arXiv subjects

Huan Xu

Publications and source records attributed to Huan Xu.

At least 55 records · Page 3Linked to original sources

arXiv2021

RobustPeriod: Time-Frequency Mining for Robust Multiple Periodicity Detection

Periodicity detection is a crucial step in time series tasks, including monitoring and forecasting of metrics in many areas, such as IoT applications and self-driving database management system. In many of these applications, multiple periodic components exist and are often interlaced with each other. Such dynamic and complicated periodic patterns make the accurate periodicity detection difficult. In addition, other components in the time series, such as trend, outliers and noises, also pose additional challenges for accurate periodicity detection. In this paper, we propose a robust and general framework for multiple periodicity detection. Our algorithm applies maximal overlap discrete wavelet transform to transform the time series into multiple temporal-frequency scales such that different periodic components can be isolated. We rank them by wavelet variance, and then at each scale detect single periodicity by our proposed Huber-periodogram and Huber-ACF robustly. We rigorously prove the theoretical properties of Huber-periodogram and justify the use of Fisher's test on Huber-periodogram for periodicity detection. To further refine the detected periods, we compute unbiased autocorrelation function based on Wiener-Khinchin theorem from Huber-periodogram for improved robustness and efficiency. Experiments on synthetic and real-world datasets show that our algorithm outperforms other popular ones for both single and multiple periodicity detection.

cs.LG↗

arXiv2021

Adversaries in Online Learning Revisited: with applications in Robust Optimization and Adversarial training

We revisit the concept of "adversary" in online learning, motivated by solving robust optimization and adversarial training using online learning methods. While one of the classical setups in online learning deals with the "adversarial" setup, it appears that this concept is used less rigorously, causing confusion in applying results and insights from online learning. Specifically, there are two fundamentally different types of adversaries, depending on whether the "adversary" is able to anticipate the exogenous randomness of the online learning algorithms. This is particularly relevant to robust optimization and adversarial training because the adversarial sequences are often anticipative, and many online learning algorithms do not achieve diminishing regret in such a case. We then apply this to solving robust optimization problems or (equivalently) adversarial training problems via online learning and establish a general approach for a large variety of problem classes using imaginary play. Here two players play against each other, the primal player playing the decisions and the dual player playing realizations of uncertain data. When the game terminates, the primal player has obtained an approximately robust solution. This meta-game allows for solving a large variety of robust optimization and multi-objective optimization problems and generalizes the approach of arXiv:1402.6361.

cs.LG↗

arXiv2021

Bayesian Pool-based Active Learning With Abstention Feedbacks

We study pool-based active learning with abstention feedbacks, where a labeler can abstain from labeling a queried example with some unknown abstention rate. This is an important problem with many useful applications. We take a Bayesian approach to the problem and develop two new greedy algorithms that learn both the classification problem and the unknown abstention rate at the same time. These are achieved by simply incorporating the estimated abstention rate into the greedy criteria. We prove that both of our algorithms have near-optimality guarantees: they respectively achieve a ${(1-\frac{1}{e})}$ constant factor approximation of the optimal expected or worst-case value of a useful utility function. Our experiments show the algorithms perform well in various practical scenarios.

stat.ML↗

arXiv2020

Bayesian Active Learning With Abstention Feedbacks

We study pool-based active learning with abstention feedbacks where a labeler can abstain from labeling a queried example with some unknown abstention rate. This is an important problem with many useful applications. We take a Bayesian approach to the problem and develop two new greedy algorithms that learn both the classification problem and the unknown abstention rate at the same time. These are achieved by simply incorporating the estimated average abstention rate into the greedy criteria. We prove that both algorithms have near-optimality guarantees: they respectively achieve a ${(1-\frac{1}{e})}$ constant factor approximation of the optimal expected or worst-case value of a useful utility function. Our experiments show the algorithms perform well in various practical scenarios.

cs.LG↗

arXiv2020

Multi-Agent Coverage in Urban Environments

We study multi-agent coverage algorithms for autonomous monitoring and patrol in urban environments. We consider scenarios in which a team of flying agents uses downward facing cameras (or similar sensors) to observe the environment outside of buildings at street-level. Buildings are considered obstacles that impede movement, and cameras are assumed to be ineffective above a maximum altitude. We study multi-agent urban coverage problems related to this scenario, including: (1) static multi-agent urban coverage, in which agents are expected to observe the environment from static locations, and (2) dynamic multi-agent urban coverage where agents move continuously through the environment. We experimentally evaluate six different multi-agent coverage methods, including: three types of ergodic coverage (that avoid buildings in different ways), lawn-mower sweep, voronoi region based control, and a naive grid method. We evaluate all algorithms with respect to four performance metrics (percent coverage, revist count, revist time, and the integral of area viewed over time), across four types of urban environments [low density, high density] x [short buildings, tall buildings], and for team sizes ranging from 2 to 25 agents. We believe this is the first extensive comparison of these methods in an urban setting. Our results highlight how the relative performance of static and dynamic methods changes based on the ratio of team size to search area, as well the relative effects that different characteristics of urban environments (tall, short, dense, sparse, mixed) have on each algorithm.

