Journal of the ACM最新文献

{"title":"Learning Equilibria in Matching Markets with Bandit Feedback","authors":"Meena Jagadeesan, Alexander Wei, Yixin Wang, Michael I. Jordan, Jacob Steinhardt","doi":"10.1145/3583681","DOIUrl":"https://doi.org/10.1145/3583681","url":null,"abstract":"Large-scale, two-sided matching platforms must find market outcomes that align with user preferences while simultaneously learning these preferences from data. Classical notions of stability (Gale and Shapley, 1962; Shapley and Shubik, 1971) are, unfortunately, of limited value in the learning setting, given that preferences are inherently uncertain and destabilizing while they are being learned. To bridge this gap, we develop a framework and algorithms for learning stable market outcomes under uncertainty. Our primary setting is matching with transferable utilities, where the platform both matches agents and sets monetary transfers between them. We design an incentive-aware learning objective that captures the distance of a market outcome from equilibrium. Using this objective, we analyze the complexity of learning as a function of preference structure, casting learning as a stochastic multi-armed bandit problem. Algorithmically, we show that “optimism in the face of uncertainty,” the principle underlying many bandit algorithms, applies to a primal-dual formulation of matching with transfers and leads to near-optimal regret bounds. Our work takes a first step toward elucidating when and how stable matchings arise in large, data-driven marketplaces.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"11 1","pages":"1 - 46"},"PeriodicalIF":2.5,"publicationDate":"2023-02-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83992234","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Robustly Learning General Mixtures of Gaussians","authors":"Allen Liu, Ankur Moitra","doi":"10.1145/3583680","DOIUrl":"https://doi.org/10.1145/3583680","url":null,"abstract":"This work represents a natural coalescence of two important lines of work — learning mixtures of Gaussians and algorithmic robust statistics. In particular, we give the first provably robust algorithm for learning mixtures of any constant number of Gaussians. We require only mild assumptions on the mixing weights and that the total variation distance between components is bounded away from zero. At the heart of our algorithm is a new method for proving a type of dimension-independent polynomial identifiability — which we call robust identifiability — through applying a carefully chosen sequence of differential operations to certain generating functions that not only encode the parameters we would like to learn but also the system of polynomial equations we would like to solve. We show how the symbolic identities we derive can be directly used to analyze a natural sum-of-squares relaxation.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"117 1","pages":"1 - 53"},"PeriodicalIF":2.5,"publicationDate":"2023-02-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79878742","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"A Correctness and Incorrectness Program Logic","authors":"R. Bruni, R. Giacobazzi, R. Gori, Francesco Ranzato","doi":"10.1145/3582267","DOIUrl":"https://doi.org/10.1145/3582267","url":null,"abstract":"Abstract interpretation is a well-known and extensively used method to extract over-approximate program invariants by a sound program analysis algorithm. Soundness means that no program errors are lost and it is, in principle, guaranteed by construction. Completeness means that the abstract interpreter reports no false alarms for all possible inputs, but this is extremely rare because it needs a very precise analysis. We introduce a weaker notion of completeness, called local completeness, which requires that no false alarms are produced only relatively to some fixed program inputs. Based on this idea, we introduce a program logic, called Local Completeness Logic for an abstract domain A, for proving both the correctness and incorrectness of program specifications. Our proof system, which is parameterized by an abstract domain A, combines over- and under-approximating reasoning. In a provable triple ⊦A [p] 𝖼 [q], 𝖼 is a program, q is an under-approximation of the strongest post-condition of 𝖼 on input p such that their abstractions in A coincide. This means that q is never too coarse, namely, under some mild assumptions, the abstract interpretation of 𝖼 does not yield false alarms for the input p iff q has no alarm. Therefore, proving ⊦A [p] 𝖼 [q] not only ensures that all the alarms raised in q are true ones, but also that if q does not raise alarms, then 𝖼 is correct. We also prove that if A is the straightforward abstraction making all program properties equivalent, then our program logic coincides with O’Hearn’s incorrectness logic, while for any other abstraction, contrary to the case of incorrectness logic, our logic can also establish program correctness.