arXiv research

A new method reduces communication in Federated Learning by pulling less often.

Lisa Jeffrey and Frances Kirwan developed an integration theory for symplectic reductions. That is, given a symplectic manifold with symplectic group action, they developed a way of pulling the integration of forms on the reduction back to an integration of group-equivariant forms on the original space. We seek an anal…

The paper proves rigidity theorems for forms on reductive symmetric spaces.

Reductive G-structures on a principal bundle Q are considered. It is shown that these structures, i.e. reductive G-subbundles P of Q, admit a canonical decomposition of the pull-back vector bundle $i_P^*(TQ) = P \times_Q TQ$ over P. For classical G-structures, i.e. reductive G-subbundles of the linear frame bundle, suc…

Develops a new geometric framework for quantum metrics.

We define the pull-back of a smooth principal fibre bundle, and show that it has a natural principal fibre bundle structure. Next, we analyse the relationship between pull-backs by homotopy equivalent maps. The main result of this article is to show that for a principal fibre bundle over a paracompact manifold, there i…

Study connects taffy pulling, fractions, and rational tangles.

Under a pulled-back approach given in [1] and firstly presented in [2], we introduce, in this paper, the concepts of almost contact and normal almost contact Finsler structures on the pulled-back bundle. Properties of structures partly Sasakians are studied. Using the hh-curvature tensor of Chern connection given in [2…

We develop a new approach to the pulling back fixed point theorem of W. Browder and use it in order to prove various generalizations of this result.

The paper constructs a multi-valued inverse of quasiregular maps and develops pull-back theory for differential forms.

Narasihman and Ramanan proved that an arbitrary connection in a vector bundle over a base space B can be obtained as the pull-back (via a correctly chosen classifying map from B into the appropriate Grassmannian) of the universal connection in the universal bundle over the Grassmannian. The purpose of this paper is to …

New algorithm finds high-reward combinatorial sets with fewest pulls.

Starting from the general concept of a Lie derivative of an arbitrary differentiable map, we develop a systematic theory of Lie differentiation in the framework of reductive G-structures P on a principal bundle Q. It is shown that these structures admit a canonical decomposition of the pull-back vector bundle i_P^*(TQ)…

The Thresholding Bandit Problem (TBP) aims to find the set of arms with mean rewards greater than a given threshold. We consider a new setting of TBP, where in addition to pulling arms, one can also \emph{duel} two arms and get the arm with a greater mean. In our motivating application from crowdsourcing, dueling two a…

This paper studies Thompson sampling's arm-pull dynamics and inference, revealing key differences from UCB algorithms.

Develops a framework for clustering and distribution matching with bandit feedback.

We reexamine the notions of generalized Ricci tensor and scalar curvature on a general Courant algebroid, reformulate them using objects natural w.r.t. pull-backs and reductions, and obtain them from the variation of a natural action functional. This allows us to prove, in a very general setup, the compatibility of the…

This paper considers the multi-armed thresholding bandit problem -- identifying all arms whose expected rewards are above a predefined threshold via as few pulls (or rounds) as possible -- proposed by Locatelli et al. [2016] recently. Although the proposed algorithm in Locatelli et al. [2016] achieves the optimal round…

An obstruction theory for representing homotopy classes of surfaces in 4-manifolds by immersions with pairwise disjoint images is developed, using the theory of non-repeating Whitney towers. The accompanying higher-order intersection invariants provide a geometric generalization of Milnor's link-homotopy invariants, an…

ODC protocol improves learning in asynchronous multi-agent bandits.

We consider the multi-armed bandit setting with a twist. Rather than having just one decision maker deciding which arm to pull in each round, we have $n$ different decision makers (agents). In the simple stochastic setting, we show that a "free-riding" agent observing another "self-reliant" agent can achieve just $O(1)…

We prove that stability -- a strong quasiconvexity property -- pulls back under proper actions on proper metric spaces. This result has several applications, including that convex cocompact subgroups of both mapping class groups and outer automorphism groups of free groups are stable. We also characterize stability in …

We formulate and study a novel multi-armed bandit problem called the qualitative dueling bandit (QDB) problem, where an agent observes not numeric but qualitative feedback by pulling each arm. We employ the same regret as the dueling bandit (DB) problem where the duel is carried out by comparing the qualitative feedbac…

In this paper, we investigate the impact of diverse user preference on learning under the stochastic multi-armed bandit (MAB) framework. We aim to show that when the user preferences are sufficiently diverse and each arm can be optimal for certain users, the O(log T) regret incurred by exploring the sub-optimal arms un…

Proposes a fair RMAB framework ensuring equal exposure to arms.

