Information Technology Convergence and Services最新文献_第3页

Comparative Learning: A Sample Complexity Theory for Two Hypothesis Classes 比较学习:两个假设类的样本复杂性理论

Information Technology Convergence and Services Pub Date : 2022-11-16 DOI: 10.48550/arXiv.2211.09101

Lunjia Hu, Charlotte Peale

{"title":"Comparative Learning: A Sample Complexity Theory for Two Hypothesis Classes","authors":"Lunjia Hu, Charlotte Peale","doi":"10.48550/arXiv.2211.09101","DOIUrl":"https://doi.org/10.48550/arXiv.2211.09101","url":null,"abstract":"In many learning theory problems, a central role is played by a hypothesis class: we might assume that the data is labeled according to a hypothesis in the class (usually referred to as the realizable setting), or we might evaluate the learned model by comparing it with the best hypothesis in the class (the agnostic setting). Taking a step beyond these classic setups that involve only a single hypothesis class, we introduce comparative learning as a combination of the realizable and agnostic settings in PAC learning: given two binary hypothesis classes $S$ and $B$, we assume that the data is labeled according to a hypothesis in the source class $S$ and require the learned model to achieve an accuracy comparable to the best hypothesis in the benchmark class $B$. Even when both $S$ and $B$ have infinite VC dimensions, comparative learning can still have a small sample complexity. We show that the sample complexity of comparative learning is characterized by the mutual VC dimension $mathsf{VC}(S,B)$ which we define to be the maximum size of a subset shattered by both $S$ and $B$. We also show a similar result in the online setting, where we give a regret characterization in terms of the mutual Littlestone dimension $mathsf{Ldim}(S,B)$. These results also hold for partial hypotheses. We additionally show that the insights necessary to characterize the sample complexity of comparative learning can be applied to characterize the sample complexity of realizable multiaccuracy and multicalibration using the mutual fat-shattering dimension, an analogue of the mutual VC dimension for real-valued hypotheses. This not only solves an open problem proposed by Hu, Peale, Reingold (2022), but also leads to independently interesting results extending classic ones about regression, boosting, and covering number to our two-hypothesis-class setting.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"192 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114249718","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 4

Certificate games 证书的游戏

Information Technology Convergence and Services Pub Date : 2022-11-07 DOI: 10.48550/arXiv.2211.03396

Sourav Chakraborty, Anna G'al, Sophie Laplante, Rajat Mittal, Anupa Sunny

{"title":"Certificate games","authors":"Sourav Chakraborty, Anna G'al, Sophie Laplante, Rajat Mittal, Anupa Sunny","doi":"10.48550/arXiv.2211.03396","DOIUrl":"https://doi.org/10.48550/arXiv.2211.03396","url":null,"abstract":"We introduce and study Certificate Game complexity, a measure of complexity based on the probability of winning a game where two players are given inputs with different function values and are asked to output $i$ such that $x_ineq y_i$ (zero-communication setting). We give upper and lower bounds for private coin, public coin, shared entanglement and non-signaling strategies, and give some separations. We show that complexity in the public coin model is upper bounded by Randomized query and Certificate complexity. On the other hand, it is lower bounded by fractional and randomized certificate complexity, making it a good candidate to prove strong lower bounds on randomized query complexity. Complexity in the private coin model is bounded from below by zero-error randomized query complexity. The quantum measure highlights an interesting and surprising difference between classical and quantum query models. Whereas the public coin certificate game complexity is bounded from above by randomized query complexity, the quantum certificate game complexity can be quadratically larger than quantum query complexity. We use non-signaling, a notion from quantum information, to give a lower bound of $n$ on the quantum certificate game complexity of the $OR$ function, whose quantum query complexity is $Theta(sqrt{n})$, then go on to show that this ``non-signaling bottleneck'' applies to all functions with high sensitivity, block sensitivity or fractional block sensitivity. We consider the single-bit version of certificate games (inputs of the two players have Hamming distance $1$). We prove that the single-bit version of certificate game complexity with shared randomness is equal to sensitivity up to constant factors, giving a new characterization of sensitivity. The single-bit version with private randomness is equal to $lambda^2$, where $lambda$ is the spectral sensitivity.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125905633","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Online Learning and Bandits with Queried Hints 在线学习和强盗查询提示

Information Technology Convergence and Services Pub Date : 2022-11-04 DOI: 10.48550/arXiv.2211.02703