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"47 1","pages":"1 - 45"},"PeriodicalIF":2.5,"publicationDate":"2023-02-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73583749","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Need for Large Quantum Depth","authors":"Nai-Hui Chia, Kai-Min Chung, Ching-Yi Lai","doi":"https://dl.acm.org/doi/10.1145/3570637","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3570637","url":null,"abstract":"<p>Near-term quantum computers are likely to have small depths due to short coherence time and noisy gates. A natural approach to leverage these quantum computers is interleaving them with classical computers. Understanding the capabilities and limits of this hybrid approach is an essential topic in quantum computation. Most notably, the quantum Fourier transform can be implemented by a hybrid of logarithmic-depth quantum circuits and a classical polynomial-time algorithm. Therefore, it seems possible that quantum polylogarithmic depth is as powerful as quantum polynomial depth in the presence of classical computation. Indeed, Jozsa conjectured that “<i>Any quantum polynomial-time algorithm can be implemented with only <i>O</i>(log <i>n</i>) quantum depth interspersed with polynomial-time classical computations.</i>” This can be formalized as asserting the equivalence of <monospace>BQP</monospace> and “<monospace>BQNC^BPP</monospace>.” However, Aaronson conjectured that “<i>there exists an oracle separation between <monospace>BQP</monospace> and <monospace>BPP^BQNC</monospace>.</i>” <monospace>BQNC^BPP</monospace> and <monospace>BPP^BQNC</monospace> are two natural and seemingly incomparable ways of hybrid classical-quantum computation.</p><p>In this work, we manage to prove Aaronson’s conjecture and in the meantime prove that Jozsa’s conjecture, relative to an oracle, is false. In fact, we prove a stronger statement that for any depth parameter <i>d</i>, there exists an oracle that separates quantum depth <i>d</i> and 2<i>d</i>+1 in the presence of classical computation. Thus, our results show that relative to oracles, doubling the quantum circuit depth does make the hybrid model more powerful, and this cannot be traded by classical computation.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"20 13","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525672","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Convex Hulls of Random Order Types","authors":"Xavier Goaoc, Emo Welzl","doi":"https://dl.acm.org/doi/10.1145/3570636","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3570636","url":null,"abstract":"<p>We establish the following two main results on order types of points in general position in the plane (realizable simple planar order types, realizable uniform acyclic oriented matroids of rank 3):\u0000<p><table border=\"0\" list-type=\"ordered\" width=\"95%\"><tr><td valign=\"top\"><p>(a)</p></td><td colspan=\"5\" valign=\"top\"><p>The number of extreme points in an <i>n</i>-point order type, chosen uniformly at random from all such order types, is on average 4+<i>o</i>(1). For labeled order types, this number has average (4- mbox{$frac{8}{n^2 - n +2}$}) and variance at most 3.</p></td></tr><tr><td valign=\"top\"><p>(b)</p></td><td colspan=\"5\" valign=\"top\"><p>The (labeled) order types read off a set of <i>n</i> points sampled independently from the uniform measure on a convex planar domain, smooth or polygonal, or from a Gaussian distribution are concentrated, i.e., such sampling typically encounters only a vanishingly small fraction of all order types of the given size.</p></td></tr></table></p> Result (a) generalizes to arbitrary dimension <i>d</i> for labeled order types with the average number of extreme points 2<i>d</i>+<i>o</i> (1) and constant variance. We also discuss to what extent our methods generalize to the abstract setting of uniform acyclic oriented matroids. Moreover, our methods show the following relative of the Erdős-Szekeres theorem: for any fixed <i>k</i>, as <i>n</i> → ∞, a proportion 1 - <i>O</i>(1/<i>n</i>) of the <i>n</i>-point simple order types contain a triangle enclosing a convex <i>k</i>-chain over an edge.