Decidability of Sample Complexity of PAC Learning in finite setting

• URL: http://arxiv.org/abs/2002.11519v1
• Date: Wed, 26 Feb 2020 14:27:36 GMT
• Title: Decidability of Sample Complexity of PAC Learning in finite setting
• Authors: Alberto Gandolfi
• Abstract summary: PAC machine learning of various concepts can be exactly determined when the support of the probability measures considered as models satisfies an a-priori bound. This result contrasts with the recently discovered undecidability of EMX within ZFC for finitely supported probabilities.
• Score: 1.8130068086063333
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: In this short note we observe that the sample complexity of PAC machine learning of various concepts, including learning the maximum (EMX), can be exactly determined when the support of the probability measures considered as models satisfies an a-priori bound. This result contrasts with the recently discovered undecidability of EMX within ZFC for finitely supported probabilities (with no a priori bound). Unfortunately, the decision procedure is at present, at least doubly exponential in the number of points times the uniform bound on the support size.

Related papers

• Efficient Learning for Entropy-Regularized Markov Decision Processes via Multilevel Monte Carlo [3.439970905480239]
  We propose a novel family of multilevel Monte Carlo (MLMC) algorithms that integrate fixed-point iteration with a generic approximation of the Bellman operator. We show that using a biased plain MC estimate for the Bellman operator results in quasi-polynomial sample complexity. Notably, these algorithms are independent of the dimensions or cardinalities of the state and action spaces.
  arXiv  Detail & Related papers  (2025-03-27T07:35:23Z)
• Near-Optimal Learning and Planning in Separated Latent MDPs [70.88315649628251]
  We study computational and statistical aspects of learning Latent Markov Decision Processes (LMDPs) In this model, the learner interacts with an MDP drawn at the beginning of each epoch from an unknown mixture of MDPs.
  arXiv  Detail & Related papers  (2024-06-12T06:41:47Z)
• Metric Entropy-Free Sample Complexity Bounds for Sample Average Approximation in Convex Stochastic Programming [0.6906005491572401]
  This paper studies sample average approximation (SAA) in solving convex or strongly convex programming (SP) problems. We show -- perhaps for the first time -- that SAA's sample complexity can be completely free from any quantification of metric entropy.
  arXiv  Detail & Related papers  (2024-01-01T04:35:53Z)
• Optimal Multi-Distribution Learning [88.3008613028333]
  Multi-distribution learning seeks to learn a shared model that minimizes the worst-case risk across $k$ distinct data distributions. We propose a novel algorithm that yields an varepsilon-optimal randomized hypothesis with a sample complexity on the order of (d+k)/varepsilon2.
  arXiv  Detail & Related papers  (2023-12-08T16:06:29Z)
• Towards Instance-Optimality in Online PAC Reinforcement Learning [28.156332484814616]
  We propose the first instance-dependent lower bound on the sample complexity required for the PAC identification of a near-optimal policy. We demonstrate that the sample complexity of the PEDEL algorithm of citeWagenmaker22linearMDP closely approaches this lower bound.
  arXiv  Detail & Related papers  (2023-10-31T19:26:36Z)
• Online POMDP Planning with Anytime Deterministic Guarantees [11.157761902108692]
  Planning under uncertainty can be mathematically formalized using partially observable Markov decision processes (POMDPs) Finding an optimal plan for POMDPs can be computationally expensive and is feasible only for small tasks. We derive a deterministic relationship between a simplified solution that is easier to obtain and the theoretically optimal one.
  arXiv  Detail & Related papers  (2023-10-03T04:40:38Z)
• Provably Efficient UCB-type Algorithms For Learning Predictive State Representations [55.00359893021461]
  The sequential decision-making problem is statistically learnable if it admits a low-rank structure modeled by predictive state representations (PSRs) This paper proposes the first known UCB-type approach for PSRs, featuring a novel bonus term that upper bounds the total variation distance between the estimated and true models. In contrast to existing approaches for PSRs, our UCB-type algorithms enjoy computational tractability, last-iterate guaranteed near-optimal policy, and guaranteed model accuracy.
  arXiv  Detail & Related papers  (2023-07-01T18:35:21Z)
• Asymptotically Unbiased Instance-wise Regularized Partial AUC Optimization: Theory and Algorithm [101.44676036551537]
  One-way Partial AUC (OPAUC) and Two-way Partial AUC (TPAUC) measures the average performance of a binary classifier. Most of the existing methods could only optimize PAUC approximately, leading to inevitable biases that are not controllable. We present a simpler reformulation of the PAUC problem via distributional robust optimization AUC.
  arXiv  Detail & Related papers  (2022-10-08T08:26:22Z)
• Optimistic MLE -- A Generic Model-based Algorithm for Partially Observable Sequential Decision Making [48.87943416098096]
  This paper introduces a simple efficient learning algorithms for general sequential decision making. We prove that OMLE learns near-optimal policies of an enormously rich class of sequential decision making problems.
  arXiv  Detail & Related papers  (2022-09-29T17:56:25Z)
• Sample-Efficient Reinforcement Learning of Undercomplete POMDPs [91.40308354344505]
  This work shows that these hardness barriers do not preclude efficient reinforcement learning for rich and interesting subclasses of Partially Observable Decision Processes (POMDPs) We present a sample-efficient algorithm, OOM-UCB, for episodic finite undercomplete POMDPs, where the number of observations is larger than the number of latent states and where exploration is essential for learning, thus distinguishing our results from prior works.
  arXiv  Detail & Related papers  (2020-06-22T17:58:54Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.