate the whole assignment process. Finally, we utilize the merits of $k$-skip cover points for ridesharing and propose a novel algorithm, namely SMDB, to solve MORP. Extensive experiments on real and synthetic datasets validate the effectiveness and efficiency of our algorithms.Comment: 18 page

Medical Dialogue Generation via Dual Flow Modeling

Medical dialogue systems (MDS) aim to provide patients with medical services, such as diagnosis and prescription. Since most patients cannot precisely describe their symptoms, dialogue understanding is challenging for MDS. Previous studies mainly addressed this by extracting the mentioned medical entities as critical dialogue history information. In this work, we argue that it is also essential to capture the transitions of the medical entities and the doctor's dialogue acts in each turn, as they help the understanding of how the dialogue flows and enhance the prediction of the entities and dialogue acts to be adopted in the following turn. Correspondingly, we propose a Dual Flow enhanced Medical (DFMed) dialogue generation framework. It extracts the medical entities and dialogue acts used in the dialogue history and models their transitions with an entity-centric graph flow and a sequential act flow, respectively. We employ two sequential models to encode them and devise an interweaving component to enhance their interactions. Experiments on two datasets demonstrate that our method exceeds baselines in both automatic and manual evaluations.Comment: Accepted as Findings of ACL 202