cs.RO↗

arXiv2020

Maximizing Cumulative User Engagement in Sequential Recommendation: An Online Optimization Perspective

To maximize cumulative user engagement (e.g. cumulative clicks) in sequential recommendation, it is often needed to tradeoff two potentially conflicting objectives, that is, pursuing higher immediate user engagement (e.g., click-through rate) and encouraging user browsing (i.e., more items exposured). Existing works often study these two tasks separately, thus tend to result in sub-optimal results. In this paper, we study this problem from an online optimization perspective, and propose a flexible and practical framework to explicitly tradeoff longer user browsing length and high immediate user engagement. Specifically, by considering items as actions, user's requests as states and user leaving as an absorbing state, we formulate each user's behavior as a personalized Markov decision process (MDP), and the problem of maximizing cumulative user engagement is reduced to a stochastic shortest path (SSP) problem. Meanwhile, with immediate user engagement and quit probability estimation, it is shown that the SSP problem can be efficiently solved via dynamic programming. Experiments on real-world datasets demonstrate the effectiveness of the proposed approach. Moreover, this approach is deployed at a large E-commerce platform, achieved over 7% improvement of cumulative clicks.

cs.IR↗

arXiv2020

Structure/property relationship of semi-crystalline polymer during tensile deformation: A molecular dynamics approach

A coarse-grained molecular dynamics model of linear polyethylene-like polymer chain system was built to investigate the responds of structure and mechanical properties during uniaxial deformation. The influence of chain length, temperature, and strain rate were studied. The molecular dynamic tests showed that yielding may governed by different mechanisms at temperatures above and below Tg. Melt-recrystallization was observed at higher temperature, and destruction of crystal structures was observed at lower temperatures beyond yield point. While the higher temperature and lower strain rate have similar effects on mechanical properties. The correlated influences of time and temperature in the microscopic structures are more complicated. The evolution of microscopic characteristics such as the orientation parameter, the bond length, and the content of trans-trans conformation were calculated from the simulation. The results showed that the temperature have double effects on polymer chains. Higher temperature on one hand makes the chains more flexible, while on the other hand shortens the relaxation time of polymers. It is the interaction of these two aspects that determine the orientation parameter. During deformation, the trans conformation has experienced a rising process after the first drop process. And these microscopic structure parameters exhibit critical transaction, which are closely related to the yield point. A hypothetical model was thus proposed to describe the micro-structure and property relations based the investigations of this study.

cond-mat.soft↗

arXiv2020

The Online Saddle Point Problem and Online Convex Optimization with Knapsacks

We study the online saddle point problem, an online learning problem where at each iteration a pair of actions need to be chosen without knowledge of the current and future (convex-concave) payoff functions. The objective is to minimize the gap between the cumulative payoffs and the saddle point value of the aggregate payoff function, which we measure using a metric called "SP-Regret". The problem generalizes the online convex optimization framework but here we must ensure both players incur cumulative payoffs close to that of the Nash equilibrium of the sum of the games. We propose an algorithm that achieves SP-Regret proportional to $\sqrt{\ln(T)T}$ in the general case, and $\log(T)$ SP-Regret for the strongly convex-concave case. We also consider the special case where the payoff functions are bilinear and the decision sets are the probability simplex. In this setting we are able to design algorithms that reduce the bounds on SP-Regret from a linear dependence in the dimension of the problem to a \textit{logarithmic} one. We also study the problem under bandit feedback and provide an algorithm that achieves sublinear SP-Regret. We then consider an online convex optimization with knapsacks problem motivated by a wide variety of applications such as: dynamic pricing, auctions, and crowdsourcing. We relate this problem to the online saddle point problem and establish $O(\sqrt{T})$ regret using a primal-dual algorithm.

stat.ML↗

arXiv2019

Value Propagation for Decentralized Networked Deep Multi-agent Reinforcement Learning

We consider the networked multi-agent reinforcement learning (MARL) problem in a fully decentralized setting, where agents learn to coordinate to achieve the joint success. This problem is widely encountered in many areas including traffic control, distributed control, and smart grids. We assume that the reward function for each agent can be different and observed only locally by the agent itself. Furthermore, each agent is located at a node of a communication network and can exchanges information only with its neighbors. Using softmax temporal consistency and a decentralized optimization method, we obtain a principled and data-efficient iterative algorithm. In the first step of each iteration, an agent computes its local policy and value gradients and then updates only policy parameters. In the second step, the agent propagates to its neighbors the messages based on its value function and then updates its own value function. Hence we name the algorithm value propagation. We prove a non-asymptotic convergence rate 1/T with the nonlinear function approximation. To the best of our knowledge, it is the first MARL algorithm with convergence guarantee in the control, off-policy and non-linear function approximation setting. We empirically demonstrate the effectiveness of our approach in experiments.

