arXiv subjects

Zihe Wang

Publications and source records attributed to Zihe Wang.

53 records · Page 3Linked to original sources

arXiv2021

Practical distributed quantum information processing with LOCCNet

Distributed quantum information processing is essential for building quantum networks and enabling more extensive quantum computations. In this regime, several spatially separated parties share a multipartite quantum system, and the most natural set of operations is Local Operations and Classical Communication (LOCC). As a pivotal part in quantum information theory and practice, LOCC has led to many vital protocols such as quantum teleportation. However, designing practical LOCC protocols is challenging due to LOCC's intractable structure and limitations set by near-term quantum devices. Here we introduce LOCCNet, a machine learning framework facilitating protocol design and optimization for distributed quantum information processing tasks. As applications, we explore various quantum information tasks such as entanglement distillation, quantum state discrimination, and quantum channel simulation. We discover protocols with evident improvements, in particular, for entanglement distillation with quantum states of interest in quantum information. Our approach opens up new opportunities for exploring entanglement and its applications with machine learning, which will potentially sharpen our understanding of the power and limitations of LOCC. An implementation of LOCCNet is available in Paddle Quantum, a quantum machine learning Python package based on PaddlePaddle deep learning platform.

quant-ph↗

arXiv2021

Identifying Ransomware Actors in the Bitcoin Network

Due to the pseudo-anonymity of the Bitcoin network, users can hide behind their bitcoin addresses that can be generated in unlimited quantity, on the fly, without any formal links between them. Thus, it is being used for payment transfer by the actors involved in ransomware and other illegal activities. The other activity we consider is related to gambling since gambling is often used for transferring illegal funds. The question addressed here is that given temporally limited graphs of Bitcoin transactions, to what extent can one identify common patterns associated with these fraudulent activities and apply them to find other ransomware actors. The problem is rather complex, given that thousands of addresses can belong to the same actor without any obvious links between them and any common pattern of behavior. The main contribution of this paper is to introduce and apply new algorithms for local clustering and supervised graph machine learning for identifying malicious actors. We show that very local subgraphs of the known such actors are sufficient to differentiate between ransomware, random and gambling actors with 85% prediction accuracy on the test data set.

cs.CR↗

arXiv2021

Anomalous Hall effect in distorted kagome magnets (Nd, Sm)Mn$_6$Sn$_6$

We report magnetic and electrical properties for single crystals of NdMn$_6$Sn$_6$ and SmMn$_6$Sn$_6$. They crystallize into a structure which has distorted, Mn-based kagome lattices, compared to the pristine kagome lattices in heavy-rare-earth-bearing RMn$_6$Sn$_6$ compounds. They are hightemperature ferromagnets of which the R moment is parallel with the Mn moment. We observed a large intrinsic anomalous Hall effect (AHE) that is comparable to the ferrimagnetic, heavy-R siblings in a wide range of temperature. We conclude that their intrinsic AHE is stemming from the Mn-based kagome lattice, just as in the heavy RMn$_6$Sn$_6$.

cond-mat.str-el↗

arXiv2021

A Game-theoretical Approach to Analyze Film Release Time

Film release dates play an important part in box office revenues because of the facts of obvious seasonality demand in the film industry and severe competition among films shown at the same time. In this paper, we study how film studios choose release time for movies they produce to maximize their box offices. We first formalize this problem as an attraction competition game where players (film studios) consider both potential profits and competitors' choices when deciding the release time. Then we prove that there always exists a pure Nash equilibrium and give the sufficient condition of the uniqueness of the Nash equilibrium. Our model can be generalized to an extensive game and we compute the subgame-perfect equilibrium for homogeneous players. For the case that one film studio could have multiple movies to release, we prove that finding a player's best response is NP-hard and it does not guarantee the existence of a pure Nash equilibrium. Experiments are provided to support the soundness of our model. In the final state, most of film studios, accounting for 84 percent of the market, would not change their release time. The behaviors of film studios imply they are following some strategies to reach a Nash equilibrium.

