arXiv research

Groups satisfy linear surface isoperimetric functions.

Study one-dimensional topological theories with linear generating functions.

A new complexity measure for neural networks improves upon classical methods.

Study on distributional TD learning with linear approximations for better return estimation.

Logarithmic regret achieved in RL with linear function approximation.

Entropy-regularized NPG converges linearly with linear function approximation.

Papers learn from data to make decisions without interacting, improving on previous methods.

New algorithms improve distributional TD learning with linear approximations.

New neural network models for functional data.

Graph Neural Nets (GNNs) have received increasing attentions, partially due to their superior performance in many node and graph classification tasks. However, there is a lack of understanding on what they are learning and how sophisticated the learned graph functions are. In this work, we propose a dissection of GNNs …

We study the Ollivier-Ricci curvature of graphs as a function of the chosen idleness. We show that this idleness function is concave and piecewise linear with at most $3$ linear parts, with at most $2$ linear parts in the case of a regular graph. We then apply our result to show that the idleness function of the Cartes…

We study Jacobi structures on the dual bundle $A^\ast$ to a vector bundle $A$ such that the Jacobi bracket of linear functions is again linear and the Jacobi bracket of a linear function and the constant function 1 is a basic function. We prove that a Lie algebroid structure on $A$ and a 1-cocycle $φ\in Γ(A^\ast)$ indu…

New RL algorithm achieves nearly optimal performance for linear MDPs.

Paper proposes a new activation function to reduce overfitting and large weight update issues.

The paper introduces a non-linear version of the process convolution formalism for building covariance functions for multi-output Gaussian processes. The non-linearity is introduced via Volterra series, one series per each output. We provide closed-form expressions for the mean function and the covariance function of t…

This paper analyzes divide-and-conquer estimators for functional linear regression without assuming target function in the RKHS.

Enhances Cox model for survival analysis with symbolic non-linear log-risk functions.

UCRL2-VTR achieves nearly optimal regret for learning MDPs with linear function approximation.

Global approximation for piecewise linear paths via signatures.

Optimal algorithms for non-linear ridge bandits reduce burn-in cost.

The paper splits manifolds using infinity harmonic functions with linear growth.

ENIAC method optimizes and explores complex RL problems with non-linear policies.

The critical locus of the loss function of a neural network is determined by the geometry of the functional space and by the parameterization of this space by the network's weights. We introduce a natural distinction between pure critical points, which only depend on the functional space, and spurious critical points, …

The paper provides risk bounds for learning many response functions using linear regression.

Paper presents a machine learning method to improve significance tests for misspecified linear models.

Diffusion Maps improves on Functional PCA for non-linear functional data.

Linear-Core Surrogates combine fast optimization and statistical efficiency in classification and structured prediction.

New algorithm for offline RL with linear approx in MDPs and MGs, nearly optimal.

Study non-linear combinatorial bandits with polynomial rewards, finding significant differences from linear cases.

New method uses DC functions for piecewise linear regression.

Uniqueness of asymptotic limits for Ricci-flat manifolds with linear volume growth is proven.

New proof shows efficient ReLU networks for piecewise linear functions.

This article considers algorithmic and statistical aspects of linear regression when the correspondence between the covariates and the responses is unknown. First, a fully polynomial-time approximation scheme is given for the natural least squares optimization problem in any constant dimension. Next, in an average-case…

New algorithm for reward-free RL with linear function approximation, reducing sample complexity.

Modern Reinforcement Learning (RL) is commonly applied to practical problems with an enormous number of states, where function approximation must be deployed to approximate either the value function or the policy. The introduction of function approximation raises a fundamental set of challenges involving computational …

New neural network models for complex functional data analysis.

Artificial neural networks typically have a fixed, non-linear activation function at each neuron. We have designed a novel form of piecewise linear activation function that is learned independently for each neuron using gradient descent. With this adaptive activation function, we are able to improve upon deep neural ne…

New algorithm FLUTE achieves uniform-PAC convergence in RL with linear approx.

New RL algorithm tackles nonstationary MDPs with linear approximations and varying rewards.

Paper analyzes agnostic learning of mixed linear regression without generative models.

The paper analyzes methods for estimating linear functionals from observational data, proving upper bounds and showing optimal procedures.

Study improves hypothesis transfer learning for functional linear models.

In this paper, we propose and study random maxout features, which are constructed by first projecting the input data onto sets of randomly generated vectors with Gaussian elements, and then outputing the maximum projection value for each set. We show that the resulting random feature map, when used in conjunction with …

We design a new provably efficient algorithm for episodic reinforcement learning with generalized linear function approximation. We analyze the algorithm under a new expressivity assumption that we call "optimistic closure," which is strictly weaker than assumptions from prior analyses for the linear setting. With opti…

Introduces HTV to measure function complexity in learning schemes.

Two discretizations, linear and nonlinear, of basic notions of the complex analysis are considered. The underlying lattice is an arbitrary quasicrystallic rhombic tiling of a plane. The linear theory is based on the discrete Cauchy-Riemann equations, the nonlinear one is based on the notion of circle patterns. We clari…

This paper studies robust regression in the settings of Huber's $ε$-contamination models. We consider estimators that are maximizers of multivariate regression depth functions. These estimators are shown to achieve minimax rates in the settings of $ε$-contamination models for various regression problems including nonpa…

Constructs a Morse-Bott function on symplectic Grassmannians.