arXiv subjects

Xiaocheng Li

Publications and source records attributed to Xiaocheng Li.

46 records · Page 3Linked to original sources

arXiv2022

Learning from Stochastically Revealed Preference

We study the learning problem of revealed preference in a stochastic setting: a learner observes the utility-maximizing actions of a set of agents whose utility follows some unknown distribution, and the learner aims to infer the distribution through the observations of actions. The problem can be viewed as a single-constraint special case of the inverse linear optimization problem. Existing works all assume that all the agents share one common utility which can easily be violated under practical contexts. In this paper, we consider two settings for the underlying utility distribution: a Gaussian setting where the customer utility follows the von Mises-Fisher distribution, and a $δ$-corruption setting where the customer utility distribution concentrates on one fixed vector with high probability and is arbitrarily corrupted otherwise. We devise Bayesian approaches for parameter estimation and develop theoretical guarantees for the recovery of the true parameter. We illustrate the algorithm performance through numerical experiments.

math.OC↗

arXiv2022

Fairer LP-based Online Allocation via Analytic Center

In this paper, we consider an online resource allocation problem where a decision maker accepts or rejects incoming customer requests irrevocably in order to maximize expected reward given limited resources. At each time, a new order/customer/bid is revealed with a request of some resource(s) and a reward. We consider a stochastic setting where all the orders are i.i.d. sampled from an unknown distribution. Such formulation arises from many classic applications such as the canonical (quantity-based) network revenue management problem and the Adwords problem. While the literature on the topic mainly focuses on regret minimization, our paper considers the \textit{fairness} aspect of the problem. On a high level, we define the fairness in a way that a fair online algorithm should treat similar agents/customers similarly, and the decision made for similar agents/customers should be consistent over time. To achieve this goal, we define the fair offline solution as the analytic center of the offline optimal solution set, and introduce \textit{cumulative unfairness} as the cumulative deviation from the online solutions to the fair offline solution over time. We propose a fair algorithm based on an interior-point LP solver and a mechanism that dynamically detects unfair resource spending. Our algorithm achieves cumulative unfairness on the scale of order $O(\log(T))$, while maintains the regret to be bounded without dependency on $T$. In addition, compared to the literature, our result is produced under less restrictive assumptions on the degeneracy of the underlying linear program.

cs.DS↗

arXiv2022

An Improved Analysis of LP-based Control for Revenue Management

In this paper, we study a class of revenue management problems where the decision maker aims to maximize the total revenue subject to budget constraints on multiple type of resources over a finite horizon. At each time, a new order/customer/bid is revealed with a request of some resource(s) and a reward, and the decision maker needs to either accept or reject the order. Upon the acceptance of the order, the resource request must be satisfied and the associated revenue (reward) can be collected. We consider a stochastic setting where all the orders are i.i.d. sampled, i.e., the reward-request pair at each time is drawn from an unknown distribution with finite support. The formulation contains many classic applications such as the quantity-based network revenue management problem and the Adwords problem. We focus on the classic LP-based adaptive algorithm and consider regret as the performance measure defined by the gap between the optimal objective value of the certainty-equivalent linear program (LP) and the expected revenue obtained by the online algorithm. Our contribution is two-fold: (i) when the underlying LP is nondegenerate, the algorithm achieves a problem-dependent regret upper bound that is independent of the horizon/number of time periods $T$; (ii) when the underlying LP is degenerate, the algorithm achieves a regret upper bound that scales on the order of $\sqrt{T}\log T$. To our knowledge, both results are new and improve the best existing bounds for the LP-based adaptive algorithm in the corresponding setting. We conclude with numerical experiments to further demonstrate our findings.

