arXiv research

We prove non-asymptotic lower bounds on the expectation of the maximum of $d$ independent Gaussian variables and the expectation of the maximum of $d$ independent symmetric random walks. Both lower bounds recover the optimal leading constant in the limit. A simple application of the lower bound for random walks is an (…

The paper establishes bounds on scalar curvature on asymptotically flat manifolds.

The paper finds lower bounds for the first eigenvalue of p-Laplacian in specific manifolds.

Optimal sequential testing for Markovian data with lower and upper bounds.

We consider the problem of tracking a target whose dynamics is modeled by a continuous Itō semi-martingale. The aim is to minimize both deviation from the target and tracking efforts. We establish the existence of asymptotic lower bounds for this problem, depending on the cost structure. These lower bounds can be relat…

Study non-asymptotic estimation bounds for LTI models with Gaussian noise.

We consider a sequential learning problem with Gaussian payoffs and side information: after selecting an action $i$, the learner receives information about the payoff of every action $j$ in the form of Gaussian observations whose mean is the same as the mean payoff, but the variance depends on the pair $(i,j)$ (and may…

Sharp inequality linking interior and boundary Yamabe invariants on specific manifolds.

The study finds a limit on the volume growth of certain 3-manifolds.

Study on conditions for achieving optimal robustness in statistical estimators.

The paper explores sharp isoperimetric properties on non-compact spaces with Ricci bounds.

Optimizes arm selection with side information in Gaussian bandits.

The paper provides a uniform lower bound for intersection numbers of psi-classes on moduli spaces.

Establishes inequality for multiple black holes, proving mass lower bound.

The paper develops new methods to study sharp isoperimetric properties on complex spaces.

Proposes online debiasing estimators for adaptive linear regression.

Detecting a planted submatrix in random matrices with non-asymptotic methods.

Sharp asymptotic lower bounds of the expected quadratic variation of discretization error in stochastic integration are given. The theory relies on inequalities for the kurtosis and skewness of a general random variable which are themselves seemingly new. Asymptotically efficient schemes which attain the lower bounds a…

We determine the sample complexity of pure exploration bandit problems with multiple good answers. We derive a lower bound using a new game equilibrium argument. We show how continuity and convexity properties of single-answer problems ensures that the Track-and-Stop algorithm has asymptotically optimal sample complexi…

We show that the type function of a space with finite asymptotic dimension estimates its Hilbert (or any $l^p$) compression. The method allows to obtain the lower bound of the compression of the lamplighter group $Z\wr Z$, which has infinite asymptotic dimension.

For a risk vector $V$, whose components are shared among agents by some random mechanism, we obtain asymptotic lower and upper bounds for the individual agents' exposure risk and the aggregated risk in the market. Risk is measured by Value-at-Risk or Conditional Tail Expectation. We assume Pareto tails for the componen…

We study new heat kernel estimates for the Neumann heat kernel on a compact manifold with positive Ricci curvature and convex boundary. As a consequence, we obtain new lower bounds for the Neumann eigenvalues which are consistent with Weyl's asymptotics.

Asymptotically optimal algorithm for contextual linear bandits.

CD algorithm achieves near-optimal convergence rate for unnormalized models.

We prove an asymptotic analog of the classical Hurewicz theorem on mappings which lower dimension. This theorem allows us to find sharp upper bound estimates for the asymptotic dimension of groups acting on finite dimensional metric spaces and allows us to prove a useful extension theorem for asymptotic dimension. As a…

For an $n$-dimensional polytope $Ω$ in $\mathbb{R}^{n}$, we study lower bounds for eigenvalues of the Dirichlet eigenvalue problem of the Laplacian. In the asymptotic formula on the average of the first $k$ eigenvalues, Li and Yau (1983) obtained the first term with the order $k^{\frac2n}$, which is optimal. The next l…

Researchers prove a Penrose inequality for spacetime with specific conditions.

Prove rigidity and classification results for quasilinear Liouville equation on manifolds with nonnegative Ricci curvature.

Optimal strategy identified for minimizing regret in fixed-budget best arm selection.

The Bartnik mass is a quasi-local mass tailored to asymptotically flat Riemannian manifolds with non-negative scalar curvature. From the perspective of general relativity, these model time-symmetric domains obeying the dominant energy condition without a cosmological constant. There is a natural analogue of the Bartnik…

The paper proves unique geodesics on hyperbolic surfaces and finds lower bounds.

Study best arm identification with limited precision sampling in bandits.

In this note, we obtain the asymptotic estimate for the time derivative of the $Φ$-entropy in terms of the lower bound on the Bakry-Emery $Γ_2$ curvature. In the cases of Hyperbolic space and Heisenberg group, we show that the time derivative of the $Φ$-entropy is non-increasing, and we also get sharp asymptotic bound …

This paper tightens the law of the iterated logarithm for empirical KL_inf, applicable to unbounded data.

Researchers prove positive mass theorem for manifolds with arbitrary ends.

In statistical inference problems, we wish to obtain lower bounds on the minimax risk, that is to bound the performance of any possible estimator. A standard technique to obtain risk lower bounds involves the use of Fano's inequality. In an information-theoretic setting, it is known that Fano's inequality typically doe…

Optimal multi-fidelity best-arm identification reduces cost with better accuracy.

Study minimal translation lengths on curve complexes, providing bounds and constructing examples.

Method bounds tail probabilities of continuous RVs.

We consider complete noncompact Riemannian manifolds with quadratically decaying lower Ricci curvature bounds and minimal volume growth. We first prove a rigidity result showing that ends with strongly minimal volume growth are isometric to warped product manifolds. Next we consider the almost rigid case in which manif…

We study the $K$-armed dueling bandit problem, a variation of the standard stochastic bandit problem where the feedback is limited to relative comparisons of a pair of arms. We introduce a tight asymptotic regret lower bound that is based on the information divergence. An algorithm that is inspired by the Deterministic…

Optimal best-arm identification with known number of optimal arms.

Algorithm identifies best policy in MDPs with adaptive sampling.

The paper finds a lower bound for a Neumann eigenvalue of surfaces with flat ends.

Let p and l be two distinct prime numbers and let G be a group. We study the asymptotic behaviour of the mod-l Betti numbers in p-adic analytic towers of finite index subgroups. If X is a finite l-group of automorphisms of G, our main theorem allows to lift lower bounds for the mod-l cohomology growth in the fixed poin…

In this paper, we first prove a folklore conjecture on a greatest lower bound of the Calabi energy in all Kähler manifold. Similar result in algebriac setting was obtained by S. K. Donaldson. Secondly, we give an upper/lower bound estimate of the K energy in terms of the geodesic distance and the Calabi energy. This is…

New algorithm reduces clustering cost in bandit feedback.

Define mass invariant for asymptotically hyperbolic 3-manifolds with toroidal infinity.