cs.GT↗

arXiv2020

Detecting and quantifying entanglement on near-term quantum devices

Quantum entanglement is a key resource in quantum technology, and its quantification is a vital task in the current Noisy Intermediate-Scale Quantum (NISQ) era. This paper combines hybrid quantum-classical computation and quasi-probability decomposition to propose two variational quantum algorithms, called Variational Entanglement Detection (VED) and Variational Logarithmic Negativity Estimation (VLNE), for detecting and quantifying entanglement on near-term quantum devices, respectively. VED makes use of the positive map criterion and works as follows. Firstly, it decomposes a positive map into a combination of quantum operations implementable on near-term quantum devices. It then variationally estimates the minimal eigenvalue of the final state, obtained by executing these implementable operations on the target state and averaging the output states. Deterministic and probabilistic methods are proposed to compute the average. At last, it asserts that the target state is entangled if the optimized minimal eigenvalue is negative. VLNE builds upon a linear decomposition of the transpose map into Pauli terms and the recently proposed trace distance estimation algorithm. It variationally estimates the well-known logarithmic negativity entanglement measure and could be applied to quantify entanglement on near-term quantum devices. Experimental and numerical results on the Bell state, isotropic states, and Breuer states show the validity of the proposed entanglement detection and quantification methods.

quant-ph↗

arXiv2020

Inference from Auction Prices

Econometric inference allows an analyst to back out the values of agents in a mechanism from the rules of the mechanism and bids of the agents. This paper gives an algorithm to solve the problem of inferring the values of agents in a dominant-strategy mechanism from the social choice function implemented by the mechanism and the per-unit prices paid by the agents (the agent bids are not observed). For single-dimensional agents, this inference problem is a multi-dimensional inversion of the payment identity and is feasible only if the payment identity is uniquely invertible. The inversion is unique for single-unit proportional weights social choice functions (common, for example, in bandwidth allocation); and its inverse can be found efficiently. This inversion is not unique for social choice functions that exhibit complementarities. Of independent interest, we extend a result of Rosen (1965), that the Nash equilbria of "concave games" are unique and pure, to an alternative notion of concavity based on Gale and Nikaido (1965).

cs.GT↗

arXiv2020

Continuous Regular Functions

Following Chaudhuri, Sankaranarayanan, and Vardi, we say that a function $f:[0,1] \to [0,1]$ is $r$-regular if there is a Büchi automaton that accepts precisely the set of base $r \in \mathbb{N}$ representations of elements of the graph of $f$. We show that a continuous $r$-regular function $f$ is locally affine away from a nowhere dense, Lebesgue null, subset of $[0,1]$. As a corollary we establish that every differentiable $r$-regular function is affine. It follows that checking whether an $r$-regular function is differentiable is in $\operatorname{PSPACE}$. Our proofs rely crucially on connections between automata theory and metric geometry developed by Charlier, Leroy, and Rigo.

cs.LO↗

arXiv2020

Bounded Incentives in Manipulating the Probabilistic Serial Rule

The Probabilistic Serial mechanism is well-known for its desirable fairness and efficiency properties. It is one of the most prominent protocols for the random assignment problem. However, Probabilistic Serial is not incentive-compatible, thereby these desirable properties only hold for the agents' declared preferences, rather than their genuine preferences. A substantial utility gain through strategic behaviors would trigger self-interested agents to manipulate the mechanism and would subvert the very foundation of adopting the mechanism in practice. In this paper, we characterize the extent to which an individual agent can increase its utility by strategic manipulation. We show that the incentive ratio of the mechanism is $\frac{3}{2}$. That is, no agent can misreport its preferences such that its utility becomes more than 1.5 times of what it is when reports truthfully. This ratio is a worst-case guarantee by allowing an agent to have complete information about other agents' reports and to figure out the best response strategy even if it is computationally intractable in general. To complement this worst-case study, we further evaluate an agent's utility gain on average by experiments. The experiments show that an agent' incentive in manipulating the rule is very limited. These results shed some light on the robustness of Probabilistic Serial against strategic manipulation, which is one step further than knowing that it is not incentive-compatible.

cs.GT↗

arXiv2019

Optimal Common Contract with Heterogeneous Agents

We consider the principal-agent problem with heterogeneous agents. Previous works assume that the principal signs independent incentive contracts with every agent to make them invest more efforts on the tasks. However, in many circumstances, these contracts need to be identical for the sake of fairness. We investigate the optimal common contract problem. To our knowledge, this is the first attempt to consider this natural and important generalization. We first show this problem is NP-complete. Then we provide a dynamic programming algorithm to compute the optimal contract in $O(n^2m)$ time, where $n,m$ are the number of agents and actions, under the assumption that the agents' cost functions obey increasing difference property. At last, we generalize the setting such that each agent can choose to directly produce a reward in $[0,1]$. We provide an $O(\log n)$-approximate algorithm for this generalization.

