Xingyu Zhou

Harshavardhan Kamarthi, Aditya B. Sasanur, Xinjie Tong et al.

Hierarchical time-series forecasting (HTSF) is an important problem for many real-world business applications where the goal is to simultaneously forecast multiple time-series that are related to each other via a hierarchical relation. Recent works, however, do not address two important challenges that are typically observed in many demand forecasting applications at large companies. First, many time-series at lower levels of the hierarchy have high sparsity i.e., they have a significant number of zeros. Most HTSF methods do not address this varying sparsity across the hierarchy. Further, they do not scale well to the large size of the real-world hierarchy typically unseen in benchmarks used in literature. We resolve both these challenges by proposing HAILS, a novel probabilistic hierarchical model that enables accurate and calibrated probabilistic forecasts across the hierarchy by adaptively modeling sparse and dense time-series with different distributional assumptions and reconciling them to adhere to hierarchical constraints. We show the scalability and effectiveness of our methods by evaluating them against real-world demand forecasting datasets. We deploy HAILS at a large chemical manufacturing company for a product demand forecasting application with over ten thousand products and observe a significant 8.5\% improvement in forecast accuracy and 23% better improvement for sparse time-series. The enhanced accuracy and scalability make HAILS a valuable tool for improved business planning and customer experience.

Sayak Ray Chowdhury, Xingyu Zhou, Ness Shroff

In this paper, we study the problem of regret minimization in reinforcement learning (RL) under differential privacy constraints. This work is motivated by the wide range of RL applications for providing personalized service, where privacy concerns are becoming paramount. In contrast to previous works, we take the first step towards non-tabular RL settings, while providing a rigorous privacy guarantee. In particular, we consider the adaptive control of differentially private linear quadratic (LQ) systems. We develop the first private RL algorithm, PRL, which is able to attain a sub-linear regret while guaranteeing privacy protection. More importantly, the additional cost due to privacy is only on the order of $\frac{\ln(1/δ)^{1/4}}{ε^{1/2}}$ given privacy parameters $ε, δ> 0$. Through this process, we also provide a general procedure for adaptive control of LQ systems under changing regularizers, which not only generalizes previous non-private controls, but also serves as the basis for general private controls.

Yuntian Deng, Xingyu Zhou, Baekjin Kim et al.

In this paper, we consider the Gaussian process (GP) bandit optimization problem in a non-stationary environment. To capture external changes, the black-box function is allowed to be time-varying within a reproducing kernel Hilbert space (RKHS). To this end, we develop WGP-UCB, a novel UCB-type algorithm based on weighted Gaussian process regression. A key challenge is how to cope with infinite-dimensional feature maps. To that end, we leverage kernel approximation techniques to prove a sublinear regret bound, which is the first (frequentist) sublinear regret guarantee on weighted time-varying bandits with general nonlinear rewards. This result generalizes both non-stationary linear bandits and standard GP-UCB algorithms. Further, a novel concentration inequality is achieved for weighted Gaussian process regression with general weights. We also provide universal upper bounds and weight-dependent upper bounds for weighted maximum information gains. These results are of independent interest for applications such as news ranking and adaptive pricing, where weights can be adopted to capture the importance or quality of data. Finally, we conduct experiments to highlight the favorable gains of the proposed algorithm in many cases when compared to existing methods.

Xingyu Zhou, Ness Shroff

In this paper, we consider the time-varying Bayesian optimization problem. The unknown function at each time is assumed to lie in an RKHS (reproducing kernel Hilbert space) with a bounded norm. We adopt the general variation budget model to capture the time-varying environment, and the variation is characterized by the change of the RKHS norm. We adapt the restart and sliding window mechanism to introduce two GP-UCB type algorithms: R-GP-UCB and SW-GP-UCB, respectively. We derive the first (frequentist) regret guarantee on the dynamic regret for both algorithms. Our results not only recover previous linear bandit results when a linear kernel is used, but complement the previous regret analysis of time-varying Gaussian process bandit under a Bayesian-type regularity assumption, i.e., each function is a sample from a Gaussian process.

Xingyu Zhou, Jian Tan

Motivated by the increasing concern about privacy in nowadays data-intensive online learning systems, we consider a black-box optimization in the nonparametric Gaussian process setting with local differential privacy (LDP) guarantee. Specifically, the rewards from each user are further corrupted to protect privacy and the learner only has access to the corrupted rewards to minimize the regret. We first derive the regret lower bounds for any LDP mechanism and any learning algorithm. Then, we present three almost optimal algorithms based on the GP-UCB framework and Laplace DP mechanism. In this process, we also propose a new Bayesian optimization (BO) method (called MoMA-GP-UCB) based on median-of-means techniques and kernel approximations, which complements previous BO algorithms for heavy-tailed payoffs with a reduced complexity. Further, empirical comparisons of different algorithms on both synthetic and real-world datasets highlight the superior performance of MoMA-GP-UCB in both private and non-private scenarios.

Wenbo Ren, Xingyu Zhou, Jia Liu et al.

This paper investigates the problem of regret minimization for multi-armed bandit (MAB) problems with local differential privacy (LDP) guarantee. In stochastic bandit systems, the rewards may refer to the users' activities, which may involve private information and the users may not want the agent to know. However, in many cases, the agent needs to know these activities to provide better services such as recommendations and news feeds. To handle this dilemma, we adopt differential privacy and study the regret upper and lower bounds for MAB algorithms with a given LDP guarantee. In this paper, we prove a lower bound and propose algorithms whose regret upper bounds match the lower bound up to constant factors. Numerical experiments also confirm our conclusions.