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 "the step decay schedule a near optimal geometrically decaying learning rate procedure for least squares"):
  Abstract: Minimax optimal convergence rates for classes of stochastic convex optimization problems are well characterized, where the majority of results utilize iterate averaged stochastic gradient descent (SGD) with polynomially decaying step sizes. In contrast, SGD's final iterate behavior has received much less attention despite their widespread use in practice. Motivated by this observation, this work provides a detailed study of the following question: what rate is achievable using the final iterate of SGD for the streaming least squares regression problem with and without strong convexity?  First, this work shows that even if the time horizon T (i.e. the number of iterations SGD is run for) is known in advance, SGD's final iterate behavior with any polynomially decaying learning rate scheme is highly sub-optimal compared to the minimax rate (by a condition number factor in the strongly convex case and a factor of $\sqrt{T}$ in the non-strongly convex case). In contrast, this paper shows that Step Decay schedules, which cut the learning rate by a constant factor every constant number of epochs (i.e., the learning rate decays geometrically) offers significant improvements over any polynomially decaying step sizes. In particular, the final iterate behavior with a step decay schedule is off the minimax rate by only $log$ factors (in the condition number for strongly convex case, and in T for the non-strongly convex case). Finally, in stark contrast to the known horizon case, this paper shows that the anytime (i.e. the limiting) behavior of SGD's final iterate is poor (in that it queries iterates with highly sub-optimal function value infinitely often, i.e. in a limsup sense) irrespective of the stepsizes employed. These results demonstrate the subtlety in establishing optimal learning rate schemes (for the final iterate) for stochastic gradient procedures in fixed time horizon settings.

Includes members:
  Member "iterate averaging as regularization for stochastic gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "efficient and robust algorithms for adversarial linear contextual bandits")
  Member "tight analyses for non smooth stochastic gradient descent":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "high probability generalization bounds for uniformly stable algorithms with nearly optimal rate")
  Member "how to make the gradients small stochastically":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "asymmetric valleys beyond sharp and flat local minima")
  Member "hyperband a novel bandit based approach to hyperparameter optimization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "using a thousand optimization tasks to learn hyperparameter search strategies")
  Member "identity mappings in deep residual networks":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "overfitting in adversarially robust deep learning")
  Member "deep residual learning for image recognition":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "discrimination aware network pruning for deep model compression")
  Member "non strongly convex smooth stochastic approximation with convergence rate o 1 n":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "efficient and robust algorithms for adversarial linear contextual bandits")
  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-8 (induced by source paper "simple and fast algorithm for binary integer and online linear programming")

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)