Aditya Bhaskara, Sreenivas Gollapudi, Sungjin Im, Kostas Kollias, Kamesh Munagala

{"title":"Online Learning and Bandits with Queried Hints","authors":"Aditya Bhaskara, Sreenivas Gollapudi, Sungjin Im, Kostas Kollias, Kamesh Munagala","doi":"10.48550/arXiv.2211.02703","DOIUrl":"https://doi.org/10.48550/arXiv.2211.02703","url":null,"abstract":"We consider the classic online learning and stochastic multi-armed bandit (MAB) problems, when at each step, the online policy can probe and find out which of a small number ($k$) of choices has better reward (or loss) before making its choice. In this model, we derive algorithms whose regret bounds have exponentially better dependence on the time horizon compared to the classic regret bounds. In particular, we show that probing with $k=2$ suffices to achieve time-independent regret bounds for online linear and convex optimization. The same number of probes improve the regret bound of stochastic MAB with independent arms from $O(sqrt{nT})$ to $O(n^2 log T)$, where $n$ is the number of arms and $T$ is the horizon length. For stochastic MAB, we also consider a stronger model where a probe reveals the reward values of the probed arms, and show that in this case, $k=3$ probes suffice to achieve parameter-independent constant regret, $O(n^2)$. Such regret bounds cannot be achieved even with full feedback after the play, showcasing the power of limited ``advice'' via probing before making the play. We also present extensions to the setting where the hints can be imperfect, and to the case of stochastic MAB where the rewards of the arms can be correlated.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114026160","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 3

Certification with an NP Oracle NP Oracle认证

Information Technology Convergence and Services Pub Date : 2022-11-04 DOI: 10.48550/arXiv.2211.02257

Guy Blanc, Caleb M. Koch, Jane Lange, Carmen Strassle, Li-Yang Tan

{"title":"Certification with an NP Oracle","authors":"Guy Blanc, Caleb M. Koch, Jane Lange, Carmen Strassle, Li-Yang Tan","doi":"10.48550/arXiv.2211.02257","DOIUrl":"https://doi.org/10.48550/arXiv.2211.02257","url":null,"abstract":"In the certification problem, the algorithm is given a function $f$ with certificate complexity $k$ and an input $x^star$, and the goal is to find a certificate of size $le text{poly}(k)$ for $f$'s value at $x^star$. This problem is in $mathsf{NP}^{mathsf{NP}}$, and assuming $mathsf{P} ne mathsf{NP}$, is not in $mathsf{P}$. Prior works, dating back to Valiant in 1984, have therefore sought to design efficient algorithms by imposing assumptions on $f$ such as monotonicity. Our first result is a $mathsf{BPP}^{mathsf{NP}}$ algorithm for the general problem. The key ingredient is a new notion of the balanced influence of variables, a natural variant of influence that corrects for the bias of the function. Balanced influences can be accurately estimated via uniform generation, and classic $mathsf{BPP}^{mathsf{NP}}$ algorithms are known for the latter task. We then consider certification with stricter instance-wise guarantees: for each $x^star$, find a certificate whose size scales with that of the smallest certificate for $x^star$. In sharp contrast with our first result, we show that this problem is $mathsf{NP}^{mathsf{NP}}$-hard even to approximate. We obtain an optimal inapproximability ratio, adding to a small handful of problems in the higher levels of the polynomial hierarchy for which optimal inapproximability is known. Our proof involves the novel use of bit-fixing dispersers for gap amplification.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"205 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-11-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122690481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 0

Exact Completeness of LP Hierarchies for Linear Codes 线性码的LP层次的精确完备性

Information Technology Convergence and Services Pub Date : 2022-11-02 DOI: 10.48550/arXiv.2211.01248

L. N. Coregliano, F. G. Jeronimo, C. Jones

引用次数: 0

Improved Inapproximability of VC Dimension and Littlestone's Dimension via (Unbalanced) Biclique 通过(不平衡)Biclique改进了VC维和Littlestone维的不近似性

Information Technology Convergence and Services Pub Date : 2022-11-02 DOI: 10.48550/arXiv.2211.01443

Pasin Manurangsi

引用次数: 4

Loss Minimization through the Lens of Outcome Indistinguishability 从结果不可区分的角度将损失最小化

Information Technology Convergence and Services Pub Date : 2022-10-16 DOI: 10.48550/arXiv.2210.08649

