arXiv research

KL-regularized RL from expert demos can lead to slow, unstable learning.

We introduce a new approach for comparing reinforcement learning policies, using Wasserstein distances (WDs) in a newly defined latent behavioral space. We show that by utilizing the dual formulation of the WD, we can learn score functions over policy behaviors that can in turn be used to lead policy optimization towar…

Proposes a new regularization technique for neural networks using elliptic operators.

New insights into tail behavior of heavy-tailed random vectors and processes.

Double descent risk in L2-regularized models explained and mitigated.

Paper tackles offline RL from mixed datasets with adaptive KL regularizer.

Study compares dropout and l2 regularization in linear models.

Machine learning forecasts show bias at long horizons, contrary to standard tests.

Paper introduces a new topological loss for better convergence.

Dual behavior policy improves reinforcement learning across various environments.

Study on high-codimensional minimal surfaces in hyperbolic space.

FOCAL tackles offline meta-reinforcement learning with efficient task inference and behavior regularization.

Paper analyzes blowup of regularized Jang solutions and constant expansion surfaces.

A framework for analyzing regularizers to ensure trustworthy theory-driven model estimation.

The behavior of geodesic curves on even seemingly simple surfaces can be surprisingly complex. In this paper we use the Hamiltonian formulation of the geodesic equations to analyze their integrability properties. In particular, we examine the behavior of geodesics on surfaces defined by the spherical harmonics. Using t…

Unified DICE estimators as regularized Lagrangians for improved off-policy evaluation.

Survey on geodesics on tetrahedra in curved spaces.

Inspired by the concept of evolutoids of planar curves, we present the concept of evolutoids for regular surfaces as an envelope of a two-parameter family of lines in Euclidean 3-space. We give an explicit parametrization for such evolutoids. Besides, we used the theory of singularities to study the local behavior of r…

A new model captures car-following and lane-changing behaviors in traffic.

Whereas deep neural network (DNN) is increasingly applied to choice analysis, it is challenging to reconcile domain-specific behavioral knowledge with generic-purpose DNN, to improve DNN's interpretability and predictive power, and to identify effective regularization methods for specific tasks. This study designs a pa…

New framework learns interaction rules from animal trajectories.

Study explores learning behavior of GFlowNets, revealing key mechanisms.

Study boundary behavior of limit interfaces in Riemannian manifolds without convexity assumptions.

The paper studies a flow of Legendre curves, generalizing the inverse curvature flow of regular curves.

A new framework for offline RL improves policy flexibility and regularity.

Given a null-cobordant oriented framed link $L$ in a closed oriented $3$--manifold $M$, we determine those links in $M \setminus L$ which can be realized as the singular point set of a generic map $M \to \mathbb{R}^2$ that has $L$ as an oriented framed regular fiber. Then, we study the linking behavior between the sing…

As reinforcement learning agents are tasked with solving more challenging and diverse tasks, the ability to incorporate prior knowledge into the learning system and to exploit reusable structure in solution space is likely to become increasingly important. The KL-regularized expected reward objective constitutes one po…

We define regularity scales to study the behavior of the Calabi flow. Based on estimates of the regularity scales, we obtain convergence theorems of the Calabi flow on extremal Kahler surfaces, under the assumption of global existence of the Calabi flow solutions. Our results partially confirm Donaldson's conjectural p…

Demonstration-regularized RL reduces sample complexity for policy identification.

Study geodesics in conformally compact manifolds, showing smoothness and asymptotic behavior.

Flow adjusts curvature to avoid a fixed region, proving bounds and regularity.

SAM improves generalization in overparameterized models, but its behavior in tensorized models is less understood.

Using ultra-high-frequency data extracted from the order flows of 23 stocks traded on the Shenzhen Stock Exchange, we study the empirical regularities of order placement in the opening call auction, cool period and continuous auction. The distributions of relative logarithmic prices against reference prices in the thre…

The generalized Jang equation was introduced in an attempt to prove the Penrose inequality in the setting of general initial data for the Einstein equations. In this paper we give an extensive study of this equation, proving existence, regularity, and blow-up results. In particular, precise asymptotics for the blow-up …

In this short note we announce a regularity theorem for Kähler-Ricci flow on a compact Fano manifold (Kähler manifold with positive first Chern class) and its application to the limiting behavior of Kähler-Ricci flow on Fano 3-manifolds. Moreover, we also present a partial $C^0$ estimate to the Kähler-Ricci flow under …

The study examines the regularity of branched immersions using special coordinate systems.

In multi-agent reinforcement learning, discovering successful collective behaviors is challenging as it requires exploring a joint action space that grows exponentially with the number of agents. While the tractability of independent agent-wise exploration is appealing, this approach fails on tasks that require elabora…

We investigate if kernel regularization methods can achieve minimax convergence rates over a source condition regularity assumption for the target function. These questions have been considered in past literature, but only under specific assumptions about the decay, typically polynomial, of the spectrum of the the kern…

We consider properties of the total absolute geodesic curvature functional on circle immersions into a Riemann surface. In particular, we study its behavior under regular homotopies, its infima in regular homotopy classes, and the homotopy types of spaces of its local minima. We consider properties of the total curvatu…

Recently, path norm was proposed as a new capacity measure for neural networks with Rectified Linear Unit (ReLU) activation function, which takes the rescaling-invariant property of ReLU into account. It has been shown that the generalization error bound in terms of the path norm explains the empirical generalization b…

In reinforcement learning (RL) research, it is common to assume access to direct online interactions with the environment. However in many real-world applications, access to the environment is limited to a fixed offline dataset of logged experience. In such settings, standard RL algorithms have been shown to diverge or…

Continual learning of deep neural networks is a key requirement for scaling them up to more complex applicative scenarios and for achieving real lifelong learning of these architectures. Previous approaches to the problem have considered either the progressive increase in the size of the networks, or have tried to regu…

Generative adversarial networks (GANs) are notoriously difficult to train and the reasons underlying their (non-)convergence behaviors are still not completely understood. By first considering a simple yet representative GAN example, we mathematically analyze its local convergence behavior in a non-asymptotic way. Furt…

New algorithm stabilizes bi-level hyperparameter optimization.

A simple regularization method improves model generalization.

This paper is devoted to problem of detecting critical events at finiacial markets using methods of multifractal analysis. Namely, the local regularity of time-series is studied. As a result, one can find out a special behavior or signal of regularity before crashes. This spesial behaviour of local Hoelder exponents in…

Motivated by the equation satisfied by the extremals of certain Hardy-Sobolev type inequalities, we show sharp $L^q$ regularity for finite energy solutions of p-laplace equations involving critical exponents and possible singularity on a sub-space of $\mathbb{R}^n$, which imply asymptotic behavior of the solutions at i…

Study the limiting shape of solutions to the L_p-Minkowski problem as p approaches negative infinity.