cs.MA↗

arXiv2019

Optimal mechanisms with budget for user generated contents

In this paper, we design gross product maximization mechanisms which incentivize users to upload high-quality contents on user-generated-content (UGC) websites. We show that, the proportional division mechanism, which is widely used in practice, can perform arbitrarily bad in the worst case. The problem can be formulated using a linear program with bounded and increasing variables. We then present an $O(n\log n)$ algorithm to find the optimal mechanism, where n is the number of players.

cs.GT↗

arXiv2019

Bayesian Nash Equilibrium in First-Price Auction with Discrete Value Distributions

First price auctions are widely used in government contracts and industrial auctions. In this paper, we consider the Bayesian Nash Equilibrium (BNE) in first price auctions with discrete value distributions. We study the characterization of the BNE in the first price auction and provide an algorithm to compute the BNE at the same time. Moreover, we prove the existence and the uniqueness of the BNE. Some of the previous results in the case of continuous value distributions do not apply to the case of discrete value distributions. In the meanwhile, the uniqueness result in discrete case cannot be implied by the uniqueness property in the continuous case. Unlike in the continuous case, we do not need to solve ordinary differential equations and thus do not suffer from the solution errors therein. Compared to the method of using continuous distributions to approximate discrete ones, our experiments show that our algorithm is both faster and more accurate. The results in this paper are derived in the asymmetric independent private values model, which assumes that the buyers' value distributions are common knowledge.

cs.GT↗

arXiv2018

An Improved Welfare Guarantee for First Price Auctions

This paper proves that the welfare of the first price auction in Bayes-Nash equilibrium is at least a $.743$-fraction of the welfare of the optimal mechanism assuming agents' values are independently distributed. The previous best bound was $1-1/e \approx .63$, derived in Syrgkanis and Tardos (2013) using smoothness, the standard technique for reasoning about welfare of games in equilibrium. In the worst known example (from Hartline et al. (2014)), the first price auction achieves a $\approx .869$-fraction of the optimal welfare, far better than the theoretical guarantee. Despite this large gap, it was unclear whether the $1-1/e \approx .63$ bound was tight. We prove that it is not. Our analysis eschews smoothness, and instead uses the independence assumption on agents' value distributions to give a more careful accounting of the welfare contribution of agents who win despite not having the highest value.

cs.GT↗

arXiv2016

Hotelling-Downs Model with Limited Attraction

In this paper we study variations of the standard Hotelling-Downs model of spatial competition, where each agent attracts the clients in a restricted neighborhood, each client randomly picks one attractive agent for service. Two utility functions for agents are considered: support utility and winner utility. We generalize the results by Feldman et al. to the case where the clients are distributed arbitrarily. In the support utility setting, we show that a pure Nash equilibrium always exists by formulating the game as a potential game. In the winner utility setting, we show that there exists a Nash equilibrium in two cases: when there are at most 3 agents and when the size of attraction area is at least half of the entire space. We also consider the price of anarchy and the fairness of equilibria and give tight bounds on these criteria.

cs.GT↗

arXiv2016

Optimal Auctions for Negatively Correlated Items

We consider the problem of designing revenue-optimal auctions for selling two items and bidders' valuations are independent among bidders but negatively correlated among items. In this paper, we obtain the closed-form optimal auction for this setting, by directly addressing the two difficulties above. In particular, the first difficulty is that when pointwise maximizing virtual surplus under multi-dimensional feasibility (i.e., the Border feasibility), (1) neither the optimal interim allocation is trivially monotone in the virtual value, (2) nor the virtual value is monotone in the bidder's type. As a result, the optimal interim allocations resulting from virtual surplus maximization no longer guarantees BIC. To address (1), we prove a generalization of Border's theorem and show that optimal interim allocation is indeed monotone in the virtual value. To address (2), we adapt Myerson's ironing procedure to this setting by redefining the (ironed) virtual value as a function of the lowest utility point. The second difficulty, perhaps a more challenging one, is that the lowest utility type in general is no longer at the endpoints of the type interval. To address this difficulty, we show by construction that there exist an allocation rule and an induced lowest utility type such that they form a solution of the virtual surplus maximization and in the meanwhile guarantees IIR. In the single bidder case, the optimal auction consists of a randomized bundle menu and a deterministic bundle menu; while in the multiple bidder case, the optimal auction is a randomization between two extreme mechanisms. The optimal solutions of our setting can be implemented by a Bayesian IC and IR auction, however, perhaps surprisingly, the revenue of this auction cannot be achieved by any (dominant-strategy) IC and IR auction.

