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Dual VC Dimension Obstructs Sample Compression by Embeddings
In particular, we prove that for every $d$ there is a class with VC dimension $d$ that cannot be embedded in any extremal class of VC dimension smaller than exponential in $d$.
Local Borsuk-Ulam, Stability, and Replicability
To offer a broader and more comprehensive view of our topological approach, we prove a local variant of the Borsuk-Ulam theorem in topology and a result in combinatorics concerning Kneser colorings.
Replicability and stability in learning
Impagliazzo et al. showed how to boost any replicable algorithm so that it produces the same output with probability arbitrarily close to 1.
Optimally compressing VC classes
Resolving a conjecture of Littlestone and Warmuth, we show that any concept class of VC-dimension $d$ has a sample compression scheme of size $d$.
Experimental Evidence for Asymptotic Non-Optimality of Comb Adversary Strategy
For the problem of prediction with expert advice in the adversarial setting with finite stopping time, we give strong computer evidence that the comb strategy for $k=5$ experts is not asymptotically optimal, thereby giving strong evidence against a conjecture of Gravin, Peres, and Sivan.
Learning Time Dependent Choice
We find that the commonly studied stream-based setting is in general difficult to analyze for preference models, but we provide a redeeming situation in which the learner can indeed improve upon the guarantees provided by PAC learning.
