# Zhiyi HuangThe University of Hong Kong | HKU · Department of Computer Science

Zhiyi Huang

Doctor of Philosophy

## About

105

Publications

5,233

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1,869

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Introduction

Additional affiliations

September 2013 - July 2014

September 2008 - August 2013

## Publications

Publications (105)

The prophet secretary problem is a combination of the prophet inequality and the secretary problem, where elements are drawn from known independent distributions and arrive in uniformly random order. In this work, we design 1) a $0.688$-competitive algorithm, that breaks the $0.675$ barrier of blind strategies (Correa, Saona, Ziliotto, 2021), and 2...

Sampling without replacement is a natural online rounding strategy for converting fractional bipartite matching into an integral one. In Online Bipartite Matching, we can use the Balance algorithm to fractionally match each online vertex, and then sample an unmatched offline neighbor with probability proportional to the fractional matching. In Onli...

Matching, capturing allocation of items to unit-demand buyers, or tasks to workers, or pairs of collaborators, is a central problem in economics. Indeed, the growing prevalence of matching-based markets, many of which online in nature, has motivated much research in economics, operations research, computer science, and their intersection. This brie...

Matching, capturing allocation of items to unit-demand buyers, or tasks to workers, or pairs of collaborators, is a central problem in economics. Indeed, the growing prevalence of matching-based markets, many of which online in nature, has motivated much research in economics, operations research, computer science, and their intersection. This brie...

The maximization of Nash welfare, which equals the geometric mean of agents’ utilities, is widely studied because it balances efficiency and fairness in resource allocation problems. Banerjee, Gkatzelis, Gorokh, and Jin (2022) recently introduced the model of online Nash welfare maximization for T divisible items and N agents with additive utilitie...

Mehta and Panigrahi (2012) proposed Online Matching with Stochastic Rewards, which generalizes the Online Bipartite Matching problem of Karp, Vazirani, and Vazirani (1990) by associating the edges with success probabilities. This new feature captures the pay-per-click model in online advertising. Recently, Huang and Zhang (2020) studied this proble...

We show that a simple greedy algorithm is $4.75$ probability-competitive for the Laminar Matroid Secretary Problem, improving the $3\sqrt{3} \approx 5.17$-competitive algorithm based on the forbidden sets technique (Soto, Turkieltaub, and Verdugo, 2018).

We analyze union-find using potential functions motivated by continuous algorithms, and give alternate proofs of the $O(\log\log{n})$, $O(\log^{*}n)$, $O(\log^{**}n)$, and $O(\alpha(n))$ amortized cost upper bounds. The proof of the $O(\log\log{n})$ amortized bound goes as follows. Let each node's potential be the square root of its size, i.e., the...

We initiate the study of fairness among classes of agents in online bipartite matching where there is a given set of offline vertices (aka agents) and another set of vertices (aka items) that arrive online and must be matched irrevocably upon arrival. In this setting, agents are partitioned into a set of classes and the matching is required to be f...

Nash welfare maximization is widely studied because it balances efficiency and fairness in resource allocation problems. Banerjee, Gkatzelis, Gorokh, and Jin (2022) recently introduced the model of online Nash welfare maximization with predictions for $T$ divisible items and $N$ agents with additive utilities. They gave online algorithms whose comp...

Given a spectrally sparse signal $\mathbf{y} = \sum_{i=1}^s x_i\mathbf{f}(\tau_i) \in \mathbb{C}^{2n+1}$ consisting of $s$ complex sinusoids, we consider the super-resolution problem, which is about estimating frequency components $\{\tau_i\}_{i=1}^s$ of $\mathbf y$. We consider the OMP-type algorithms for super-resolution, which is more efficient...

Online bipartite matching is one of the most fundamental problems in the online algorithms literature. Karp, Vazirani, and Vazirani (STOC 1990) gave an elegant algorithm for unweighted bipartite matching that achieves an optimal competitive ratio of 1 − 1/ e . Aggarwal et al. (SODA 2011) later generalized their algorithm and analysis to the vertex-...

The deterministic $k$-server conjecture states that there is a $k$-competitive deterministic algorithm for the $k$-server problem for any metric space. We show that the work function algorithm is $3$-competitive for the $3$-server problem on circle metrics, a case left open by Coester and Koutsoupias (2021). Our analysis follows the existing framew...

Consider Myerson's optimal auction with respect to an inaccurate prior, e.g., estimated from data, which is an underestimation of the true value distribution. Can the auctioneer expect getting at least the optimal revenue w.r.t. the inaccurate prior since the true value distribution is bigger? This so-called strong revenue monotonicity is known to...