cs.LG↗

arXiv2019

Inductive Bias of Gradient Descent based Adversarial Training on Separable Data

Adversarial training is a principled approach for training robust neural networks. Despite of tremendous successes in practice, its theoretical properties still remain largely unexplored. In this paper, we provide new theoretical insights of gradient descent based adversarial training by studying its computational properties, specifically on its inductive bias. We take the binary classification task on linearly separable data as an illustrative example, where the loss asymptotically attains its infimum as the parameter diverges to infinity along certain directions. Specifically, we show that when the adversarial perturbation during training has bounded $\ell_2$-norm, the classifier learned by gradient descent based adversarial training converges in direction to the maximum $\ell_2$-norm margin classifier at the rate of $\tilde{\mathcal{O}}(1/\sqrt{T})$, significantly faster than the rate $\mathcal{O}(1/\log T)$ of training with clean data. In addition, when the adversarial perturbation during training has bounded $\ell_q$-norm for some $q\ge 1$, the resulting classifier converges in direction to a maximum mixed-norm margin classifier, which has a natural interpretation of robustness, as being the maximum $\ell_2$-norm margin classifier under worst-case $\ell_q$-norm perturbation to the data. Our findings provide theoretical backups for adversarial training that it indeed promotes robustness against adversarial perturbation.

cs.LG↗

arXiv2019

Competing Against Equilibria in Zero-Sum Games with Evolving Payoffs

We study the problem of repeated play in a zero-sum game in which the payoff matrix may change, in a possibly adversarial fashion, on each round; we call these Online Matrix Games. Finding the Nash Equilibrium (NE) of a two player zero-sum game is core to many problems in statistics, optimization, and economics, and for a fixed game matrix this can be easily reduced to solving a linear program. But when the payoff matrix evolves over time our goal is to find a sequential algorithm that can compete with, in a certain sense, the NE of the long-term-averaged payoff matrix. We design an algorithm with small NE regret--that is, we ensure that the long-term payoff of both players is close to minimax optimum in hindsight. Our algorithm achieves near-optimal dependence with respect to the number of rounds and depends poly-logarithmically on the number of available actions of the players. Additionally, we show that the naive reduction, where each player simply minimizes its own regret, fails to achieve the stated objective regardless of which algorithm is used. We also consider the so-called bandit setting, where the feedback is significantly limited, and we provide an algorithm with small NE regret using one-point estimates of each payoff matrix.

cs.LG↗

arXiv2019

Robustness and Tractability for Non-convex M-estimators

We investigate two important properties of M-estimator, namely, robustness and tractability, in linear regression setting, when the observations are contaminated by some arbitrary outliers. Specifically, robustness means the statistical property that the estimator should always be close to the underlying true parameters {\em regardless of the distribution of the outliers}, and tractability indicates the computational property that the estimator can be computed efficiently, even if the objective function of the M-estimator is {\em non-convex}. In this article, by learning the landscape of the empirical risk, we show that under mild conditions, many M-estimators enjoy nice robustness and tractability properties simultaneously, when the percentage of outliers is small. We further extend our analysis to the high-dimensional setting, where the number of parameters is greater than the number of samples, $p \gg n$, and prove that when the proportion of outliers is small, the penalized M-estimators with {\em $L_1$} penalty will enjoy robustness and tractability simultaneously. Our research provides an analytic approach to see the effects of outliers and tuning parameters on the robustness and tractability for some families of M-estimators. Simulation and case study are presented to illustrate the usefulness of our theoretical results for M-estimators under Welsch's exponential squared loss.

math.ST↗

arXiv2019

LSwarm: Efficient Collision Avoidance for Large Swarms with Coverage Constraints in Complex Urban Scenes

In this paper, we address the problem of collision avoidance for a swarm of UAVs used for continuous surveillance of an urban environment. Our method, LSwarm, efficiently avoids collisions with static obstacles, dynamic obstacles and other agents in 3-D urban environments while considering coverage constraints. LSwarm computes collision avoiding velocities that (i) maximize the conformity of an agent to an optimal path given by a global coverage strategy and (ii) ensure sufficient resolution of the coverage data collected by each agent. Our algorithm is formulated based on ORCA (Optimal Reciprocal Collision Avoidance) and is scalable with respect to the size of the swarm. We evaluate the coverage performance of LSwarm in realistic simulations of a swarm of quadrotors in complex urban models. In practice, our approach can compute collision avoiding velocities for a swarm composed of tens to hundreds of agents in a few milliseconds on dense urban scenes consisting of tens of buildings.

