Yun Kuen Cheung
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View article: Proportional Response Dynamics in Gross Substitutes Markets
Proportional Response Dynamics in Gross Substitutes Markets Open
View article: Proportional Response Dynamics in Gross Substitutes Markets
Proportional Response Dynamics in Gross Substitutes Markets Open
Proportional response is a well-established distributed algorithm which has been shown to converge to competitive equilibria in both Fisher and Arrow-Debreu markets, for various sub-families of homogeneous utilities, including linear and c…
View article: Online Learning in Betting Markets: Profit versus Prediction
Online Learning in Betting Markets: Profit versus Prediction Open
We examine two types of binary betting markets, whose primary goal is for profit (such as sports gambling) or to gain information (such as prediction markets). We articulate the interplay between belief and price-setting to analyse both ty…
View article: Stability and Efficiency of Personalised Cultural Markets
Stability and Efficiency of Personalised Cultural Markets Open
This work is concerned with the dynamics of online cultural markets, namely, attention allocation of many users on a set of digital goods with infinite supply. Such dynamic is important in shaping processes and outcomes in society, from tr…
View article: Fair Division of Indivisible Goods for a Class of Concave Valuations
Fair Division of Indivisible Goods for a Class of Concave Valuations Open
We study the fair and efficient allocation of a set of indivisible goods among agents, where each good has several copies, and each agent has an additively separable concave valuation function with a threshold. These valuations capture the…
View article: Learning in Markets: Greed Leads to Chaos but Following the Price is Right
Learning in Markets: Greed Leads to Chaos but Following the Price is Right Open
We study learning dynamics in distributed production economies such as blockchain mining, peer-to-peer file sharing and crowdsourcing. These economies can be modelled as multi-product Cournot competitions or all-pay auctions (Tullock conte…
View article: From Griefing to Stability in Blockchain Mining Economies
From Griefing to Stability in Blockchain Mining Economies Open
We study a game-theoretic model of blockchain mining economies and show that griefing, a practice according to which participants harm other participants at some lesser cost to themselves, is a prevalent threat at its Nash equilibria. The …
View article: Online Optimization in Games via Control Theory: Connecting Regret, Passivity and Poincaré Recurrence
Online Optimization in Games via Control Theory: Connecting Regret, Passivity and Poincaré Recurrence Open
We present a novel control-theoretic understanding of online optimization and learning in games, via the notion of passivity. Passivity is a fundamental concept in control theory, which abstracts energy conservation and dissipation in phys…
View article: Learning in Markets: Greed Leads to Chaos but Following the Price is\n Right
Learning in Markets: Greed Leads to Chaos but Following the Price is\n Right Open
We study learning dynamics in distributed production economies such as\nblockchain mining, peer-to-peer file sharing and crowdsourcing. These economies\ncan be modelled as multi-product Cournot competitions or all-pay auctions\n(Tullock co…
View article: Chaos of Learning Beyond Zero-sum and Coordination via Game Decompositions
Chaos of Learning Beyond Zero-sum and Coordination via Game Decompositions Open
Machine learning processes, e.g. ''learning in games'', can be viewed as non-linear dynamical systems. In general, such systems exhibit a wide spectrum of behaviors, ranging from stability/recurrence to the undesirable phenomena of chaos (…
View article: Chaos, Extremism and Optimism: Volume Analysis of Learning in Games
Chaos, Extremism and Optimism: Volume Analysis of Learning in Games Open
We present volume analyses of Multiplicative Weights Updates (MWU) and Optimistic Multiplicative Weights Updates (OMWU) in zero-sum as well as coordination games. Such analyses provide new insights into these game dynamical systems, which …
View article: Vortices Instead of Equilibria in MinMax Optimization: Chaos and Butterfly Effects of Online Learning in Zero-Sum Games
Vortices Instead of Equilibria in MinMax Optimization: Chaos and Butterfly Effects of Online Learning in Zero-Sum Games Open
We establish that algorithmic experiments in zero-sum games fail miserably to confirm the unique, sharp prediction of maxmin equilibration. Contradicting nearly a century of economic thought that treats zero-sum games nearly axiomatically …
View article: Vortices Instead of Equilibria in MinMax Optimization: Chaos and Butterfly Effects of Online Learning in Zero-Sum Games
Vortices Instead of Equilibria in MinMax Optimization: Chaos and Butterfly Effects of Online Learning in Zero-Sum Games Open
We establish that algorithmic experiments in zero-sum games "fail miserably" to confirm the unique, sharp prediction of maxmin equilibration. Contradicting nearly a century of economic thought that treats zero-sum games nearly axiomaticall…
View article: Tracing Equilibrium in Dynamic Markets via Distributed Adaptation
Tracing Equilibrium in Dynamic Markets via Distributed Adaptation Open
Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a …
View article: Parallel Stochastic Asynchronous Coordinate Descent: Tight Bounds on the Possible Parallelism
Parallel Stochastic Asynchronous Coordinate Descent: Tight Bounds on the Possible Parallelism Open
