Algorithms and matching lower bounds for s-sparse contextual bandits yield Õ((s/ε² + |A|/ε) log |Π|/δ) samples to output an ε-optimal policy.
arXiv preprint arXiv:2410.05117 , year=
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Establishes a variance-aware pointwise majorizing-measure theorem for Gaussian fields, records Bayesian algorithmic lower bounds, and constructs a separation example among classical, algorithmic, and pointwise quantities.
Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
Proposes Bellman-sufficient state representations and information indices Y=χ(Ω) to organize sequential decision making with a conditional Bellman information-risk sandwich providing matching upper and lower complexity bounds.
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The Sample Complexity of Multiclass and Sparse Contextual Bandits
Algorithms and matching lower bounds for s-sparse contextual bandits yield Õ((s/ε² + |A|/ε) log |Π|/δ) samples to output an ε-optimal policy.
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Pointwise Complexity for Gaussian Fields: Upper Envelopes, Algorithmic Lower Bounds, and Separation
Establishes a variance-aware pointwise majorizing-measure theorem for Gaussian fields, records Bayesian algorithmic lower bounds, and constructs a separation example among classical, algorithmic, and pointwise quantities.
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Pointwise Generalization in Deep Neural Networks
Proposes pointwise Riemannian Dimension from feature eigenvalues to derive tighter, representation-aware generalization bounds for deep networks in the nonlinear regime.
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Bellman-sufficient Information Complexity
Proposes Bellman-sufficient state representations and information indices Y=χ(Ω) to organize sequential decision making with a conditional Bellman information-risk sandwich providing matching upper and lower complexity bounds.