</p><p>For the unlabeled case in (a), we prove that for any antipodal, finite subset of the two-dimensional sphere, the group of orientation preserving bijections is cyclic, dihedral, or one of <i>A</i>₄, <i>S</i>₄, or <i>A</i>₅ (and each case is possible). These are the finite subgroups of <i>SO</i>(3) and our proof follows the lines of their characterization by Felix Klein.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"78 8","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-01-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525688","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Lower Bounds on Implementing Mediators in Asynchronous Systems with Rational and Malicious Agents","authors":"I. Geffner, Joseph Y. Halpern","doi":"10.1145/3578579","DOIUrl":"https://doi.org/10.1145/3578579","url":null,"abstract":"Abraham, Dolev, Geffner, and Halpern [1] proved that, in asynchronous systems, a (k, t)-robust equilibrium for n players and a trusted mediator can be implemented without the mediator as long as n > 4(k+t), where an equilibrium is (k, t)-robust if, roughly speaking, no coalition of t players can decrease the payoff of any of the other players, and no coalition of k players can increase their payoff by deviating. We prove that this bound is tight, in the sense that if n ≤ 4(k+t) there exist (k, t)-robust equilibria with a mediator that cannot be implemented by the players alone. Even though implementing (k, t)-robust mediators seems closely related to implementing asynchronous multiparty (k+t)-secure computation [6], to the best of our knowledge there is no known straightforward reduction from one problem to another. Nevertheless, we show that there is a non-trivial reduction from a slightly weaker notion of (k+t)-secure computation, which we call (k+t)-strict secure computation, to implementing (k, t)-robust mediators. We prove the desired lower bound by showing that there are functions on n variables that cannot be (k+t)-strictly securely computed if n ≤ 4(k+t). This also provides a simple alternative proof for the well-known lower bound of 4t+1 on asynchronous secure computation in the presence of up to t malicious agents [4, 8, 10].","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"2 1","pages":"1 - 21"},"PeriodicalIF":2.5,"publicationDate":"2023-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80073995","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Directed Shortest Paths via Approximate Cost Balancing","authors":"James B. Orlin, László Végh","doi":"https://dl.acm.org/doi/10.1145/3565019","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3565019","url":null,"abstract":"<p>We present an <i>O(nm)</i> algorithm for all-pairs shortest paths computations in a directed graph with <i>n</i> nodes, <i>m</i> arcs, and nonnegative integer arc costs. This matches the complexity bound attained by Thorup [31] for the all-pairs problems in undirected graphs. The main insight is that shortest paths problems with approximately balanced directed cost functions can be solved similarly to the undirected case. The algorithm finds an approximately balanced reduced cost function in an <i>O(m</i>√ <i>n</i> log <i>n</i>) preprocessing step. Using these reduced costs, every shortest path query can be solved in <i>O(m)</i> time using an adaptation of Thorup’s component hierarchy method. The balancing result can also be applied to the ℓ_∞-matrix balancing problem.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"23 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525687","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"The Complexity of Gradient Descent: CLS = PPAD ∩ PLS","authors":"John Fearnley, Paul Goldberg, Alexandros Hollender, Rahul Savani","doi":"https://dl.acm.org/doi/10.1145/3568163","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3568163","url":null,"abstract":"<p>We study search problems that can be solved by performing Gradient Descent on a bounded convex polytopal domain and show that this class is equal to the intersection of two well-known classes: PPAD and PLS. As our main underlying technical contribution, we show that computing a Karush-Kuhn-Tucker (KKT) point of a continuously differentiable function over the domain [0,1]² is PPAD ∩ PLS-complete. This is the first non-artificial problem to be shown complete for this class. Our results also imply that the class CLS (Continuous Local Search) – which was defined by Daskalakis and Papadimitriou as a more “natural” counterpart to PPAD ∩ PLS and contains many interesting problems – is itself equal to PPAD ∩ PLS.