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Kevin Li

Publications and source records attributed to Kevin Li.

70 records · Page 4Linked to original sources

MURAL: Meta-Learning Uncertainty-Aware Rewards for Outcome-Driven Reinforcement Learning

Exploration in reinforcement learning is a challenging problem: in the worst case, the agent must search for high-reward states that could be hidden anywhere in the state space. Can we define a more tractable class of RL problems, where the agent is provided with examples of successful outcomes? In this problem setting, the reward function can be obtained automatically by training a classifier to categorize states as successful or not. If trained properly, such a classifier can provide a well-shaped objective landscape that both promotes progress toward good states and provides a calibrated exploration bonus. In this work, we show that an uncertainty aware classifier can solve challenging reinforcement learning problems by both encouraging exploration and provided directed guidance towards positive outcomes. We propose a novel mechanism for obtaining these calibrated, uncertainty-aware classifiers based on an amortized technique for computing the normalized maximum likelihood (NML) distribution. To make this tractable, we propose a novel method for computing the NML distribution by using meta-learning. We show that the resulting algorithm has a number of intriguing connections to both count-based exploration methods and prior algorithms for learning reward functions, while also providing more effective guidance towards the goal. We demonstrate that our algorithm solves a number of challenging navigation and robotic manipulation tasks which prove difficult or impossible for prior methods.

cs.LG↗

Collective Effects -- an introduction

Collective effects in particle accelerators are one of the key constituents for determining the ultimate particle accelerator performance. Their role is becoming increasingly important as particle accelerators are being pushed ever closer towards the intensity and beam brightness frontiers. They are slightly peculiar in their nature as their impact and significance depend not only on external fields but also on the beam properties themselves. This results in a highly coupled and convoluted system. In these lectures we will give a brief overview over collective effects in particle accelerators in general. We will cover the topics in a highly conceptual and illustrative manner. The goal will be for the students to get an intuitive impression on the nature and the aftermath of collective effects. The lectures will cover different types of collective effects along with their manifestation in accelerators and briefly outline the limitations they impose along with a few means for potential mitigation techniques.

physics.acc-ph↗

Bounded cohomology of classifying spaces for families of subgroups

We introduce a bounded version of Bredon cohomology for groups relative to a family of subgroups. Our theory generalizes bounded cohomology and differs from Mineyev--Yaman's relative bounded cohomology for pairs. We obtain cohomological characterizations of relative amenability and relative hyperbolicity, analogous to the results of Johnson and Mineyev for bounded cohomology.

math.GR↗

Asymptotic Normality for Multivariate Random Forest Estimators

Regression trees and random forests are popular and effective non-parametric estimators in practical applications. A recent paper by Athey and Wager shows that the random forest estimate at any point is asymptotically Gaussian; in this paper, we extend this result to the multivariate case and show that the vector of estimates at multiple points is jointly normal. Specifically, the covariance matrix of the limiting normal distribution is diagonal, so that the estimates at any two points are independent in sufficiently deep trees. Moreover, the off-diagonal term is bounded by quantities capturing how likely two points belong to the same partition of the resulting tree. Our results relies on certain a certain stability property when constructing splits, and we give examples of splitting rules for which this assumption is and is not satisfied. We test our proposed covariance bound and the associated coverage rates of confidence intervals in numerical simulations.

econ.EM↗

FlowDB a large scale precipitation, river, and flash flood dataset

Flooding results in 8 billion dollars of damage annually in the US and causes the most deaths of any weather related event. Due to climate change scientists expect more heavy precipitation events in the future. However, no current datasets exist that contain both hourly precipitation and river flow data. We introduce a novel hourly river flow and precipitation dataset and a second subset of flash flood events with damage estimates and injury counts. Using these datasets we create two challenges (1) general stream flow forecasting and (2) flash flood damage estimation. We have created several publicly available benchmarks and an easy to use package. Additionally, in the future we aim to augment our dataset with snow pack data and soil index moisture data to improve predictions.

cs.AI↗

The Optimal Double Bubble for Density $r^p$

In 1993 Foisy et al. proved that the optimal Euclidean planar double bubble---the least-perimeter way to enclose and separate two given areas---is three circular arcs meeting at 120 degrees. We consider the plane with density $r^p$, joining the surge of research on manifolds with density after their appearance in Perelman's 2006 proof of the Poincaré Conjecture. Dahlberg et al. proved that the best single bubble in the plane with density $r^p$ is a circle through the origin. We conjecture that the best double bubble is the Euclidean solution with one of the vertices at the origin, for which we have verified equilibrium (first variation or "first derivative" zero). To prove the exterior of the minimizer connected, it would suffice to show that least perimeter is increasing as a function of the prescribed areas. We give the first direct proof of such monotonicity for the Euclidean case. Such arguments were important in the 2002 Annals proof of the double bubble in Euclidean 3-space

math.MG↗

Dynamic Transitions of the Swift-Hohenberg Equation with Third-Order Dispersion

The Swift-Hohenberg equation is ubiquitous in the study of bistable dynamics. In this paper, we study the dynamic transitions of the Swift-Hohenberg equation with a third-order dispersion term in one spacial dimension with a periodic boundary condition. As a control parameter crosses a critical value, the trivial stable equilibrium solution will lose its stability, and undergoes a dynamic transition to a new physical state, described by a local attractor. The main result of this paper is to fully characterize the type and detailed structure of the transition using dynamic transition theory. In particular, employing techniques from center manifold theory, we reduce this infinite dimensional problem to a finite one since the space on which the exchange of stability occurs is finite dimensional. The problem then reduces to analysis of single or double Hopf bifurcations, and we completely classify the possible phase changes depending on the dispersion for every spacial period.

