A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
Introduces Conditional Action Trees to simplify RL action spaces.
Study polar actions on Damek-Ricci spaces, proving existence and finding examples.
Classifies polar actions on 3D homogeneous spaces.
We analyze polar actions on Hermitian and quaternion-Kähler symmetric spaces of compact type. For complex integrable polar actions on Hermitian symmetric spaces of compact type we prove a reduction theorem and several corollaries concerning the geometry of these actions. The results are independent of the classificatio…
Proper actions on bornological spaces are characterized with compatible coarse structures.
We study isometric actions on Riemannian symmetric spaces of noncompact type which are induced by reductive algebraic subgroups of the isometry group. We show that for such an action there exists a corresponding isometric action on a dual compact symmetric space, which reflects many properties of the original action. F…
Most existing deep reinforcement learning (DRL) frameworks consider either discrete action space or continuous action space solely. Motivated by applications in computer games, we consider the scenario with discrete-continuous hybrid action space. To handle hybrid action space, previous works either approximate the hyb…
We first investigate the geometry of orbits of the isotropy action on a semi-simple pseudo-Riemannian symmetric space by investigating the complexified action. Next we investigate the geometry of the orbits of Hermann type actions on the symmetric spaces. By considering two special Hermann type actions on the symmetric…
Complete classification of symmetric spaces actions.
This work tackles large action spaces in RL by binarizing actions.
New method reduces bias and variance in OPE for large action spaces.
In complex tasks, such as those with large combinatorial action spaces, random exploration may be too inefficient to achieve meaningful learning progress. In this work, we use a curriculum of progressively growing action spaces to accelerate learning. We assume the environment is out of our control, but that the agent …
Extends PF submanifold results and connects Kac-Moody spaces.
Simplifies large action space bandits by selecting representative actions.
Lecture notes on group actions on injective spaces and Helly graphs.
Cohomogeneity-one actions on symmetric spaces of mixed type
In this paper we propose a hybrid architecture of actor-critic algorithms for reinforcement learning in parameterized action space, which consists of multiple parallel sub-actor networks to decompose the structured action space into simpler action spaces along with a critic network to guide the training of all sub-acto…
Applying Q-learning to high-dimensional or continuous action spaces can be difficult due to the required maximization over the set of possible actions. Motivated by techniques from amortized inference, we replace the expensive maximization over all actions with a maximization over a small subset of possible actions sam…
We study hyperpolar actions on reducible symmetric spaces of the compact type. Our main result is that an indecomposable hyperpolar action on a symmetric space of the compact type is orbit equivalent to a Hermann action or of cohomogeneity one.
We study isometric cohomogeneity one actions on the (n+1)-dimensional Minkowski space up to orbit-equivalence. We give examples of isometric cohomogeneity one actions on the Minkowski space whose orbit spaces are non-Hausdorff. We show that there exist isometric cohomogeneity one actions on the Minkowski space which ar…
New findings on when to use action space exploration in reinforcement learning.
Intelligent agents can learn to represent the action spaces of other agents simply by observing them act. Such representations help agents quickly learn to predict the effects of their own actions on the environment and to plan complex action sequences. In this work, we address the problem of learning an agent's action…
The paper extends Thompson Sampling to infinite action spaces using information theory.
The paper studies curvatures and austere properties of orbits in symmetric spaces.
We classify infinitesimally polar actions on compact Riemannian symmetric spaces of rank one. We also prove that every polar action on one of those spaces has the same orbits as an asystatic action.
New method QMLE performs well in complex action spaces without policy gradients.
No exceptional orbits found in Hilbert spaces actions.
Study on actions on symmetric spaces, focusing on orbit properties.
An isometric action of a Lie group on a Riemannian manifold is of cohomogeneity one if the corresponding orbit space is one-dimensional. In this article we develop a conceptual approach to the classification of cohomogeneity one actions on Riemannian symmetric spaces of noncompact type in terms of orbit equivalence. As…
New criteria for non-isometric group actions in metric spaces.
Solves action selection for large spaces in RL, achieving near-optimal performance.
Study proper actions of Lie groups on symmetric spaces, finding rigidity results and Hurwitz-Radon numbers.
Reinforcement learning (RL) in discrete action space is ubiquitous in real-world applications, but its complexity grows exponentially with the action-space dimension, making it challenging to apply existing on-policy gradient based deep RL algorithms efficiently. To effectively operate in multidimensional discrete acti…
Practical algorithm for contextual bandits with large action spaces.
Study boundary actions on CAT(0) spaces, proving topological freeness.
New structural result classifies actions on symmetric spaces.
We study polar actions with horizontal sections on the total space of certain principal bundles with base a symmetric space of compact type. We classify such actions up to orbit equivalence in many cases. In particular, we exhibit examples of hyperpolar actions with cohomogeneity greater than one on locall…
Study group actions in metric spaces, proving convergence of lens spaces.
Generic groups can't move spaces but have rich actions.
We study isometric Lie group actions on symmetric spaces admitting a section, i.e. a submanifold which meets all orbits orthogonally at every intersection point. We classify such actions on the compact symmetric spaces with simple isometry group and rank greater than one. In particular we show that these actions are hy…
Black-box optimizers that explore in parameter space have often been shown to outperform more sophisticated action space exploration methods developed specifically for the reinforcement learning problem. We examine these black-box methods closely to identify situations in which they are worse than action space explorat…
We use the combinatorial harmonic map theory to study the isometric actions of discrete groups on Hadamard spaces. Given a finitely generated group acting by automorphisms, properly discontinuously and cofinitely on a simplicial complex and its isometric action on a Hadamard space, we formulate criterions for the actio…
Smooth torus actions on moduli spaces of super stable curves and maps of genus zero.
New spaces found without certain actions, using special subgroups.
Given a group action on a simplicial complex such that each simplex stabiliser admits a cocompact model of classifying space for proper actions, we give conditions implying the existence of a cocompact model of classifying space for proper actions for the whole group. This is used to generalise previous combination res…
The paper connects polygon spaces with quotient spaces using spin actions and normed division algebras.
Reconstruct flows from their orbit spaces using group actions.
Conditions for reducing quasi-actions to tree actions and group properties.