Parikshit Gopalan, Lunjia Hu, Michael P. Kim, Omer Reingold, Udi Wieder

{"title":"Loss Minimization through the Lens of Outcome Indistinguishability","authors":"Parikshit Gopalan, Lunjia Hu, Michael P. Kim, Omer Reingold, Udi Wieder","doi":"10.48550/arXiv.2210.08649","DOIUrl":"https://doi.org/10.48550/arXiv.2210.08649","url":null,"abstract":"We present a new perspective on loss minimization and the recent notion of Omniprediction through the lens of Outcome Indistingusihability. For a collection of losses and hypothesis class, omniprediction requires that a predictor provide a loss-minimization guarantee simultaneously for every loss in the collection compared to the best (loss-specific) hypothesis in the class. We present a generic template to learn predictors satisfying a guarantee we call Loss Outcome Indistinguishability. For a set of statistical tests--based on a collection of losses and hypothesis class--a predictor is Loss OI if it is indistinguishable (according to the tests) from Nature's true probabilities over outcomes. By design, Loss OI implies omniprediction in a direct and intuitive manner. We simplify Loss OI further, decomposing it into a calibration condition plus multiaccuracy for a class of functions derived from the loss and hypothesis classes. By careful analysis of this class, we give efficient constructions of omnipredictors for interesting classes of loss functions, including non-convex losses. This decomposition highlights the utility of a new multi-group fairness notion that we call calibrated multiaccuracy, which lies in between multiaccuracy and multicalibration. We show that calibrated multiaccuracy implies Loss OI for the important set of convex losses arising from Generalized Linear Models, without requiring full multicalibration. For such losses, we show an equivalence between our computational notion of Loss OI and a geometric notion of indistinguishability, formulated as Pythagorean theorems in the associated Bregman divergence. We give an efficient algorithm for calibrated multiaccuracy with computational complexity comparable to that of multiaccuracy. In all, calibrated multiaccuracy offers an interesting tradeoff point between efficiency and generality in the omniprediction landscape.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"118 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130170083","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 14

Beeping Shortest Paths via Hypergraph Bipartite Decomposition 基于超图二部分解的最短路径蜂鸣器

Information Technology Convergence and Services Pub Date : 2022-10-13 DOI: 10.48550/arXiv.2210.06882

Fabien Dufoulon, Y. Emek, R. Gelles

{"title":"Beeping Shortest Paths via Hypergraph Bipartite Decomposition","authors":"Fabien Dufoulon, Y. Emek, R. Gelles","doi":"10.48550/arXiv.2210.06882","DOIUrl":"https://doi.org/10.48550/arXiv.2210.06882","url":null,"abstract":"Constructing a shortest path between two network nodes is a fundamental task in distributed computing. This work develops schemes for the construction of shortest paths in randomized beeping networks between a predetermined source node and an arbitrary set of destination nodes. Our first scheme constructs a (single) shortest path to an arbitrary destination in $O (D loglog n + log^3 n)$ rounds with high probability. Our second scheme constructs multiple shortest paths, one per each destination, in $O (D log^2 n + log^3 n)$ rounds with high probability. Our schemes are based on a reduction of the above shortest path construction tasks to a decomposition of hypergraphs into bipartite hypergraphs: We develop a beeping procedure that partitions the (polynomially-large) hyperedge set of a hypergraph $H = (V_H, E_H)$ into $k = Theta (log^2 n)$ disjoint subsets $F_1 cup cdots cup F_k = E_H$ such that the (sub-)hypergraph $(V_H, F_i)$ is bipartite in the sense that there exists a vertex subset $U subseteq V$ such that $|U cap e| = 1$ for every $e in F_i$. This procedure turns out to be instrumental in speeding up shortest path constructions under the beeping model.","PeriodicalId":123734,"journal":{"name":"Information Technology Convergence and Services","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2022-10-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130247684","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}

引用次数: 1

Unitary property testing lower bounds by polynomials 用多项式检验下界的酉性

Information Technology Convergence and Services Pub Date : 2022-10-12 DOI: 10.48550/arXiv.2210.05885

Adrian She, H. Yuen

引用次数: 5

Low-Stabilizer-Complexity Quantum States Are Not Pseudorandom 低稳定复杂性量子态不是伪随机的

Information Technology Convergence and Services Pub Date : 2022-09-29 DOI: 10.4230/LIPIcs.ITCS.2023.64

Sabee Grewal, Vishnu Iyer, William Kretschmer, Daniel Liang

引用次数: 5