In the classical version of online bipartite matching, there is a given set of offline vertices (aka agents) and another set of vertices (aka items) that arrive online. When each item arrives, its incident edges -- the agents who like the item -- are revealed and the algorithm must irrevocably match the item to such agents. We initiate the study of...

We study the power of multiple choices in online stochastic matching. Despite a long line of research, existing algorithms still only consider two choices of offline neighbors for each online vertex because of the technical challenge in analyzing multiple choices. This paper introduces two approaches for designing and analyzing algorithms that use...

Online algorithms are an important branch in algorithm design. Designing online algorithms with a bounded competitive ratio (in terms of worst-case performance) can be hard and usually relies on problem-specific assumptions. Inspired by adversarial training from Generative Adversarial Net and the fact that the competitive ratio of an online algorit...

Online algorithm is an important branch in algorithm design. Designing online algorithms with a bounded competitive ratio (in terms of worst-case performance) can be hard and usually relies on problem-specific assumptions. Inspired by adversarial training from Generative Adversarial Net (GAN) and the fact that competitive ratio of an online algorit...

This paper studies the online correlated selection (OCS) problem introduced by Fahrbach, Huang, Tao, and Zadimoghaddam (2020) to get the first edge-weighted online bipartite matching algorithm that breaks the $0.5$ barrier. Suppose that we receive a pair of elements in each round and select one of them. Can we select with negative correlation to be...

This paper introduces the targeted sampling model in optimal auction design. In this model, the seller may specify a quantile interval and sample from a buyer's prior restricted to the interval. This can be interpreted as allowing the seller to, for example, examine the top $40$ percents bids from previous buyers with the same characteristics. The...

We study the online stochastic matching problem. Consider a bipartite graph with offline vertices on one side, and with i.i.d.online vertices on the other side. The offline vertices and the distribution of online vertices are known to the algorithm beforehand. The realization of the online vertices, however, is revealed one at a time, upon which th...

Three decades ago, Karp, Vazirani, and Vazirani (STOC 1990) defined the online matching problem and gave an optimal $1-\frac{1}{e} \approx 0.632$-competitive algorithm. %introduced the Ranking algorithm with the optimal $1-\frac{1}{e}$ competitive ratio. Fifteen years later, Mehta, Saberi, Vazirani, and Vazirani (FOCS 2005) introduced the first gen...

Karp, Vazirani, and Vazirani (STOC 1990) initiated the study of online bipartite matching, which has held a central role in online algorithms ever since. Of particular importance are the Ranking algorithm for integral matching and the Water-filling algorithm for fractional matching. Most algorithms in the literature can be viewed as adaptations of...

We introduce a fully online model of maximum cardinality matching in which all vertices arrive online. On the arrival of a vertex, its incident edges to previously arrived vertices are revealed. Each vertex has a deadline that is after all its neighbors’ arrivals. If a vertex remains unmatched until its deadline, then the algorithm must irrevocably...

Online bipartite matching and its variants are among the most fundamental problems in the online algorithms literature. Karp, Vazirani, and Vazirani (STOC 1990) introduced an elegant algorithm for the unweighted problem that achieves an optimal competitive ratio of $1-1/e$. Later, Aggarwal et al. (SODA 2011) generalized their algorithm and analysis...

Mehta and Panigrahi (FOCS 2012) introduce the problem of online matching with stochastic rewards, where edges are associated with success probabilities and a match succeeds with the probability of the corresponding edge. It is one of the few online matching problems that have defied the randomized online primal dual framework by Devanur, Jain, and...

The sample complexity of learning Myerson's optimal auction from i.i.d. samples of bidders' values has received much attention since its introduction by Cole and Roughgarden (STOC 2014). This letter gives a brief introduction of a recent work that settles the sample complexity by showing matching upper and lower bounds, up to a poly-logarithmic fac...

We consider a generalization of the third degree price discrimination problem studied in Bergemann et al. (2015), where an intermediary between the buyer and the seller can design market segments to maximize any linear combination of consumer surplus and seller revenue. Unlike in Bergemann et al. (2015), we assume that the intermediary only has par...

This paper explores a theory of generalization for learning problems on product distributions, complementing the existing learning theories in the sense that it does not rely on any complexity measures of the hypothesis classes. The main contributions are two general sample complexity bounds: (1) $\tilde{O} \big( \frac{nk}{\epsilon^2} \big)$ sample...

This article presents a simplification of Zadimoghaddam's algorithm for the edge-weighted online bipartite matching problem, under the online primal dual framework. In doing so, we obtain an improved competitive ratio of $0.514$. We first combine the online correlated selection (OCS), an ingredient distilled from Zadimoghaddam (2017) by Huang and T...