math.OC↗

arXiv2021

Online Bin Packing with Known T

In the online bin packing problem, a sequence of items is revealed one at a time, and each item must be packed into an available bin instantly upon its arrival. In this paper, we revisit the problem under a setting where the total number of items T is known in advance, also known as the closed online bin packing problem. Specifically, we study both the stochastic model and the random permutation model. We develop and analyze an adaptive algorithm that solves an offline bin packing problem at geometric time intervals and uses the offline optimal solution to guide online packing decisions. Under both models, we show that the algorithm achieves C\sqrt{T} regret (in terms of the number of used bins) compared to the hindsight optimal solution, where C is a universal constant (<= 13) that bears no dependence on the underlying distribution or the item sizes. The result shows the lower bound barrier of Ω(\sqrt{T \log T}) in Shor (1986) can be broken with solely the knowledge of the horizon T, but without a need of knowing the underlying distribution. As to the algorithm analysis, we develop a new approach to analyzing the packing dynamic using the notion of exchangeable random variables. The approach creates a symmetrization between the offline solution and the online solution, and it is used to analyze both the algorithm performance and various benchmarks related to the bin packing problem. For the latter one, our analysis provides an alternative (probably simpler) treatment and tightens the analysis of the asymptotic benchmark of the stochastic bin packing problem in Rhee and Talagrand (1989a,b). As the analysis only relies on a symmetry between the offline and online problems, the algorithm and benchmark analyses can be naturally extended from the stochastic model to the random permutation model.

cs.DS↗

arXiv2021

The Symmetry between Arms and Knapsacks: A Primal-Dual Approach for Bandits with Knapsacks

In this paper, we study the bandits with knapsacks (BwK) problem and develop a primal-dual based algorithm that achieves a problem-dependent logarithmic regret bound. The BwK problem extends the multi-arm bandit (MAB) problem to model the resource consumption associated with playing each arm, and the existing BwK literature has been mainly focused on deriving asymptotically optimal distribution-free regret bounds. We first study the primal and dual linear programs underlying the BwK problem. From this primal-dual perspective, we discover symmetry between arms and knapsacks, and then propose a new notion of sub-optimality measure for the BwK problem. The sub-optimality measure highlights the important role of knapsacks in determining algorithm regret and inspires the design of our two-phase algorithm. In the first phase, the algorithm identifies the optimal arms and the binding knapsacks, and in the second phase, it exhausts the binding knapsacks via playing the optimal arms through an adaptive procedure. Our regret upper bound involves the proposed sub-optimality measure and it has a logarithmic dependence on length of horizon $T$ and a polynomial dependence on $m$ (the numbers of arms) and $d$ (the number of knapsacks). To the best of our knowledge, this is the first problem-dependent logarithmic regret bound for solving the general BwK problem.

cs.LG↗

arXiv2021

Online Linear Programming: Dual Convergence, New Algorithms, and Regret Bounds

We study an online linear programming (OLP) problem under a random input model in which the columns of the constraint matrix along with the corresponding coefficients in the objective function are generated i.i.d. from an unknown distribution and revealed sequentially over time. Virtually all pre-existing online algorithms were based on learning the dual optimal solutions/prices of the linear programs (LP), and their analyses were focused on the aggregate objective value and solving the packing LP where all coefficients in the constraint matrix and objective are nonnegative. However, two major open questions were: (i) Does the set of LP optimal dual prices learned in the pre-existing algorithms converge to those of the "offline" LP, and (ii) Could the results be extended to general LP problems where the coefficients can be either positive or negative. We resolve these two questions by establishing convergence results for the dual prices under moderate regularity conditions for general LP problems. Specifically, we identify an equivalent form of the dual problem which relates the dual LP with a sample average approximation to a stochastic program. Furthermore, we propose a new type of OLP algorithm, Action-History-Dependent Learning Algorithm, which improves the previous algorithm performances by taking into account the past input data as well as decisions/actions already made. We derive an $O(\log n \log \log n)$ regret bound (under a locally strong convexity and smoothness condition) for the proposed algorithm, against the $O(\sqrt{n})$ bound for typical dual-price learning algorithms, where $n$ is the number of decision variables. Numerical experiments demonstrate the effectiveness of the proposed algorithm and the action-history-dependent design.

