arXiv research

Improved uniform convergence bound with fat-shattering dimension reduces sample complexity gap.

Improved regret bounds for bandits with expert advice.

Improved bound for optimal Moebius band aspect ratio.

Improved confidence bounds for linear logistic model with applications to bandits.

Improved bounds for discrete probability distribution estimation under the ℓ∞ norm.

In this paper, we improve the PAC-Bayesian error bound for linear regression derived in Germain et al. [10]. The improvements are twofold. First, the proposed error bound is tighter, and converges to the generalization loss with a well-chosen temperature parameter. Second, the error bound also holds for training data t…

Improves bounds on surface decompositions.

Improved bounds on ideal vertices in right-angled hyperbolic polyhedra.

This paper analyzes regret bounds for Gaussian process Thompson sampling.

Paper improves worst-case regret bounds for RLSVI in reinforcement learning.

New scalable Lipschitz bounds improve neural network robustness analysis.

Improved price bounds for multi-asset derivatives using market option data.

Improved bounds for eigenfunctions on hyperbolic surfaces found.

Improved bounds for Monte Carlo Rademacher Averages using self-bounding functions.

This paper improves reinforcement learning policies in a scalable way.

The paper shows robustness and generalization are closely connected via data-dependent bounds.

Improved bounds for estimating discrete distributions in KL divergence.

Error bounds based on worst likely assignments use permutation tests to validate classifiers. Worst likely assignments can produce effective bounds even for data sets with 100 or fewer training examples. This paper introduces a statistic for use in the permutation tests of worst likely assignments that improves error b…

Improved upper bound for online calibrated forecasting of binary sequences.

Novel analysis improves weighted majority vote in multiclass classification.

Improved upper bound for equivariant Yamabe invariant in 3D.

Paper improves SLCB regret bound for bounded noise.

If $(M,g)$ is a compact Riemannian manifold of dimension $n\ge 2$ we give necessary and sufficient conditions for improved $L^p(M)$-norms of eigenfunctions for all $2<p\ne p_c=\tfrac{2(n+1)}{n-1}$, the critical exponent. Since improved $L^{p_c}(M)$ bounds imply improvement all other exponents, these conditions are nece…

Estimates lower bounds for isoperimetric profiles and improves on previous estimates for specific manifolds.

We prove new Beckner-Sobolev type inequalities on compact Kähler manifolds with positive Ricci curvature. As an application, we obtain a diameter upper bound that improves the Bonnet-Myers bound.

Active learning algorithms propose which unlabeled objects should be queried for their labels to improve a predictive model the most. We study active learners that minimize generalization bounds and uncover relationships between these bounds that lead to an improved approach to active learning. In particular we show th…

New bounds improve generalization in learning scenarios.

The paper improves transformer generalization bounds using rank-dependent covering number bounds.

Improved lower bounds for poly-Laplacian eigenvalues in arbitrary dimensions.

We derive upper and lower bounds on the expectation of $f(\mathbf{S})$ under dependence uncertainty, i.e. when the marginal distributions of the random vector $\mathbf{S}=(S_1,\dots,S_d)$ are known but their dependence structure is partially unknown. We solve the problem by providing improved \FH bounds on the copula o…

Improved BO algorithms reduce prediction error under Gaussian noise.

We use the Dong-Sogge-Zelditch formula to obtain a lower bound for the volume of the nodal sets of eigenfunctions. Our result improves the recent results of Sogge-Zelditch and in dimensions n \leq 5 gives a new proof for the lower bounds of Colding-Minicozzi.

Improved upper bound on superbridge index from 5b-3 to 3b-1.

This paper improves Q-learning bounds using reference-advantage decomposition.

Improved bounds on geodesic lengths in Riemannian surfaces.

Improved regret bounds for linear bandits with heavy-tailed rewards.

Improved lower bound for parallel tempering's mixing time.

New invariants improve Heegaard Floer slice genus and clasp number bounds.

This paper provides a theoretical analysis of domain adaptation based on the PAC-Bayesian theory. We propose an improvement of the previous domain adaptation bound obtained by Germain et al. in two ways. We first give another generalization bound tighter and easier to interpret. Moreover, we provide a new analysis of t…

New bound improves on weighted majority vote risk estimation.

The paper improves SVM margin-based generalization bounds.

Optimistic Hedge achieves optimal regret bounds in two-player zero-sum games.

Study linear contextual bandits with confounded offline data, improving regret bounds.

In this paper, we analyze a generic algorithm scheme for sequential global optimization using Gaussian processes. The upper bounds we derive on the cumulative regret for this generic algorithm improve by an exponential factor the previously known bounds for algorithms like GP-UCB. We also introduce the novel Gaussian P…

Improved bounds on combining hypothesis classes for binary functions.

Paper improves algorithms for convex-concave minimax optimization problems.

Improved guarantees for sparse random embeddings with explicit bounds and empirical superiority.

Improves adversarial robustness by constraining logits with a bounded function.