arXiv research

There has been renewed recent interest in developing effective lower bounds for Dynamic Time Warping (DTW) distance between time series. These have many applications in time series indexing, clustering, forecasting, regression and classification. One of the key time series classification algorithms, the nearest neighbo…

We give the proof of a tight lower bound on the probability that a binomial random variable exceeds its expected value. The inequality plays an important role in a variety of contexts, including the analysis of relative deviation bounds in learning theory and generalization bounds for unbounded loss functions.

In this short note we consider a dynamic assortment planning problem under the capacitated multinomial logit (MNL) bandit model. We prove a tight lower bound on the accumulated regret that matches existing regret upper bounds for all parameters (time horizon $T$, number of items $N$ and maximum assortment capacity $K$)…

New study on regret lower bounds for multi-agent multi-armed bandit problems.

Classifies tight contact structures on specific Seifert fibered manifolds.

Paper tightens lower bounds on decentralized training complexity.

Classifies real tight contact structures on lens spaces and solid tori.

New lower bounds for combinatorial multi-armed bandits for general reward functions.

Paper proves tight lower bounds for online multicalibration, separating it from marginal calibration.

The study tightens bounds on binomial probabilities and minimums using KL-divergence.

In the past decade, sparse principal component analysis has emerged as an archetypal problem for illustrating statistical-computational tradeoffs. This trend has largely been driven by a line of research aiming to characterize the average-case complexity of sparse PCA through reductions from the planted clique (PC) con…

New lower bounds for gradient methods in strongly convex finite-sum optimization.

New lower bounds for private covariance estimation of Gaussian distributions are proven.

New bounds on ropelength for torus links improve previous estimates.

Proposes an efficient lower bound for Gromov-Wasserstein discrepancy.

Paper establishes tight lower bounds for minimizing certain smooth and convex functions.

New convergence bounds for shuffling-based SGD methods in distributed learning.

Upper and lower bounds on regret for noisy optimization of Brownian motion.

We give a general lower bound for the normal Gromov norm of genuine laminations in terms of the topology of the complementary regions. In the special case of 3-manifolds, this yields a generalization of Agol's inequality from incompressible surfaces to tight laminations. In particular, the inequality excludes the exist…

Leveraging algorithmic stability to derive sharp generalization bounds is a classic and powerful approach in learning theory. Since Vapnik and Chervonenkis [1974] first formalized the idea for analyzing SVMs, it has been utilized to study many fundamental learning algorithms (e.g., $k$-nearest neighbors [Rogers and Wag…

Optimizes quadratic bandits with tight Hessian-dependent sample complexity bounds.

In the Bayesian approach to sequential decision making, exact calculation of the (subjective) utility is intractable. This extends to most special cases of interest, such as reinforcement learning problems. While utility bounds are known to exist for this problem, so far none of them were particularly tight. In this pa…

The paper improves privacy accounting for discrete-valued mechanisms and the subsampled Gaussian mechanism.

We introduce the $k$-stellated spheres and compare and contrast them with $k$-stacked spheres. It is shown that for $d \geq 2k$, any $k$-stellated sphere of dimension $d$ bounds a unique and canonically defined $k$-stacked ball. In parallel, any $k$-stacked polytopal sphere of dimension $d\geq 2k$ bounds a unique and c…

Noiseless IO bounds inferred from demonstrations, matching adversarial settings.

Study finds optimal regret bound for multi-armed bandit problem with expert advice.

In this article we give a sharp upper bound on the possible values of the Euler characteristic for a minimal symplectic filling of a tight contact structure on a lens space. This estimate is obtained by looking at the topology of the spaces involved, extending this way what we already knew from the universally tight ca…

HAMBO estimates policy performance by hallucinating worst-case trajectories, providing valid lower bounds.

Investigates tight PAC-Bayes bounds for small datasets.

The homology groups of a manifold are important topological invariants that provide an algebraic summary of the manifold. These groups contain rich topological information, for instance, about the connected components, holes, tunnels and sometimes the dimension of the manifold. In earlier work, we have considered the s…

Quantifies tightness in 3D contact manifolds using sub-Riemannian metrics.

PAGE is a simple gradient estimator for nonconvex optimization problems.

This study tightens bounds on how GD and SGD generalize in smooth convex optimization problems.

Study minimax linear regression under quantile risk, improving existing bounds and providing new results.

The paper provides tight bounds for improving multi-armed bandits problem.

We lower bound the complexity of finding $ε$-stationary points (with gradient norm at most $ε$) using stochastic first-order methods. In a well-studied model where algorithms access smooth, potentially non-convex functions through queries to an unbiased stochastic gradient oracle with bounded variance, we prove that (i…

We obtain a tight distribution-specific characterization of the sample complexity of large-margin classification with L_2 regularization: We introduce the γ-adapted-dimension, which is a simple function of the spectrum of a distribution's covariance matrix, and show distribution-specific upper and lower bounds on the s…

Study on binding numbers of tight contact structures on lens spaces $L(n,1)$.

Sharp lower bound on GHHs' representation power of CPWL functions.

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…

New bounds on continuous random variables' right-tail probabilities.

We give a complete characterization of the complexity of best-arm identification in one-parameter bandit problems. We prove a new, tight lower bound on the sample complexity. We propose the `Track-and-Stop' strategy, which we prove to be asymptotically optimal. It consists in a new sampling rule (which tracks the optim…

New measure of robustness for estimators, with tight bounds for Gaussian mean estimation.

We introduce the $k$-stellated spheres and consider the class ${\cal W}_k(d)$ of triangulated $d$-manifolds all whose vertex links are $k$-stellated, and its subclass ${\cal W}^{\ast}_k(d)$ consisting of the $(k+1)$-neighbourly members of ${\cal W}_k(d)$. We introduce the mu-vector of any simplicial complex and show th…

Improved sample complexity for identifying best policies in risk-sensitive reinforcement learning.

Analyzes the complexity of linear hypothesis sets using Rademacher complexity.

New tensor model reduces GLM estimation error and sample complexity.

New bounds for SGD show improved performance in various settings.