Several works have shown linear speedup is achieved by an asynchronous parallel implementation of stochastic coordinate descent so long as there is not too much parallelism. More specifically, it is known that if all updates are of similar…
View article: Fully Asynchronous Stochastic Coordinate Descent: A Tight Lower Bound on the Parallelism Achieving Linear Speedup
Fully Asynchronous Stochastic Coordinate Descent: A Tight Lower Bound on the Parallelism Achieving Linear Speedup Open
We seek tight bounds on the viable parallelism in asynchronous implementations of coordinate descent that achieves linear speedup. We focus on asynchronous coordinate descent (ACD) algorithms on convex functions which consist of the sum of…
View article: Near) Optimal Parallelism Bound for Fully Asynchronous Coordinate Descent with Linear Speedup
Near) Optimal Parallelism Bound for Fully Asynchronous Coordinate Descent with Linear Speedup Open
When solving massive optimization problems in areas such as machine learning, it is a common practice to seek speedup via massive parallelism. However, especially in an asynchronous environment, there are limits on the possible parallelism…
View article: Amortized Analysis of Asynchronous Price Dynamics
Amortized Analysis of Asynchronous Price Dynamics Open
We extend a recently developed framework for analyzing asynchronous coordinate descent algorithms to show that an asynchronous version of tatonnement, a fundamental price dynamic widely studied in general equilibrium theory, converges towa…
View article: Dynamics of Distributed Updating in Fisher Markets
Dynamics of Distributed Updating in Fisher Markets Open
A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify natural distributed algorithms that converge quickly to an equilibrium. This p…
View article: Dynamics of Distributed Updating in Fisher Markets
Dynamics of Distributed Updating in Fisher Markets Open
A major goal in Algorithmic Game Theory is to justify equilibrium concepts from an algorithmic and complexity perspective. One appealing approach is to identify natural distributed algorithms that converge quickly to an equilibrium. This p…
View article: On Fair Division of Indivisible Items
On Fair Division of Indivisible Items Open
We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in mul…
View article: On Fair Division of Indivisible Items
On Fair Division of Indivisible Items Open
We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in mul…
View article: Tracing Equilibrium in Dynamic Markets via Distributed Adaptation
Tracing Equilibrium in Dynamic Markets via Distributed Adaptation Open
Competitive equilibrium is a central concept in economics with numerous applications beyond markets, such as scheduling, fair allocation of goods, or bandwidth distribution in networks. Computation of competitive equilibria has received a …
View article: Spanning Tree Congestion and Computation of Generalized Gy\H{o}ri-Lov{\'{a}}sz Partition
Spanning Tree Congestion and Computation of Generalized Gy\H{o}ri-Lov{\'{a}}sz Partition Open
We study a natural problem in graph sparsification, the Spanning Tree Congestion (\STC) problem. Informally, the \STC problem seeks a spanning tree with no tree-edge \emph{routing} too many of the original edges. The root of this problem d…
View article: Spanning Tree Congestion and Computation of Generalized Győri-Lovász Partition
Spanning Tree Congestion and Computation of Generalized Győri-Lovász Partition Open
We study a natural problem in graph sparsification, the Spanning Tree Congestion (\STC) problem. Informally, the \STC problem seeks a spanning tree with no tree-edge \emph{routing} too many of the original edges. The root of this problem d…
View article: Spanning Tree Congestion and Computation of Generalized Györi-Lovász Partition
Spanning Tree Congestion and Computation of Generalized Györi-Lovász Partition Open
We study a natural problem in graph sparsification, the Spanning Tree Congestion (STC) problem. Informally, it seeks a spanning tree with no tree-edge routing too many of the original edges. For any general connected graph with n vertices …
View article: Amortized Analysis of Asynchronous Price Dynamics
Amortized Analysis of Asynchronous Price Dynamics Open
We extend a recently developed framework for analyzing asynchronous coordinate descent algorithms to show that an asynchronous version of tatonnement, a fundamental price dynamic widely studied in general equilibrium theory, converges towa…
View article: Steiner Point Removal — Distant Terminals Don't (Really) Bother
Steiner Point Removal — Distant Terminals Don't (Really) Bother Open
Given a weighted graph G = (V, E, w) with a set of k terminals T ⊂ V, the Steiner Point Removal problem seeks for a minor of the graph with vertex set T, such that the distance between every pair of terminals is preserved within a small mu…
View article: On Fair Division for Indivisible Items
On Fair Division for Indivisible Items Open
We consider the task of assigning indivisible goods to a set of agents in a fair manner. Our notion of fairness is Nash social welfare, i.e., the goal is to maximize the geometric mean of the utilities of the agents. Each good comes in mul…
View article: Steiner Point Removal --- Distant Terminals Don't (Really) Bother
Steiner Point Removal --- Distant Terminals Don't (Really) Bother Open
Given a weighted graph $G=(V,E,w)$ with a set of $k$ terminals $T\subset V$, the Steiner Point Removal problem seeks for a minor of the graph with vertex set $T$, such that the distance between every pair of terminals is preserved within a…