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On Exact Computation with an Infinitely Wide Neural Net
TLDR
The current paper gives the first efficient exact algorithm for computing the extension of NTK to convolutional neural nets, which it is called Convolutional NTK (CNTK), as well as an efficient GPU implementation of this algorithm.
Fine-Grained Analysis of Optimization and Generalization for Overparameterized Two-Layer Neural Networks
TLDR
This paper analyzes training and generalization for a simple 2-layer ReLU net with random initialization, and provides the following improvements over recent works: a tighter characterization of training speed, an explanation for why training a neuralNet with random labels leads to slower training, and a data-dependent complexity measure.
Graph Neural Tangent Kernel: Fusing Graph Neural Networks with Graph Kernels
TLDR
A new class of graph kernels, Graph Neural Tangent Kernels (GNTKs), which correspond to infinitely wide multi-layer GNNs trained by gradient descent are presented, which enjoy the full expressive power ofGNNs and inherit advantages of GKs.
Harnessing the Power of Infinitely Wide Deep Nets on Small-data Tasks
TLDR
Results suggesting neural tangent kernels perform strongly on low-data tasks are reported, with comparing the performance of NTK with the finite-width net it was derived from, NTK behavior starts at lower net widths than suggested by theoretical analysis.
Bilinear Classes: A Structural Framework for Provable Generalization in RL
TLDR
This work provides an RL algorithm which has polynomial sample complexity for Bilinear Classes, a new structural framework which permit generalization in reinforcement learning in a wide variety of settings through the use of function approximation.
Is a Good Representation Sufficient for Sample Efficient Reinforcement Learning?
TLDR
This work provides sharp thresholds for reinforcement learning methods, showing that there are hard limitations on what constitutes good function approximation (in terms of the dimensionality of the representation), and highlighting that having a good representation in and of itself is insufficient for efficient reinforcement learning, unless the quality of this approximation passes certain hard thresholds.
Reinforcement Learning with General Value Function Approximation: Provably Efficient Approach via Bounded Eluder Dimension
TLDR
This paper establishes a provably efficient RL algorithm with general value function approximation that achieves a regret bound of $\widetilde{O}(\mathrm{poly}(dH)\sqrt{T})$ and provides a framework to justify the effectiveness of algorithms used in practice.
Nearly Optimal Sampling Algorithms for Combinatorial Pure Exploration
TLDR
This work provides a novel instance-wise lower bound for the sample complexity of the Best-Set problem, as well as a nontrivial sampling algorithm, matching the lower bound up to a factor of $\ln|\mathcal{F}|$.
Provably Efficient Reinforcement Learning with General Value Function Approximation
TLDR
This paper establishes the first provable efficiently RL algorithm with general value function approximation, and shows that if the value functions admit an approximation with a function class $\mathcal{F}$, this algorithm achieves a regret bound of $\widetilde{O}(\mathrm{poly}(dH)\sqrt{T})$.
Optimism in Reinforcement Learning with Generalized Linear Function Approximation
TLDR
This work designs a new provably efficient algorithm for episodic reinforcement learning with generalized linear function approximation that enjoys a regret bound of $\tilde{O}(\sqrt{d^3 T})$ where d is the dimensionality of the state-action features and T is the number of episodes.
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