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 "solving combinatorial games using products projections and lexicographically optimal bases"):
  Abstract: In order to find Nash-equilibria for two-player zero-sum games where each player plays combinatorial objects like spanning trees, matchings etc, we consider two online learning algorithms: the online mirror descent (OMD) algorithm and the multiplicative weights update (MWU) algorithm. The OMD algorithm requires the computation of a certain Bregman projection, that has closed form solutions for simple convex sets like the Euclidean ball or the simplex. However, for general polyhedra one often needs to exploit the general machinery of convex optimization. We give a novel primal-style algorithm for computing Bregman projections on the base polytopes of polymatroids. Next, in the case of the MWU algorithm, although it scales logarithmically in the number of pure strategies or experts $N$ in terms of regret, the algorithm takes time polynomial in $N$; this especially becomes a problem when learning combinatorial objects. We give a general recipe to simulate the multiplicative weights update algorithm in time polynomial in their natural dimension. This is useful whenever there exists a polynomial time generalized counting oracle (even if approximate) over these objects. Finally, using the combinatorial structure of symmetric Nash-equilibria (SNE) when both players play bases of matroids, we show that these can be found with a single projection or convex minimization (without using online learning).

Includes members:
  Member "the computational power of optimization in online learning":
    also connected through other hyperedges:
      - Hyperedge HE-1 (induced by source paper "taking a hint how to leverage loss predictors in contextual bandits")
  Member "second order quantile methods for experts and combinatorial games":
    also connected through other hyperedges:
      - Hyperedge HE-2 (induced by source paper "a modern introduction to online learning")
  Member "importance weighting without importance weights an efficient algorithm for combinatorial semi bandits":
    also connected through other hyperedges:
      - Hyperedge HE-3 (induced by source paper "learning with differentiable perturbed optimizers")
  Member "optimization learning and games with predictable sequences":
    also connected through other hyperedges:
      - Hyperedge HE-4 (induced by source paper "provably efficient adaptive approximate policy iteration")
  Member "the matching polytope has exponential extension complexity":
    also connected through other hyperedges:
      - Hyperedge HE-5 (induced by source paper "extended formulation lower bounds for refuting random csps")
  Member "entropy optimization and counting":
    also connected through other hyperedges:
      - Hyperedge HE-6 (induced by source paper "fair distributions from biased samples a maximum entropy optimization framework")
  Member "regret in online combinatorial optimization":
    also connected through other hyperedges:
      - Hyperedge HE-7 (induced by source paper "efficient and robust algorithms for adversarial linear contextual bandits")
  Member "on the universality of online mirror descent":
    also connected through other hyperedges:
      - Hyperedge HE-8 (induced by source paper "beyond ucb optimal and efficient contextual bandits with regression oracles")

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)