cs.GT↗

arXiv2015

Computational issues in time-inconsistent planning

Time-inconsistency refers to a paradox in decision making where agents exhibit inconsistent behaviors over time. Examples are procrastination where agents tends to costly postpone easy tasks, and abandonments where agents start a plan and quit in the middle. These behaviors are undesirable in the sense that agents make clearly suboptimal decisions over optimal ones. To capture such behaviors and more importantly, to quantify inefficiency caused by such behaviors, [Kleinberg & Oren 2014] propose a graph model which is essentially same as the standard planning model except for the cost structure. Using this model, they initiate the study of several interesting problems: 1) cost ratio: the worst ratio between the actual cost of the agent and the optimal cost, over all graph instances; 2) motivating subgraph: how to motivate the agent to reach the goal by deleting nodes and edges; 3) Intermediate rewards: how to motivate agents to reach the goal by placing intermediate rewards. Kleinberg and Oren give partial answers to these questions, but the main problems are still open. In fact, they raise these problems explicitly as open problems in their paper. In this paper, we give answers to all three open problems in [Kleinberg & Oren 2014]. First, we show a tight upper bound of cost ratio for graphs without Akerlof's structure, thus confirm the conjecture by Kleinberg and Oren that Akerlof's structure is indeed the worst case for cost ratio. Second, we prove that finding a motivating subgraph is NP-hard, showing that it is generally inefficient to motivate agents by deleting nodes and edges in the graph. Last but not least, we show that computing a strategy to place minimum amount of total reward is also NP-hard. Therefore, it is computational inefficient to motivate agents by placing intermediate rewards. The techniques we use to prove these results are nontrivial and of independent interests.

cs.GT↗

arXiv2015

Optimal commitments in auctions with incomplete information

We are interested in the problem of optimal commitments in rank-and-bid based auctions, a general class of auctions that include first price and all-pay auctions as special cases. Our main contribution is a novel approach to solve for optimal commitment in this class of auctions, for any continuous type distributions. Applying our approach, we are able to solve optimal commitments for first-price and all-pay auctions in closed-form for fairly general distribution settings. The optimal commitments functions in these auctions reveal two surprisingly opposite insights: in the optimal commitment, the leader bids passively when he has a low type. We interpret this as a credible way to alleviate competition and to collude. In sharp contrast, when his type is high enough, the leader sometimes would go so far as to bid above his own value. We interpret this as a credible way to threat. Combing both insights, we show via concrete examples that the leader is indeed willing to do so to secure more utility when his type is in the middle. Our main approach consists of a series of nontrivial innovations. In particular we put forward a concept called equal-bid function that connects both players' strategies, as well as a concept called equal-utility curve that smooths any leader strategy into a continuous and differentiable strategy. We believe these techniques and insights are general and can be applied to similar problems.

cs.GT↗

arXiv2014

Optimal mechanisms with simple menus

We consider optimal mechanism design for the case with one buyer and two items. The buyer's valuations towards the two items are independent and additive. In this setting, optimal mechanism is unknown for general valuation distributions. We obtain two categories of structural results that shed light on the optimal mechanisms. The first category of results state that, under certain mild condition, the optimal mechanism has a monotone menu. In other words, in the menu that represents the optimal mechanism, as payment increases, the allocation probabilities for both items increase simultaneously. Applying this theorem, we derive a version of revenue monotonicity theorem that states stochastically superior distributions yield more revenue. Moreover, our theorem subsumes a previous result regarding sufficient conditions under which bundling is optimal. The second category of results state that, under certain conditions, the optimal mechanisms have few menu items. Our first result in this category says, for certain distributions, the optimal menu contains at most 4 items. The condition admits power (including uniform) density functions. Based on a similar proof of this result, we are able to obtain a wide class of distributions where bundling is optimal. Our second result in this category works for a weaker condition, under which the optimal menu contains at most 6 items. This condition includes exponential density functions. Our last result in this category works for unit-demand setting. It states that, for uniform distributions, the optimal menu contains at most 5 items. All these results are in sharp contrast to Hart and Nisan's recent result that finite-sized menu cannot guarantee any positive fraction of optimal revenue for correlated valuation distributions.

cs.GT↗