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 lower bounds for multiplicative weights algorithmic families"):
  Abstract: We study the fundamental problem of prediction with expert advice and develop regret lower bounds for a large family of algorithms for this problem. We develop simple adversarial primitives, that lend themselves to various combinations leading to sharp lower bounds for many algorithmic families. We use these primitives to show that the classic Multiplicative Weights Algorithm (MWA) has a regret of $\sqrt{\frac{T \ln k}{2}}$, there by completely closing the gap between upper and lower bounds. We further show a regret lower bound of $\frac{2}{3}\sqrt{\frac{T\ln k}{2}}$ for a much more general family of algorithms than MWA, where the learning rate can be arbitrarily varied over time, or even picked from arbitrary distributions over time. We also use our primitives to construct adversaries in the geometric horizon setting for MWA to precisely characterize the regret at $\frac{0.391}{\sqrt{\delta}}$ for the case of $2$ experts and a lower bound of $\frac{1}{2}\sqrt{\frac{\ln k}{2\delta}}$ for the case of arbitrary number of experts $k$.

Includes members:
  Member "second order quantile methods for experts and combinatorial games":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "a modern introduction to online learning")
  Member "towards optimal algorithms for prediction with expert advice":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "optimal anytime regret with two experts")
  Member "unconstrained online linear learning in hilbert spaces minimax algorithms and normal approximations":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "lipschitz and comparator norm adaptivity in online learning")
  Member "minimax optimal algorithms for unconstrained linear optimization":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "a modern introduction to online learning")
  Member "a parameter free hedging algorithm":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "a modern introduction to online learning")
  Member "a stochastic view of optimal regret through minimax duality":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "connections between mirror descent thompson sampling and the information ratio")

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)