Journal of the ACM最新文献

{"title":"Learning to branch: Generalization guarantees and limits of data-independent discretization","authors":"Maria-Florina Balcan, Travis Dick, Tuomas Sandholm, Ellen Vitercik","doi":"10.1145/3637840","DOIUrl":"https://doi.org/10.1145/3637840","url":null,"abstract":"<p>Tree search algorithms, such as branch-and-bound, are the most widely used tools for solving combinatorial and non-convex problems. For example, they are the foremost method for solving (mixed) integer programs and constraint satisfaction problems. Tree search algorithms come with a variety of tunable parameters that are notoriously challenging to tune by hand. A growing body of research has demonstrated the power of using a data-driven approach to automatically optimize the parameters of tree search algorithms. These techniques use a <i>training set</i> of integer programs sampled from an application-specific instance distribution to find a parameter setting that has strong average performance over the training set. However, with too few samples, a parameter setting may have strong average performance on the training set but poor expected performance on future integer programs from the same application. Our main contribution is to provide the first <i>sample complexity guarantees</i> for tree search parameter tuning. These guarantees bound the number of samples sufficient to ensure that the average performance of tree search over the samples nearly matches its future expected performance on the unknown instance distribution. In particular, the parameters we analyze weight <i>scoring rules</i> used for variable selection. Proving these guarantees is challenging because tree size is a volatile function of these parameters: we prove that for any discretization (uniform or not) of the parameter space, there exists a distribution over integer programs such that every parameter setting in the discretization results in a tree with exponential expected size, yet there exist parameter settings between the discretized points that result in trees of constant size. In addition, we provide data-dependent guarantees that depend on the volatility of these tree-size functions: our guarantees improve if the tree-size functions can be well-approximated by simpler functions. Finally, via experiments, we illustrate that learning an optimal weighting of scoring rules reduces tree size.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"104 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139035130","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":"Faster Modular Composition","authors":"Vincent Neiger, Bruno Salvy, Éric Schost, Gilles Villard","doi":"10.1145/3638349","DOIUrl":"https://doi.org/10.1145/3638349","url":null,"abstract":"<p>A new Las Vegas algorithm is presented for the composition of two polynomials modulo a third one, over an arbitrary field. When the degrees of these polynomials are bounded by <i>n</i>, the algorithm uses <i>On</i>^1.43 field operations, breaking through the 3/2 barrier in the exponent for the first time. The previous fastest algebraic algorithms, due to Brent and Kung in 1978, require <i>On</i>^1.63 field operations in general, and <i>n</i>^{3/2 + <i>o</i>(1)} field operations in the special case of power series over a field of large enough characteristic. If cubic-time matrix multiplication is used, the new algorithm runs in <i>n</i>^{5/3 + <i>o</i>(1)} operations, while previous ones run in <i>On</i>² operations. </p><p>Our approach relies on the computation of a matrix of algebraic relations that is typically of small size. Randomization is used to reduce arbitrary input to this favorable situation.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"46 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139034967","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":"Dominantly Truthful Peer Prediction Mechanisms with a Finite Number of Tasks","authors":"Yuqing Kong","doi":"10.1145/3638239","DOIUrl":"https://doi.org/10.1145/3638239","url":null,"abstract":"<p>In the setting where participants are asked multiple similar possibly subjective multi-choice questions (e.g. Do you like Panda Express? Y/N; do you like Chick-fil-A? Y/N), a series of peer prediction mechanisms have been designed to incentivize honest reports and some of them achieve dominantly truthfulness: truth-telling is a dominant strategy and strictly dominate other “non-permutation strategy” with some mild conditions. However, those mechanisms require the participants to perform an infinite number of tasks. When the participants perform a finite number of tasks, these mechanisms only achieve approximated dominant truthfulness. The existence of a dominantly truthful multi-task peer prediction mechanism that only requires a finite number of tasks remains to be an open question that may have a negative result, even with full prior knowledge. </p><p>This paper answers this open question by proposing a family of mechanisms, VMI-Mechanisms, that are dominantly truthful with a finite number of tasks. A special case of this family, DMI-Mechanism, only requires ≥ 2<i>C</i> tasks where <i>C</i> is the number of choices for each question (<i>C</i> = 2 for binary-choice questions). The implementation of these mechanisms does not require any prior knowledge (detail-free) and only requires ≥ 2 participants. To the best of our knowledge, any mechanism of the family is the first dominantly truthful peer prediction mechanism that works for a finite number of tasks. </p><p>The core of these new mechanisms is a new family of information-monotone information measures: volume mutual information (VMI). VMI is based on a simple geometric information measure design method, the volume method. The volume method measures the informativeness of an object by “counting” the number of objects that are less informative than it. In other words, the more objects that the object of interest dominates, the more informative it is considered to be. </p><p>Finally, in the setting where agents need to invest efforts to obtain their private signals, we show how to select the mechanism to optimally incentivize efforts among a proper set of VMI-Mechanisms.