We consider a transfer-learning problem by using the parameter transfer approach, where a suitable parameter of feature mapping is learned through one task and applied to another objective task. Then, we introduce the notion of the local stability of parametric feature mapping and parameter transfer learnability, and thereby derive a learning bound for parameter transfer algorithms. As an application of parameter transfer learning, we discuss the performance of sparse coding in self-taught learning. Although self-taught learning algorithms with plentiful unlabeled data often show excellent empirical performance, their theoretical analysis has not been studied. In this paper, we also provide the first theoretical learning bound for self-taught learning.

Our code is available at GitHub.

Neural Information Processing Systems http://nips.cc/

Deep Neural Networks and Reinforcement Learning methods have empirically shown great promise in tackling challenging combinatorial problems.

Supervised classification techniques use training samples to find classification ruleswithsmallexpected0-1loss.

Deep learning models are now trained on increasingly larger datasets, making it crucial to reduce computational costs and improve data quality. Dataset distillation aims to distill a large dataset into a small synthesized dataset such that models trained on it can achieve similar performance to those trained on the original dataset. While there have been many empirical efforts to improve dataset distillation algorithms, a thorough theoretical analysis and provable, efficient algorithms are still lacking. In this paper, by focusing on dataset distillation for kernel ridge regression (KRR), we show that one data point per class is already necessary and sufficient to recover the original model's performance in many settings. For linear ridge regression and KRR with surjective feature mappings, we provide necessary and sufficient conditions for the distilled dataset to recover the original model's parameters. For KRR with injective feature mappings of deep neural networks, we show that while one data point per class is not sufficient in general, $k+1$ data points can be sufficient for deep linear neural networks, where $k$ is the number of classes. Our theoretical results enable directly constructing analytical solutions for distilled datasets, resulting in a provable and efficient dataset distillation algorithm for KRR. We verify our theory experimentally and show that our algorithm outperforms previous work such as KIP while being significantly more efficient, e.g.

We study reinforcement learning (RL) with linear function approximation under the adaptivity constraint. We consider two popular limited adaptivity models: the batch learning model and the rare policy switch model, and propose two efficient online RL algorithms for episodic linear Markov decision processes, where the transition probability and the reward function can be represented as a linear function of some known feature mapping. In specific, for the batch learning model, our proposed LSVI-UCB-Batch algorithm achieves an $\tilde O(\sqrt{d^3H^3T} + dHT/B)$ regret, where $d$ is the dimension of the feature mapping, $H$ is the episode length, $T$ is the number of interactions and $B$ is the number of batches. Our result suggests that it suffices to use only $\sqrt{T/dH}$ batches to obtain $\tilde O(\sqrt{d^3H^3T})$ regret. For the rare policy switch model, our proposed LSVI-UCB-RareSwitch algorithm enjoys an $\tilde O(\sqrt{d^3H^3T[1+T/(dH)]^{dH/B}})$ regret, which implies that $dH\log T$ policy switches suffice to obtain the $\tilde O(\sqrt{d^3H^3T})$ regret. Our algorithms achieve the same regret as the LSVI-UCB algorithm \citep{jin2020provably}, yet with a substantially smaller amount of adaptivity. We also establish a lower bound for the batch learning model, which suggests that the dependency on $B$ in our regret bound is tight.