human: Given a hyperedge-centered hypergraph: <hypergraph>, where the center hyperedge is induced by one source paper and its member nodes are the cited papers.

Details of the hypergraph:
Center hyperedge (induced by source paper "tight analyses for non smooth stochastic gradient descent"):
  Abstract: Consider the problem of minimizing functions that are Lipschitz and strongly convex, but not necessarily differentiable. We prove that after $T$ steps of stochastic gradient descent, the error of the final iterate is $O(\log(T)/T)$ with high probability. We also construct a function from this class for which the error of the final iterate of deterministic gradient descent is $\Omega(\log(T)/T)$. This shows that the upper bound is tight and that, in this setting, the last iterate of stochastic gradient descent has the same general error rate (with high probability) as deterministic gradient descent. This resolves both open questions posed by Shamir (2012). #R##N#An intermediate step of our analysis proves that the suffix averaging method achieves error $O(1/T)$ with high probability, which is optimal (for any first-order optimization method). This improves results of Rakhlin (2012) and Hazan and Kale (2014), both of which achieved error $O(1/T)$, but only in expectation, and achieved a high probability error bound of $O(\log \log(T)/T)$, which is suboptimal. #R##N#We prove analogous results for functions that are Lipschitz and convex, but not necessarily strongly convex or differentiable. After $T$ steps of stochastic gradient descent, the error of the final iterate is $O(\log(T)/\sqrt{T})$ with high probability, and there exists a function for which the error of the final iterate of deterministic gradient descent is $\Omega(\log(T)/\sqrt{T})$.

Includes members:
  Member "introduction to online convex optimization":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "beyond ucb optimal and efficient contextual bandits with regression oracles")
  Member "potential function proofs for first order methods":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "online non monotone dr submodular maximization")
  Member "efficient accelerated coordinate descent methods and faster algorithms for solving linear systems":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "spectral sparsification via bounded independence sampling")
  Member "a simpler approach to obtaining an o 1 t convergence rate for the projected stochastic subgradient method":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "simple and fast algorithm for binary integer and online linear programming")
  Member "stochastic gradient descent for non smooth optimization convergence results and optimal averaging schemes":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "encode shuffle analyze privacy revisited formalizations and empirical evaluation")
  Member "making gradient descent optimal for strongly convex stochastic optimization":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "wireless federated learning with local differential privacy")
  Member "on the number of iterations for dantzig wolfe optimization and packing covering approximation algorithms":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "approximate degree secret sharing and concentration phenomena")

Question: Please tell me which class the source paper belongs to. The 40 classes are: cs.NA(Numerical Analysis), cs.MM(Multimedia), cs.LO(Logic in Computer Science), cs.CY(Computers and Society), cs.CR(Cryptography and Security), cs.DC(Distributed, Parallel, and Cluster Computing), cs.HC(Human-Computer Interaction), cs.CE(Computational Engineering, Finance, and Science), cs.NI(Networking and Internet Architecture), cs.CC(Computational Complexity), cs.AI(Artificial Intelligence), cs.MA(Multiagent Systems), cs.GL(General Literature), cs.NE(Neural and Evolutionary Computing), cs.SC(Symbolic Computation), cs.AR(Hardware Architecture), cs.CV(Computer Vision and Pattern Recognition), cs.GR(Graphics), cs.ET(Emerging Technologies), cs.SY(Systems and Control), cs.CG(Computational Geometry), cs.OH(Other Computer Science), cs.PL(Programming Languages), cs.SE(Software Engineering), cs.LG(Machine Learning), cs.SD(Sound), cs.SI(Social and Information Networks), cs.RO(Robotics), cs.IT(Information Theory), cs.PF(Performance), cs.CL(Computation and Language), cs.IR(Information Retrieval), cs.MS(Mathematical Software), cs.FL(Formal Languages and Automata Theory), cs.DS(Data Structures and Algorithms), cs.OS(Operating Systems), cs.GT(Computer Science and Game Theory), cs.DB(Databases), cs.DL(Digital Libraries), cs.DM(Discrete Mathematics). Directly output the class name.

gpt: cs.LG(Machine Learning)