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"23 4 1","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"139031647","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":"Parallel Acyclic Joins: Optimal Algorithms and Cyclicity Separation","authors":"Xiao Hu, Yufei Tao","doi":"10.1145/3633512","DOIUrl":"https://doi.org/10.1145/3633512","url":null,"abstract":"<p>We study equi-join computation in the massively parallel computation (MPC) model. Currently, a main open question under this topic is whether it is possible to design an algorithm that can process any join with load (O(N {rm {polylog}} N / p^{1/rho ^*}) ) — measured in the number of words communicated per machine — where <i>N</i> is the total number of tuples in the input relations, <i>ρ</i>^* is the join’s fractional edge covering number, and <i>p</i> is the number of machines. We settle the question in the <i>negative</i> for the class of tuple-based algorithms (all the known MPC join algorithms fall in this class) by proving the existence of a join query with <i>ρ</i>^* = 2 that requires a load of <i>Ω</i>(<i>N</i>/<i>p</i>^1/3) to evaluate. Our lower bound provides solid evidence that the “AGM bound” alone is not sufficient for characterizing the hardness of join evaluation in MPC (a phenomenon that does not exist in RAM). The hard join instance identified in our argument is cyclic, which leaves the question of whether (O(N {rm {polylog}} N / p^{1/rho ^*}) ) is still possible for acyclic joins. We answer this question in the <i>affirmative</i> by showing that any acyclic join can be evaluated with load (O(N / p^{1/rho ^*}) ), which is asymptotically optimal (there are no polylogarithmic factors in our bound). The separation between cyclic and acyclic joins is yet another phenomenon that is absent in RAM. Our algorithm owes to the discovery of a new mathematical structure — we call “canonical edge cover” — of acyclic hypergraphs, which has numerous non-trivial properties and makes an elegant addition to database theory.</p>","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"59 12","pages":""},"PeriodicalIF":2.5,"publicationDate":"2023-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"138525673","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":"Optimal Auctions through Deep Learning: Advances in Differentiable Economics","authors":"Paul Dütting, Zhe Feng, Harikrishna Narasimhan, David C. Parkes, Sai Srivatsa Ravindranath","doi":"10.1145/3630749","DOIUrl":"https://doi.org/10.1145/3630749","url":null,"abstract":"Designing an incentive compatible auction that maximizes expected revenue is an intricate task. The single-item case was resolved in a seminal piece of work by Myerson in 1981, but more than 40 years later, a full analytical understanding of the optimal design still remains elusive for settings with two or more items. In this work, we initiate the exploration of the use of tools from deep learning for the automated design of optimal auctions. We model an auction as a multi-layer neural network, frame optimal auction design as a constrained learning problem, and show how it can be solved using standard machine learning pipelines. In addition to providing generalization bounds, we present extensive experimental results, recovering essentially all known solutions that come from the theoretical analysis of optimal auction design problems and obtaining novel mechanisms for settings in which the optimal mechanism is unknown.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"3 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135042056","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":"Probabilistic Programming with Exact Conditions","authors":"Dario Stein, Sam Staton","doi":"10.1145/3632170","DOIUrl":"https://doi.org/10.1145/3632170","url":null,"abstract":"We spell out the paradigm of exact conditioning as an intuitive and powerful way of conditioning on observations in probabilistic programs. This is contrasted with likelihood-based scoring known from languages such as Stan . We study exact conditioning in the cases of discrete and Gaussian probability, presenting prototypical languages for each case and giving semantics to them. We make use of categorical probability (namely Markov and CD categories) to give a general account of exact conditioning which avoids limits and measure theory, instead focusing on restructuring dataflow and program equations. The correspondence between such categories and a class of programming languages is made precise by defining the internal language of a CD category.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"13 5","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135087217","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 Space Complexity of Consensus from Swap","authors":"Sean Ovens","doi":"10.1145/3631390","DOIUrl":"https://doi.org/10.1145/3631390","url":null,"abstract":"Nearly thirty years ago, it was shown that (Omega (sqrt {n}) ) read/write registers are needed to solve randomized wait-free consensus among n processes. This lower bound was improved to n registers in 2018, which exactly matches known algorithms. The (Omega (sqrt {n}) ) space complexity lower bound actually applies to a class of objects called historyless objects, which includes registers, test-and-set objects, and readable swap objects. However, every known n -process obstruction-free consensus algorithm from historyless objects uses Ω ( n ) objects. In this paper, we give the first Ω ( n ) space complexity lower bounds on consensus algorithms for two kinds of historyless objects. First, we show that any obstruction-free consensus algorithm from swap objects uses at least n − 1 objects. More generally, we