cs.DS↗

arXiv2020

Simple and Fast Algorithm for Binary Integer and Online Linear Programming

In this paper, we develop a simple and fast online algorithm for solving a class of binary integer linear programs (LPs) arisen in general resource allocation problem. The algorithm requires only one single pass through the input data and is free of doing any matrix inversion. It can be viewed as both an approximate algorithm for solving binary integer LPs and a fast algorithm for solving online LP problems. The algorithm is inspired by an equivalent form of the dual problem of the relaxed LP and it essentially performs (one-pass) projected stochastic subgradient descent in the dual space. We analyze the algorithm in two different models, stochastic input and random permutation, with minimal technical assumptions on the input data. The algorithm achieves $O\left(m \sqrt{n}\right)$ expected regret under the stochastic input model and $O\left((m+\log n)\sqrt{n}\right)$ expected regret under the random permutation model, and it achieves $O(m \sqrt{n})$ expected constraint violation under both models, where $n$ is the number of decision variables and $m$ is the number of constraints. The algorithm enjoys the same performance guarantee when generalized to a multi-dimensional LP setting which covers a wider range of applications. In addition, we employ the notion of permutational Rademacher complexity and derive regret bounds for two earlier online LP algorithms for comparison. Both algorithms improve the regret bound with a factor of $\sqrt{m}$ by paying more computational cost. Furthermore, we demonstrate how to convert the possibly infeasible solution to a feasible one through a randomized procedure. Numerical experiments illustrate the general applicability and effectiveness of the algorithms.

cs.DS↗

arXiv2018

Recurrent Autoregressive Networks for Online Multi-Object Tracking

The main challenge of online multi-object tracking is to reliably associate object trajectories with detections in each video frame based on their tracking history. In this work, we propose the Recurrent Autoregressive Network (RAN), a temporal generative modeling framework to characterize the appearance and motion dynamics of multiple objects over time. The RAN couples an external memory and an internal memory. The external memory explicitly stores previous inputs of each trajectory in a time window, while the internal memory learns to summarize long-term tracking history and associate detections by processing the external memory. We conduct experiments on the MOT 2015 and 2016 datasets to demonstrate the robustness of our tracking method in highly crowded and occluded scenes. Our method achieves top-ranked results on the two benchmarks.

cs.CV↗

arXiv2017

Hierarchical Modeling of Seed Variety Yields and Decision Making for Future Planting Plans

Eradicating hunger and malnutrition is a key development goal of the 21st century. We address the problem of optimally identifying seed varieties to reliably increase crop yield within a risk-sensitive decision-making framework. Specifically, we introduce a novel hierarchical machine learning mechanism for predicting crop yield (the yield of different seed varieties of the same crop). We integrate this prediction mechanism with a weather forecasting model, and propose three different approaches for decision making under uncertainty to select seed varieties for planting so as to balance yield maximization and risk.We apply our model to the problem of soybean variety selection given in the 2016 Syngenta Crop Challenge. Our prediction model achieves a median absolute error of 3.74 bushels per acre and thus provides good estimates for input into the decision models.Our decision models identify the selection of soybean varieties that appropriately balance yield and risk as a function of the farmer's risk aversion level. More generally, our models support farmers in decision making about which seed varieties to plant.

cs.LG↗

arXiv2017

Graph Convolution: A High-Order and Adaptive Approach

In this paper, we presented a novel convolutional neural network framework for graph modeling, with the introduction of two new modules specially designed for graph-structured data: the $k$-th order convolution operator and the adaptive filtering module. Importantly, our framework of High-order and Adaptive Graph Convolutional Network (HA-GCN) is a general-purposed architecture that fits various applications on both node and graph centrics, as well as graph generative models. We conducted extensive experiments on demonstrating the advantages of our framework. Particularly, our HA-GCN outperforms the state-of-the-art models on node classification and molecule property prediction tasks. It also generates 32% more real molecules on the molecule generation task, both of which will significantly benefit real-world applications such as material design and drug screening.

cs.LG↗