math.DS↗

A practical guide to using the AngCor package

This guide contains brief, practically oriented instructions for the use of the AngCor package for computing angular correlations following nuclear reactions. This guide serves as a lasting reference for the AngCor package and complements the GitHub repository for the AngCor code.

nucl-ex↗

Certain Hyperbolic Regular Polygonal Tiles are Isoperimetric

The hexagon is the least-perimeter tile in the Euclidean plane. On hyperbolic surfaces, the isoperimetric problem differs for every given area. Cox conjectured that a regular $k$-gonal tile with 120-degree angles is isoperimetric for its area. We prove his conjecture and more.

math.MG↗

Optimal monohedral tilings of hyperbolic surfaces

The hexagon is the least-perimeter tile in the Euclidean plane for any given area. On hyperbolic surfaces, this "isoperimetric" problem differs for every given area, as solutions do not scale. Cox conjectured that a regular $k$-gonal tile with 120-degree angles is isoperimetric. For area $π/3$, the regular heptagon has 120-degree angles and therefore tiles many hyperbolic surfaces. For other areas, we show the existence of many tiles but provide no conjectured optima. On closed hyperbolic surfaces, we verify via a reduction argument using cutting and pasting transformations and convex hulls that the regular $7$-gon is the optimal $n$-gonal tile of area $π/3$ for $3\leq n \leq 10$. However, for $n>10$, it is difficult to rule out non-convex $n$-gons that tile irregularly.

math.MG↗

K- and L-theory of graph products of groups

We compute the group homology, the algebraic $K$- and $L$-groups, and the topological $K$-groups of right-angled Artin groups, right-angled Coxeter groups, and more generally, graph products.

math.KT↗

A Robust Volume Conserving Method for Character-Water Interaction

We propose a novel volume conserving framework for character-water interaction, using a novel volume-of-fluid solver on a skinned tetrahedral mesh, enabling the high degree of the spatial adaptivity in order to capture thin films and hair-water interactions. For efficiency, the bulk of the fluid volume is simulated with a standard Eulerian solver which is two way coupled to our skinned arbitrary Lagrangian-Eulerian mesh using a fast, robust, and straightforward to implement partitioned approach. This allows for a specialized and efficient treatment of the volume-of-fluid solver, since it is only required in a subset of the domain. The combination of conservation of fluid volume and a kinematically deforming skinned mesh allows us to robustly implement interesting effects such as adhesion, and anisotropic porosity. We illustrate the efficacy of our method by simulating various water effects with solid objects and animated characters.

cs.GR↗

The Gauss-Bonnet Formula for Harmonic Surfaces

We consider harmonic immersions in $\R^{\N}$ of compact Riemann surfaces with finitely many punctures where the harmonic coordinate functions are given as real parts of meromorphic functions. We prove that such surfaces have finite total Gauss curvature. The contribution of each end is a multiple of $2π$, determined by the maximal pole order of the meromorphic functions. This generalizes the well known Gackstatter-Jorge-Meeks formula for minimal surfaces. The situation is complicated as the ends are generally not conformally equivalent to punctured disks, nor does the surface have limit tangent planes.

math.DG↗

Complete Embedded Harmonic Surfaces In $\mathbb{R}^3$

Embedded minimal surfaces of finite total curvature in $\mathbb{R}^3$ are reasonably well understood: From far away, they look like intersecting catenoids and planes, suitably desingularized. We consider the larger class of harmonic embeddings in $\mathbb{R}^{3}$ of compact Riemann surfaces with finitely many punctures where the harmonic coordinate functions are given as real parts of meromorphic functions. This paper is motivated by two outstanding features of such surfaces: They can have highly complicated ends, and they still have total Gauss curvature being a multiple of $2π$. This poses the double challenge to construct and classify examples of fixed total Gauss curvature. Our results include - a classification of embedded harmonic ends of small total curvature, - the construction of examples of embedded ends of arbitrarily large total curvature, - a classification of complete embedded harmonic surfaces of small total curvature in the spirit of the corresponding classification of minimal surfaces of small total curvature, and - the largely experimental construction of complete embedded harmonic surfaces with non-trivial topology that incorporate some of the new harmonic ends.

math.DG↗

Air entrainment by a plunging jet under intermittent vortex conditions

This fluid dynamic video entry to the 2011 APS-DFD Gallery of Fluid Motion details the transient evolution of the free surface surrounding the impact region of a low-viscosity laminar liquid jet as it enters a quiescent pool. The close-up images depict the destabilization and breakup of the annular air gap and the subsequent entrainment of bubbles into the bulk liquid.

physics.flu-dyn↗