arXiv research

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

New bounds for sequential tests under power-one error levels.

Kurdyka-Lojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In particular, a KL exponent of $\frac12$ for a suitable potential function is related to local linear convergence. Nevertheless, KL exponent is in general extremely hard to estimate. I…

The paper finds the optimal wealth growth rate in betting games.

Optimal tests for composite nulls achieve the KL inf lower bound.

INF-clip optimizes heavy-tailed MAB problems with improved performance.

In this paper we will discuss the optimal risk transfer problems when risk measures are generated by G-expectations, and we present the relationship between inf-convolution of G-expectations and the inf-convolution of drivers G.

Inequality found for a specific equation on 5D manifolds.

Study risk sharing among agents with varying risk preferences.

SurvLIME-Inf simplifies explanation of survival models using a linear programming approach.

Simplified proof for Tsallis-INF algorithm without conjugate functions.

Extends inf-convolution to countable risk measures for risk sharing.

We prove an a priori estimate of type sup*inf on Riemannian manifold of dimension 3 (not necessarily compact).

The paper studies properties of optimal metrics associated to curves on surfaces.

Study uncovers new phase transitions in asymmetric causal inference scenarios.

Study risk sharing with Lambda VaR under diverse beliefs.

We give some a priori estimates of type sup*inf for Yamabe and prescribed scalar curvature type equations on Riemannian manifolds of dimension >2. The product sup*inf is caracteristic of those equations, like the usual Harnack inequalities for non negative harmonic functions. First, we have a lower bound for sup*inf fo…

Let $M^n\subset\mathbb R^{n+1}$ be the graph of a $C^2$-real valued function defined in a closed ball of $\mathbb R^n$. In this work, we obtain upper bounds for $\inf_M|H|$ and $\inf_M|R|$, where $H$ and $R$ are, respectively, the mean curvature and the scalar curvature of $M^n$, generalizing estimates given by Heinz i…

Optimizes convex functions in finite vs infinite dimensions, revealing slow convergence rates.

Improved regret bounds for Tsallis-INF in adversarial bandits and corruptions.

We connect Causal inference and low-rank recovery via RDT and free probability theory.

In this paper, we study a family of non-convex and possibly non-smooth inf-projection minimization problems, where the target objective function is equal to minimization of a joint function over another variable. This problem include difference of convex (DC) functions and a family of bi-convex functions as special cas…

We study the existence of optimal actions in a zero-sum game $\inf_τ\sup_PE^P[X_τ]$ between a stopper and a controller choosing a probability measure. This includes the optimal stopping problem $\inf_τ\mathcal{E}(X_τ)$ for a class of sublinear expectations $\mathcal{E}(\cdot)$ such as the $G$-expectation. We show that …

Algorithmic solutions to the conjugacy problem in the braid groups B_n were given by Elrifai-Morton in 1994 and by the authors in 1998. Both solutions yield two conjugacy class invariants which are known as `inf' and `sup'. A problem which was left unsolved in both papers was the number m of times one must `cycle' (res…

We show how an operation of inf-convolution can be used to approximate convex functions with $C^{1}$ smooth convex functions on Riemannian manifolds with nonpositive curvature (in a manner that not only is explicit but also preserves some other properties of the original functions, such as ordering, symmetries, infima …

Optimizes quickest change detection with bounded means under ARL constraint.

The paper explores numerical characteristics of compact Riemannian manifolds and proves inequalities.

In this paper, we consider an infinite dimensional exponential family, $\mathcal{P}$ of probability densities, which are parametrized by functions in a reproducing kernel Hilbert space, $H$ and show it to be quite rich in the sense that a broad class of densities on $\mathbb{R}^d$ can be approximated arbitrarily well i…

We define a new differential invariant a compact manifold by $V_{\mathcal M}(M)=\inf_g V_c(M,[g])$, where $V_c(M,[g])$ is the conformal volume of $M$ for the conformal class $[g]$, and prove that it is uniformly bounded above. The main motivation is that this bound provides a upper bound of the Friedlander-Nadirashvili…

Paper analyzes inclusive KL inference using Wasserstein gradient flows.

TSC uses HMC and adaptive transport maps to optimize forward KL for variational inference.

A classic setting of the stochastic K-armed bandit problem is considered in this note. In this problem it has been known that KL-UCB policy achieves the asymptotically optimal regret bound and KL-UCB+ policy empirically performs better than the KL-UCB policy although the regret bound for the original form of the KL-UCB…

Establishes relationships between prudence and stability properties of risk functionals.

Improved fast rates for decision making with forward-KL regularization in contextual bandits.

Causal KL improves on existing metrics for evaluating causal models.

New algorithm minimizes inclusive KL for VI, improving accuracy.

Sharp analysis improves RLHF sample complexity with KL-regularization.

Lewis and Mordecki have computed the Wiener-Hopf factorization of a Lévy process whose restriction on $]0,+\infty[$ of their Lévy measure has a rational Laplace transform. That allows to compute the distribution of $(X_t,\inf_{0\leq s\leq t}X_s)$. For the same class of Lévy processes, we compute the distribution of $ (…

Given a spacelike 2-surface $Σ$ in a spacetime $N$ and a constant future timelike unit vector $T_0$ in $\R^{3,1}$, we derive upper and lower estimates of Wang-Yau quasilocal energy $E(Σ, X, T_0)$ for a given isometric embedding $X$ of $Σ$ into a flat 3-slice in $\R^{3,1}$. The quantity $E(Σ, X, T_0)$ itself depends …

The paper develops new algorithms for KL-divergence NMF, proving convergence and performance.

Inf-FS selects features by graph paths, ranking them for infinite feature sets.

Paper analyzes and improves KL-regularized RL for LLMs with logarithmic regret.

Paper relaxes triangle inequality for KL divergence between Gaussian distributions.

Theory for RLHF generalization under reward shift and clipped KL.

KALE flow approximates KL divergence for distributions with disjoint support.

The Dirichlet mechanism protects privacy while minimizing KL divergence.

Improved bounds for estimating discrete distributions in KL divergence.

Paper analyzes sample complexity of offline MABs with KL regularization.