Characterizes UCB algorithm performance in bandit problems.

In this note, we reconcile two approaches that have been used to construct stringy multiplications. The pushing forward after pulling back that has been used to give a global stringy extension of the functors K_0,K^{top},A^*,H^* [CR, FG, AGV, JKK2], and the pulling back after having pushed forward, which we have previo…

Detects potential rug pulls in Uniswap tokens before they occur.

We consider a multi-armed bandit framework where the rewards obtained by pulling different arms are correlated. We develop a unified approach to leverage these reward correlations and present fundamental generalizations of classic bandit algorithms to the correlated setting. We present a unified proof technique to anal…

Paper generalizes paracomposition and change of variables for paradifferential operators.

We consider a novel multi-armed bandit framework where the rewards obtained by pulling the arms are functions of a common latent random variable. The correlation between arms due to the common random source can be used to design a generalized upper-confidence-bound (UCB) algorithm that identifies certain arms as $non-c…

In this work we consider adversarial contextual bandits with risk constraints. At each round, nature prepares a context, a cost for each arm, and additionally a risk for each arm. The learner leverages the context to pull an arm and then receives the corresponding cost and risk associated with the pulled arm. In additi…

PAC best arm identification with a deadline, improving efficiency over sequential methods.

Learning preferences implicit in the choices humans make is a well studied problem in both economics and computer science. However, most work makes the assumption that humans are acting (noisily) optimally with respect to their preferences. Such approaches can fail when people are themselves learning about what they wa…

The harmonic map energy of a map from a closed, constant-curvature surface to a closed target manifold can be seen as a functional on the space of maps and domain metrics. We consider the gradient flow for this energy. In the absence of singularities, previous theory established that the flow converges to a branched mi…

UCB-V algorithm improves on UCB for MAB problems with variance estimates.

Let $X$ be a smooth projective complex variety of maximal Albanese dimension, and let $L \to X$ be a big line bundle. We prove that the moving Seshadri constants of the pull-backs of $L$ to suitable finite abelian étale covers of $X$ are arbitrarily large. As an application, given any integer $k\geq 1$, there exists an…

The motivation for this paper stems \cite{CR} from the need to construct explicit isomorphisms of (possibly nontrivial) principal $G$-bundles on the space of loops or, more generally, of paths in some manifold $M$, over which I consider a fixed principal bundle $P$; the aforementioned bundles are then pull-backs of $P$…

Given a Riemannian metric on a homotopy $n$-sphere, sweep it out by a continuous one-parameter family of closed curves starting and ending at point curves. Pull the sweepout tight by, in a continuous way, pulling each curve as tight as possible yet preserving the sweepout. We show: Each curve in the tightened sweepout …

New algorithm uses machine learning to predict rewards for decision-making problems.

The paper studies how geometric transformations affect semi-classical operators on specific Lie groups.

The paper proves global invertibility for certain local diffeomorphisms and biholomorphisms in higher dimensions.

A new algorithm for fair decision-making in bandit problems with biased feedback.

Relating the Dirac operators on the total space and on the base manifold of a horizontally conformal submersion, we characterize Dirac morphisms, i.e. maps which pull back (local) harmonic spinor fields onto (local) harmonic spinor fields.

Motivated by cognitive radio networks, we consider the stochastic multiplayer multi-armed bandit problem, where several players pull arms simultaneously and collisions occur if one of them is pulled by several players at the same stage. We present a decentralized algorithm that achieves the same performance as a centra…

New algorithm tackles multi-player bandit problems with limited access to arms.

A modular functor is constructed from non-semisimple 3d TFTs.

We explore a novel setting of the Multi-Armed Bandit (MAB) problem inspired from real world applications which we call bandits with "stochastic delayed composite anonymous feedback (SDCAF)". In SDCAF, the rewards on pulling arms are stochastic with respect to time but spread over a fixed number of time steps in the fut…