arXiv research

Study tackles infinitely many-armed bandits with rotting rewards, achieving tight regret bounds.

New algorithm handles both decaying and non-decaying bandit problems.

New algorithm reduces regret in infinitely many-armed bandits with decreasing rewards.

Graph-Triggered Bandits unify rested and restless bandits with graph-defined arm interactions.

In stochastic multi-armed bandits, the reward distribution of each arm is assumed to be stationary. This assumption is often violated in practice (e.g., in recommendation systems), where the reward of an arm may change whenever is selected, i.e., rested bandit setting. In this paper, we consider the non-parametric rott…

The Multi-Armed Bandits (MAB) framework highlights the tension between acquiring new knowledge (Exploration) and leveraging available knowledge (Exploitation). In the classical MAB problem, a decision maker must choose an arm at each time step, upon which she receives a reward. The decision maker's objective is to maxi…

New method tracks shifts in infinite-armed bandits without prior knowledge.

TURB-Rot provides a large database of turbulent rotating flow snapshots for research.

ROTS improves sentence similarity by incorporating structural information.

Thomas Rot discusses a topology theorem at a math conference.

We investigate Legendrian graphs in $(\R^3, ξ_{std})$. We extend the classical invariants, Thurston-Bennequin number and rotation number to Legendrian graphs. We prove that a graph can be Legendrian realized with all its cycles Legendrian unknots with $tb=-1$ and $rot=0$ if and only if it does not contain $K_4$ as a mi…

New R-equivalence classes found for torus knot diagrams.

Enhanced rotation prediction improves SSL models by capturing both shape and texture information.

Develops a novel global pooling framework using optimal transport.

Researchers predict butt rot volume using harvester data and remote sensing.

Global existence of Willmore flow with boundary via Li-Yau inequality.

We prove two results on the classification of trivial Legendrian embeddings $g: G \rightarrow (S^3,ξ_{std})$ of planar graphs. First, the oriented Legendrian ribbon $R_g$ and rotation invariant $\text{rot}_g$ are a complete set of invariants. Second, if $G$ is 3-connected or contains $K_4$ as a minor, then the unique t…

In this paper, as the second in our series of papers on differential geometry of microlinear Frolicher spaces, we study differenital forms. The principal result is that the exterior differentiation is uniquely determined geometrically, just as grad (ient), div (ergence) and rot (ation) are uniquely determined geometric…

This paper presents a unified framework for smooth convex regularization of discrete optimal transport problems. In this context, the regularized optimal transport turns out to be equivalent to a matrix nearness problem with respect to Bregman divergences. Our framework thus naturally generalizes a previously proposed …

Let $M_n$ be the topological moduli space of all parallel n-cables of long framed oriented knots in 3-space. We construct in a combinatorial way for each natural number $n>1$ a 1-cocycle $R_n$ which represents a non trivial class in $H^1(M_n; \mathbb{Z} [x_1,x_2,...,x_1^{-1},x_2^{-1},...])$, where the number of variabl…

We advocate an optimization-centric view on and introduce a novel generalization of Bayesian inference. Our inspiration is the representation of Bayes' rule as infinite-dimensional optimization problem (Csiszar, 1975; Donsker and Varadhan; 1975, Zellner; 1988). First, we use it to prove an optimality result of standard…

Let $(M^n,g,\nabla f)$, $n\geq 3$, be an expanding gradient Ricci soliton with nonnegative sectional curvature whose asymptotic cone is isometric to $C(\mathbb{S}^{n-1}(c))$ where $\mathbb{S}^{n-1}(c)$ is the standard $(n-1)$-sphere of curvature $1/c^2$, with $c\in(0,1)$. We prove that if the convergence to the asympto…

New examples of non-simple knots in Lens spaces show rich botany.

New Legendrian bounds for non-fibered knots in 3-manifolds.

The paper proves $n$-transitivity for equivariant diffeomorphisms of manifolds.

The following three geometrical structures on a manifold are studied in detail: (1) Leibnizian: a non-vanishing 1-form $Ω$ plus a Riemannian metric $\h$ on its annhilator vector bundle. In particular, the possible dimensions of the automorphism group of a Leibnizian G-structure are characterized. (2) Galilean: Leibnizi…

Let $Ω$ be a smooth compact oriented 3-dimensional Riemannian manifold with boundary. A quaternion field is a pair $q=\{α,u\}$ of a function $α$ and a vector field $u$ on $Ω$. A field $q$ is {\it harmonic} if $α, u$ are continuous in $Ω$ and $\nablaα={\rm rot\,}u,\,{\rm div\,}u=0$ holds into $Ω$. The space ${\mathscr Q…

New algorithms tackle RKHS bandits with reduced complexity and improved performance.

Unified formulation bridges adversarial and nonstationary bandits.

We classify Legendrian unknots in overtwisted contact structures on $S^3$. In particular, we show that up to contact isotopy for every pair $(n,\pm(n-1))$ with $n>0$ there are exactly two oriented non-loose Legendrian unknots in $S^3$ with Thurston-Bennequin invariant $n$ and rotation number $\pm(n-1)$. (Only one overt…

Paper solves stochastic contextual linear bandits using linear bandit algorithms.

Paper tackles LDP bandits learning with improved results and sub-linear regret.

We propose a novel visual context-aware filter generation module which incorporates contextual information present in images into Convolutional Neural Networks (CNNs). In contrast to traditional CNNs, we do not employ the same set of learned convolution filters for all input image instances. Our proposed input-conditio…

New definition resolves ambiguity in non-stationary bandit classification.

Unified approach for non-stationary and clustered bandits.

A framework for auto-tuning hyper-parameters in contextual bandit algorithms.

Stochastic multi-armed bandits form a class of online learning problems that have important applications in online recommendation systems, adaptive medical treatment, and many others. Even though potential attacks against these learning algorithms may hijack their behavior, causing catastrophic loss in real-world appli…

New algorithm learns optimal exploration parameters for contextual bandits.

Investigates sequential problems on graph structures and large action spaces.

Study on indexability of restless multi-armed bandits and rollout policy performance.

New insights into multi-armed bandits with budget constraints.

Optimal algorithm for identifying best arm in stochastic linear bandits with fixed confidence.

A meta-UCB method combines stochastic bandit algorithms.

New method for contextual bandits with corrupted context.

A new framework for structured bandits using influence diagrams and variational Thompson sampling.

New algorithm for nonstationary multi-armed bandits with optimal performance.

First robust bandit algorithm for contextual bandits with sub-linear regret.

Unified framework for high-dimensional bandit problems with low-dimensional structures.