prove that any obstruction-free k -set agreement algorithm from swap objects uses at least (lceil frac{n}{k}rceil - 1 ) objects. The k -set agreement problem is a generalization of consensus in which processes agree on no more than k different output values. This is the first non-constant lower bound on the space complexity of solving k -set agreement with swap objects when k &gt; 1. We also present an obstruction-free k -set agreement algorithm from n − k swap objects, which exactly matches our lower bound when k = 1. Second, we show that any obstruction-free binary consensus algorithm from readable swap objects with domain size b uses at least (frac{n-2}{3b+1} ) objects. When b is a constant, this asymptotically matches the best known obstruction-free consensus algorithms from readable swap objects with unbounded domains. Since any historyless object can be simulated by a readable swap object with the same domain, our results imply that any obstruction-free consensus algorithm from historyless objects with domain size b uses at least (frac{n-2}{3b+1} ) objects. For b = 2, we show a slightly better lower bound of n − 2. There is an obstruction-free binary consensus algorithm using 2 n − 1 readable swap objects with domain size 2, asymptotically matching our lower bound.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"15 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-11-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135875758","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 New Minimax Theorem for Randomized Algorithms","authors":"Shalev Ben-David, Eric Blais","doi":"10.1145/3626514","DOIUrl":"https://doi.org/10.1145/3626514","url":null,"abstract":"The celebrated minimax principle of Yao (1977) says that for any Boolean-valued function f with finite domain, there is a distribution μ over the domain of f such that computing f to error ϵ against inputs from μ is just as hard as computing f to error ϵ on worst-case inputs. Notably, however, the distribution μ depends on the target error level ϵ: the hard distribution which is tight for bounded error might be trivial to solve to small bias, and the hard distribution which is tight for a small bias level might be far from tight for bounded error levels. In this work, we introduce a new type of minimax theorem which can provide a hard distribution μ that works for all bias levels at once. We show that this works for randomized query complexity, randomized communication complexity, some randomized circuit models, quantum query and communication complexities, approximate polynomial degree, and approximate logrank. We also prove an improved version of Impagliazzo’s hardcore lemma. Our proofs rely on two innovations over the classical approach of using Von Neumann’s minimax theorem or linear programming duality. First, we use Sion’s minimax theorem to prove a minimax theorem for ratios of bilinear functions representing the cost and score of algorithms. Second, we introduce a new way to analyze low-bias randomized algorithms by viewing them as “forecasting algorithms” evaluated by a certain proper scoring rule. The expected score of the forecasting version of a randomized algorithm appears to be a more fine-grained way of analyzing the bias of the algorithm. We show that such expected scores have many elegant mathematical properties: for example, they can be amplified linearly instead of quadratically. We anticipate forecasting algorithms will find use in future work in which a fine-grained analysis of small-bias algorithms is required.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"12 2 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135824148","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":"Relative Error Streaming Quantiles","authors":"Graham Cormode, Zohar Karnin, Edo Liberty, Justin Thaler, Pavel Veselý","doi":"10.1145/3617891","DOIUrl":"https://doi.org/10.1145/3617891","url":null,"abstract":"Estimating ranks, quantiles, and distributions over streaming data is a central task in data analysis and monitoring. Given a stream of n items from a data universe equipped with a total order, the task is to compute a sketch (data structure) of size polylogarithmic in n . Given the sketch and a query item y , one should be able to approximate its rank in the stream, i.e., the number of stream elements smaller than or equal to y . Most works to date focused on additive ε n error approximation, culminating in the KLL sketch that achieved optimal asymptotic behavior. This article investigates multiplicative (1± ε)-error approximations to the rank. Practical motivation for multiplicative error stems from demands to understand the tails of distributions, and hence for sketches to be more accurate near extreme values. The most space-efficient algorithms due to prior work store either O(log (ε 2 n )/ε 2 ) or O (log 3 (ε n )/ε) universe items. We present a randomized sketch storing O (log 1.5 (ε n )/ε) items that can (1± ε)-approximate the rank of each universe item with high constant probability; this space bound is within an (O(sqrt {log (varepsilon n)})) factor of optimal. Our algorithm does not require prior knowledge of the stream length and is fully mergeable, rendering it suitable for parallel and distributed computing environments.","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136077380","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":"First Price Auction is 1 − 1/ <i>e</i> ² Efficient","authors":"Yaonan Jin, Pinyan Lu","doi":"10.1145/3617902","DOIUrl":"https://doi.org/10.1145/3617902","url":null,"abstract":"We prove that the PoA of First Price Auctions is 1-1/ e 2 ≈ 0.8647, closing the gap between the best known bounds [0.7430, 0.8689].","PeriodicalId":50022,"journal":{"name":"Journal of the ACM","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-10-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"135767360","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}