cs.RO↗

arXiv2019

Large Scale Markov Decision Processes with Changing Rewards

We consider Markov Decision Processes (MDPs) where the rewards are unknown and may change in an adversarial manner. We provide an algorithm that achieves state-of-the-art regret bound of $O( \sqrt{τ(\ln|S|+\ln|A|)T}\ln(T))$, where $S$ is the state space, $A$ is the action space, $τ$ is the mixing time of the MDP, and $T$ is the number of periods. The algorithm's computational complexity is polynomial in $|S|$ and $|A|$ per period. We then consider a setting often encountered in practice, where the state space of the MDP is too large to allow for exact solutions. By approximating the state-action occupancy measures with a linear architecture of dimension $d\ll|S|$, we propose a modified algorithm with computational complexity polynomial in $d$. We also prove a regret bound for this modified algorithm, which to the best of our knowledge this is the first $\tilde{O}(\sqrt{T})$ regret bound for large scale MDPs with changing rewards.

cs.LG↗

arXiv2019

A Unified Framework for Marketing Budget Allocation

While marketing budget allocation has been studied for decades in traditional business, nowadays online business brings much more challenges due to the dynamic environment and complex decision-making process. In this paper, we present a novel unified framework for marketing budget allocation. By leveraging abundant data, the proposed data-driven approach can help us to overcome the challenges and make more informed decisions. In our approach, a semi-black-box model is built to forecast the dynamic market response and an efficient optimization method is proposed to solve the complex allocation task. First, the response in each market-segment is forecasted by exploring historical data through a semi-black-box model, where the capability of logit demand curve is enhanced by neural networks. The response model reveals relationship between sales and marketing cost. Based on the learned model, budget allocation is then formulated as an optimization problem, and we design efficient algorithms to solve it in both continuous and discrete settings. Several kinds of business constraints are supported in one unified optimization paradigm, including cost upper bound, profit lower bound, or ROI lower bound. The proposed framework is easy to implement and readily to handle large-scale problems. It has been successfully applied to many scenarios in Alibaba Group. The results of both offline experiments and online A/B testing demonstrate its effectiveness.

cs.DS↗

arXiv2019

Nonlinear Distributional Gradient Temporal-Difference Learning

We devise a distributional variant of gradient temporal-difference (TD) learning. Distributional reinforcement learning has been demonstrated to outperform the regular one in the recent study \citep{bellemare2017distributional}. In the policy evaluation setting, we design two new algorithms called distributional GTD2 and distributional TDC using the Cram{é}r distance on the distributional version of the Bellman error objective function, which inherits advantages of both the nonlinear gradient TD algorithms and the distributional RL approach. In the control setting, we propose the distributional Greedy-GQ using the similar derivation. We prove the asymptotic almost-sure convergence of distributional GTD2 and TDC to a local optimal solution for general smooth function approximators, which includes neural networks that have been widely used in recent study to solve the real-life RL problems. In each step, the computational complexities of above three algorithms are linear w.r.t.\ the number of the parameters of the function approximator, thus can be implemented efficiently for neural networks.

cs.LG↗

arXiv2019

Adaptive Recurrent Neural Network Based on Mixture Layer

Although Recurrent Neural Network (RNN) has been a powerful tool for modeling sequential data, its performance is inadequate when processing sequences with multiple patterns. In this paper, we address this challenge by introducing a novel mixture layer and constructing an adaptive RNN. The mixture layer augmented RNN (termed as M-RNN) partitions patterns in training sequences into several clusters and stores the principle patterns as prototype vectors of components in a mixture model. By leveraging the mixture layer, the proposed method can adaptively update states according to the similarities between encoded inputs and prototype vectors, leading to a stronger capacity in assimilating sequences with multiple patterns. Moreover, our approach can be further extended by taking advantage of prior knowledge about data. Experiments on both synthetic and real datasets demonstrate the effectiveness of the proposed method.

cs.LG↗

arXiv2019

Online Crowdsourcing

With the success of modern internet based platform, such as Amazon Mechanical Turk, it is now normal to collect a large number of hand labeled samples from non-experts. The Dawid- Skene algorithm, which is based on Expectation- Maximization update, has been widely used for inferring the true labels from noisy crowdsourced labels. However, Dawid-Skene scheme requires all the data to perform each EM iteration, and can be infeasible for streaming data or large scale data. In this paper, we provide an online version of Dawid- Skene algorithm that only requires one data frame for each iteration. Further, we prove that under mild conditions, the online Dawid-Skene scheme with projection converges to a stationary point of the marginal log-likelihood of the observed data. Our experiments demonstrate that the online Dawid- Skene scheme achieves state of the art performance comparing with other methods based on the Dawid- Skene scheme.

cs.LG↗