This article identifies a key algorithmic ingredient in the edge-weighted online matching algorithm by Zadimoghaddam (2017) and presents a simplified algorithm and its analysis to demonstrate how it works in the unweighted case.

Cloud computing has been widely adopted to support various computation services. A fundamental problem faced by cloud providers is how to efficiently allocate resources upon user requests and price the resource usage, in order to maximize resource efficiency and hence provider profit. Existing studies establish detailed performance models of cloud...

We survey some recent progress on the design and the analysis of online algorithms for optimization problems with non-linear, usually convex, objectives. We focus on an extension of the online primal dual technique, and highlight its application in a number of applications, including an online matching problem with concave returns, an online schedu...

We introduce an $(\epsilon, \delta)$-jointly differentially private algorithm for packing problems. Our algorithm not only achieves the optimal trade-off between the privacy parameter $\epsilon$ and the minimum supply requirement (up to logarithmic factors), but is also scalable in the sense that the running time is linear in the number of agents $...

We present an improved $(\epsilon, \delta)$-jointly differentially private algorithm for packing problems. Our algorithm gives a feasible output that is approximately optimal up to an $\alpha n$ additive factor as long as the supply of each resource is at least $\tilde{O}(\sqrt{m} / \alpha \epsilon)$, where $m$ is the number of resources. This impr...

This paper settles the sample complexity of single-parameter revenue maximization by showing matching upper and lower bounds, up to a poly-logarithmic factor, for all families of value distributions that have been considered in the literature. The upper bounds are unified under a novel framework, which builds on the strong revenue monotonicity by D...

Huang et al.~(STOC 2018) introduced the fully online matching problem, a generalization of the classic online bipartite matching problem in that it allows all vertices to arrive online and considers general graphs. They showed that the ranking algorithm by Karp et al.~(STOC 1990) is strictly better than $0.5$-competitive and the problem is strictly...

We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying matroid. In each round when a new element arrives, the algorithm may accept the new element into its feasible s...

We introduce a fully online model of maximum cardinality matching in which all vertices arrive online. On the arrival of a vertex, its incident edges to previously-arrived vertices are revealed. Each vertex has a deadline that is after all its neighbors’ arrivals. If a vertex remains unmatched until its deadline, the algorithm must then irrevocably...

We consider the online makespan minimization problem on identical machines. Chen and Vestjens (ORL 1997) show that the largest processing time first (LPT) algorithm is 1.5-competitive. For the special case of two machines, Noga and Seiden (TCS 2001) introduce the SLEEPY algorithm that achieves a competitive ratio of $(5 - \sqrt{5})/2 \approx 1.382$...

Today's IaaS clouds allow dynamic scaling of VMs allocated to a user, according to real-time demand of the user. There are two types of scaling: horizontal scaling (scale-out) by allocating more VM instances to the user, and vertical scaling (scale-up) by boosting resources of VMs owned by the user. It has been a daunting issue how to efficiently a...

We consider privacy-preserving k-means clustering. For the objective of minimizing the Wasserstein distance between the output and the optimal solution, we show that there is a polynomial-time (ε,δ)-differentially private algorithm which, for any sufficiently large Φ² well-separated datasets, outputs k centers that are within Wasserstein distance Ø...

We consider the problem of learning optimal reserve price in repeated auctions against non-myopic bidders, who may bid strategically in order to gain in future rounds even if the single-round auctions are truthful. Previous algorithms, e.g., empirical pricing, do not provide non-trivial regret rounds in this setting in general. We introduce algorit...

We introduce a weighted version of the ranking algorithm by Karp et al. (STOC 1990), and prove a competitive ratio of 0.6534 for the vertex-weighted online bipartite matching problem when online vertices arrive in random order. Our result shows that random arrivals help beating the 1-1/e barrier even in the vertex-weighted case. We build on the ran...

We study online auctions with production costs using an online primal dual framework. The seller allocates items to buyers and can produce multiple copies of each item subject to a non-decreasing marginal cost per copy. The buyers have arbitrary valuation functions and arrive one by one online in some arbitrary order. The goal is to design an onlin...

We introduce a fully online model of maximum cardinality matching in which all vertices arrive online. On the arrival of a vertex, its incident edges to previously-arrived vertices are revealed. Each vertex has a deadline that is after all its neighbors' arrivals. If a vertex remains unmatched until its deadline, the algorithm must then irrevocably...