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"3 2","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525665","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"On the Descriptive Complexity of Temporal Constraint Satisfaction Problems","authors":"Manuel Bodirsky, Jakub Rydval","doi":"https://dl.acm.org/doi/10.1145/3566051","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3566051","url":null,"abstract":"<p>Finite-domain constraint satisfaction problems are either solvable by Datalog or not even expressible in fixed-point logic with counting. The border between the two regimes can be described by a universal-algebraic minor condition. For infinite-domain constraint satisfaction problems (CSPs), the situation is more complicated even if the template structure of the CSP is model-theoretically tame. We prove that there is no Maltsev condition that characterizes Datalog already for the CSPs of first-order reducts of (ℚ;&lt;); such CSPs are called <i>temporal CSPs</i> and are of fundamental importance in infinite-domain constraint satisfaction. Our main result is a complete classification of temporal CSPs that can be expressed in one of the following logical formalisms: Datalog, fixed-point logic (with or without counting), or fixed-point logic with the mod-2 rank operator. The classification shows that many of the equivalent conditions in the finite fail to capture expressibility in Datalog or fixed-point logic already for temporal CSPs.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"42 9-10","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525667","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

{"title":"Minimizing Convex Functions with Rational Minimizers","authors":"Haotian Jiang","doi":"https://dl.acm.org/doi/10.1145/3566050","DOIUrl":"https://doi.org/https://dl.acm.org/doi/10.1145/3566050","url":null,"abstract":"<p>Given a separation oracle SO for a convex function <i>f</i> defined on ℝⁿ that has an integral minimizer inside a box with radius <i>R</i>, we show how to find an exact minimizer of <i>f</i> using at most\u0000<p><ul><li><p><i>O(n (n</i> log log <i>(n)/</i>log <i>(n)</i> + log (<i>R</i>))) calls to SO and poly (<i>n</i>, log (<i>R</i>)) arithmetic operations, or</p></li><li><p><i>O(n</i> log <i>(nR)</i> calls to SO and exp (<i>O(n)</i>) ⋅ poly (log <i>(R)</i>) arithmetic operations.</p></li></ul></p></p><p>When the set of minimizers of <i>f</i> has integral extreme points, our algorithm outputs an integral minimizer of <i>f</i>. This improves upon the previously best oracle complexity of <i>O(n</i>² (<i>n</i> + log (<i>R</i>))) for polynomial time algorithms and <i>O(n</i>² log (<i>nR</i>) for exponential time algorithms obtained by [Grötschel, Lovász and Schrijver, Prog. Comb. Opt. 1984, Springer 1988] over thirty years ago. Our improvement on Grötschel, Lovász and Schrijver’s result generalizes to the setting where the set of minimizers of <i>f</i> is a rational polyhedron with bounded vertex complexity.</p><p>For the Submodular Function Minimization problem, our result immediately implies a strongly polynomial algorithm that makes at most <i>O(n</i>³ log log (<i>n</i>)/log (<i>n</i>)) calls to an evaluation oracle, and an exponential time algorithm that makes at most <i>O(n</i>² log (<i>n</i>)) calls to an evaluation oracle. These improve upon the previously best <i>O(n</i>³ log²(<i>n</i>)) oracle complexity for strongly polynomial algorithms given in [Lee, Sidford and Wong, FOCS 2015] and [Dadush, Végh and Zambelli, SODA 2018], and an exponential time algorithm with oracle complexity <i>O(n</i>³ log (<i>n</i>)) given in the former work.</p><p>Our result is achieved via a reduction to the Shortest Vector Problem in lattices. We show how an approximately shortest vector of an auxiliary lattice can be used to effectively reduce the dimension of the problem. Our analysis of the oracle complexity is based on a potential function that simultaneously captures the size of the search set and the density of the lattice, which we analyze via tools from convex geometry and lattice theory.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"68 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2022-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525745","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":2,"RegionCategory":"计算机科学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}