| 1. |
Delle Rose V.♦, Kozachinskiy A.♦, Rojas C.♦, Steifer T., Find a witness or shatter: the landscape of computable PAC learning,
COLT 2023, The Thirty Sixth Annual Conference on Learning Theory, 2023-07-12/07-15, Bangalore (IN), No.195, pp.1-14, 2023 Abstract:
This paper contributes to the study of CPAC learnability—a computable version of PAC learning—by solving three open questions from recent papers. Firstly, we prove that every improperly CPAC learnable class is contained in a class which is properly CPAC learnable with polynomial sample complexity. This confirms a conjecture by Agarwal et al (COLT 2021). Secondly, we show that there exists a decidable class of hypotheses which is properly CPAC learnable, but only with uncomputably fast-growing sample complexity. This solves a question from Sterkenburg (COLT2022). Finally, we construct a decidable class of finite Littlestone dimension which is not improperly CPAC learnable, strengthening a recent result of Sterkenburg (2022) and answering a question posed by Hasrati and Ben-David (ALT 2023). Together with previous work, our results provide a complete landscape for the learnability problem in the CPAC setting Keywords:
PAC learnability, CPAC learnability, VC dimension, Littlestone dimension, computability, foundations of machine learning Affiliations:
| Delle Rose V. | - | University of Siena (IT) | | Kozachinskiy A. | - | other affiliation | | Rojas C. | - | other affiliation | | Steifer T. | - | IPPT PAN |
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| 2. |
Bienvenu L.♦, Delle Rose V.♦, Steifer T., Probabilistic vs deterministic gamblers,
STACS 2022, 39th International Symposium on Theoretical Aspects of Computer Science, 2022-03-15/03-18, Marseille (FR), DOI: 10.4230/LIPIcs.STACS.2022.11, pp.11-1-13, 2022Abstract:
Can a probabilistic gambler get arbitrarily rich when all deterministic gamblers fail? We study this problem in the context of algorithmic randomness, introducing a new notion – almost everywhere computable randomness. A binary sequence X is a.e. computably random if there is no probabilistic computable strategy which is total and succeeds on X for positive measure of oracles. Using the fireworks technique we construct a sequence which is partial computably random but not a.e. computably random. We also prove the separation between a.e. computable randomness and partial computable randomness, which happens exactly in the uniformly almost everywhere dominating Turing degrees. Keywords:
algorithmic randomness, martingales, probabilistic computation, almost everywhere domination Affiliations:
| Bienvenu L. | - | Université de Bordeaux (FR) | | Delle Rose V. | - | University of Siena (IT) | | Steifer T. | - | IPPT PAN |
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