We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution D. The seller has “data” about D in the form of m ≥ 1 independent and identically distributed samples, and the algorithmic challenge is to use these samples to obtain expected revenue as close as possible to what could be achieved with...

We consider the problem of online scheduling of jobs on unrelated machines with dynamic speed scaling to minimize the sum of energy and weighted flow-time. We give an algorithm with an almost optimal competitive ratio for arbitrary power functions. (No earlier results handled arbitrary power functions for unrelated machines.) For power functions of...

In this paper, we consider the problem of computing the minimum area triangle that circumscribes a given $n$-sided convex polygon touching edge-to-edge. In other words, we compute the minimum area triangle that is the intersection of 3 half-planes out of $n$ half-planes defined by a given convex polygon. Previously, $O(n\log n)$ time algorithms wer...

We consider revenue maximization in online auctions and pricing. A seller sells an identical item in each period to a new buyer, or a new set of buyers. For the online posted pricing problem, we show regret bounds that scale with the best fixed price, rather than the range of the values. We also show regret bounds that are almost scale free, and ma...

We consider revenue maximization in online auctions and pricing. A seller sells an identical item in each period to a new buyer, or a new set of buyers. For the online posted pricing problem, we show regret bounds that scale with the best fixed price, rather than the range of the values. We also show regret bounds that are almost scale free, and ma...

With the recent advent of Network Functions Virtualization (NFV), enterprises and businesses are looking into network service provisioning through service chains of virtual network functions (VNFs), instead of relying on dedicated hardware middleboxes. Accompanying this trend, an NFV market is emerging, where NFV service providers create VNF instan...

Auction design has recently been studied for dynamic resource bundling and virtual machine (VM) provisioning in IaaS clouds, but is mostly restricted to one-shot or offline setting. This paper targets a more realistic case of online VM auction design, where: 1) cloud users bid for resources into the future to assemble customized VMs with desired oc...

We study the online submodular maximization problem with free disposal under a matroid constraint. Elements from some ground set arrive one by one in rounds, and the algorithm maintains a feasible set that is independent in the underlying matroid. In each round when a new element arrives, the algorithm may accept the new element into its feasible s...

This paper studies the cloud market for computing jobs with completion deadlines, and designs efficient online auctions for cloud resource provisioning. A cloud user bids for future cloud resources to execute its job. Each bid includes: 1) a utility, reflecting the amount that the user is willing to pay for executing its job and 2) a soft deadline,...

Traditionally, the Bayesian optimal auction design problem has been considered either when the bidder values are i.i.d, or when each bidder is individually identifiable via her value distribution. The latter is a reasonable approach when the bidders can be classified into a few categories, but there are many instances where the classification of bi...

We consider a private variant of the classical allocation problem: given k goods and n agents with private valuation functions over bundles of goods, how can we allocate goods to agents to maximize social welfare? An important special case is when agents desire at most one good, and specify their (private) value for each good: in this case, the pro...

Traditionally, the Bayesian optimal auction design problem has been
considered either when the bidder values are i.i.d, or when each bidder is
individually identifiable via her value distribution. The latter is a
reasonable approach when the bidders can be classified into a few categories,
but there are many instances where the classification of bi...

We give a detailed characterization of optimal trades under budget
constraints in a prediction market with a cost-function-based automated market
maker. We study how the budget constraints of individual traders affect their
ability to impact the market price. As a concrete application of our
characterization, we give sufficient conditions for a pro...

Auction design has recently been studied for dynamic resource bundling and VM provisioning in IaaS clouds, but is mostly restricted to the one-shot or offline setting. This work targets a more realistic case of online VM auction design, where: (i) cloud users bid for resources into the future to assemble customized VMs with desired occupation durat...

In recent years, there has been a growing interest in speed scaling algorithms, where a set of jobs need to be scheduled on a machine with variable speed so as to optimize the flow-times of the jobs and the energy consumed by the machine. A series of results have culminated in constant-competitive algorithms for this problem in the clairvoyant mode...

We study the online convex covering problem and online convex packing
problem. The (offline) convex covering problem is modeled by the following
convex program: $\min_{x \in R_+^n} f(x) \ \text{s.t}\ A x \ge 1$, where $f :
R_+^n \mapsto R_+$ is a monotone and convex cost function, and $A$ is an $m
\times n$ matrix with non-negative entries. Each ro...

A coverage function fover a ground set [m] is associated with a universe U of weighted elements and m sets A1, . . . ,Am â U, and for any T â [m], f(T) is defined as the total weight of the elements in the union âjâTAj . Coverage functions are an important special case of submodular functions, and arise in many applications, for instance, as a clas...

We study online combinatorial auctions with production costs proposed by Blum
et al. using the online primal dual framework. In this model, buyers arrive
online, and the seller can produce multiple copies of each item subject to a
non-decreasing marginal cost per copy. The goal is to allocate items to
maximize social welfare less total production c...

In this paper we present an extremely general method for approximately
solving a large family of convex programs where the solution can be divided
between different agents, subject to joint differential privacy. This class
includes multi-commodity flow problems, general allocation problems, and
multi-dimensional knapsack problems, among other examp...

We study the problem of setting a price for a potential buyer with a valuation drawn from an unknown distribution D. The seller has "data" about D in the form of m ≥ 1 i.i.d. samples, and the algorithmic challenge is to use these samples to obtain expected revenue as close as possible to what could be achieved with advance knowledge of D.
Our first...

We consider the problem of online scheduling of jobs on unrelated machines with dynamic speed scaling to minimize the sum of energy and weighted flow time. We give an algorithm with an almost optimal competitive ratio for arbitrary power functions. (No earlier results handled arbitrary power functions for minimizing flow time plus energy with unrel...

We consider a private variant of the classical allocation problem: given k goods and n agents with individual, private valuation functions over bundles of goods, how can we partition the goods amongst the agents to maximize social welfare? An important special case is when each agent desires at most one good, and specifies her (private) value for e...

In the context of online ad serving, display ads may appear on different types of webpages, where each page includes several ad slots and therefore multiple ads can be shown on each page. The set of ads that can be assigned to ad slots of the same page needs to satisfy various prespecified constraints including exclusion constraints, diversity cons...

We consider the item pricing problem for revenue maximization, where a single seller with multiple distinct items caters to multiple buyers with unknown subadditive valuation functions who arrive in a sequence. The seller sets the prices on individual items, and we design randomized pricing strategies to maximize expected revenue. We consider dynam...

Rapid development in computing technology and the Internet has given rise to new challenges in large-scale computational problems. In particular, many problems that arise from electronic commerce rely on the private data of self-interested agents. So the algorithms need to deal with both limited computational resources and some new challenges impos...

We consider the problem of privately answering queries defined on databases
which are collections of points belonging to some metric space. We give simple,
computationally efficient algorithms for answering distance queries defined
over an arbitrary metric. Distance queries are specified by points in the
metric space, and ask for the average distan...

We provide a Polynomial Time Approximation Scheme (PTAS) for the Bayesian
optimal multi-item multi-bidder auction problem under two conditions. First,
bidders are independent, have additive valuations and are from the same
population. Second, every bidder's value distributions of items are independent
but not necessarily identical monotone hazard r...

In this paper, we study sequential auctions with two budget constrained
bidders and any number of identical items. All prior results on such
auctions consider only two items. We construct a canonical outcome of
the auction that is the only natural equilibrium and is unique under a
refinement of subgame perfect equilibria. We show certain interestin...

A coverage function
f over a ground set [m] is associated with a universe U of weighted elements and m sets A
1,…,A
m
⊆ U, and for any T ⊆ [m], f(T) is defined as the total weight of the elements in the union ∪ j ∈ T
A
j
. Coverage functions are an important special case of submodular functions, and arise in many applications, for instance as a cla...

In this paper we show that for any mechanism design problem with the
objective of maximizing social welfare, the exponential mechanism can be
implemented as a truthful mechanism while still preserving differential
privacy. Our instantiation of the exponential mechanism can be interpreted as a
generalization of the VCG mechanism in the sense that th...

We study the generalized sorting problem where we are given a set of n elements to be sorted but only a subset of all possible pair wise element comparisons is allowed. The goal is to determine the sorted order using the smallest possible number of allowed comparisons. The generalized sorting problem may be equivalently viewed as follows. Given an...

A central question in algorithmic mechanism design is to understand the additional difficulty introduced by truthfulness requirements
in the design of approximation algorithms for social welfare maximization. In this paper, by studying the problem of single-parameter
combinatorial auctions, we obtain the first black-box reduction that converts any...

Let X
1, X
2, …, X
n
be a set of random variables. Suppose that in addition to the prior distributions of these random variables we are also given linear constraints relating them. We ask for necessary and sufficient conditions under which we can efficiently sample the constrained distributions, find constrained marginal distributions for each of t...

Very recently, Hartline and Lucier studied single-parameter mechanism design problems in the Bayesian setting. They proposed a black-box reduction that converted Bayesian approximation algorithms into Bayesian-Incentive-Compatible (BIC) mechanisms while preserving social welfare. It remains a major open question if one can find similar reduction in...