arXiv research

Paper proves first non-trivial PTF testing lower bounds for NGCA.

New SQ lower bounds for NGCA without requiring chi-squared condition.

Lower bounds on Bayes risk for realizable models derived using information theory.

Paper develops conformalized survival analysis method for better prediction.

Paper proves Liouville theorems for harmonic functions under specific curvature bounds.

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.

Lower bounds on private estimation of Gaussian covariance matrices.

Lower bounds found for nonconvex-strongly-concave min-max optimization problems.

We consider the problem of estimating the underlying graph associated with a Markov random field, with the added twist that the decoding algorithm can iteratively choose which subsets of nodes to sample based on the previous samples, resulting in an active learning setting. Considering both Ising and Gaussian models, w…

Sharp bounds established for Federated Averaging (FedAvg), improving convergence rates.

The study analyzes weighted manifolds with curvature bounds, proving eigenvalue estimates and inequalities.

Paper bounds the A-hat genus using curvature and isoperimetric constants.

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

Policy iteration is a family of algorithms that are used to find an optimal policy for a given Markov Decision Problem (MDP). Simple Policy iteration (SPI) is a type of policy iteration where the strategy is to change the policy at exactly one improvable state at every step. Melekopoglou and Condon [1990] showed an exp…

Study on regret minimization in deterministic MDPs.

Paper establishes lower bounds for Gaussian process bandit optimization under various perturbation models.

Upper bounds and lower bounds show ERM outperforms DG methods in various settings.

Study compares nonsmooth spaces with integrable Ricci bounds.

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

Sum-of-Squares lower bound shows NGCA requires more samples than known algorithms.

The study finds a lower bound for the diameter of gradient ρ-Einstein solitons.

Recent successes of game-theoretic formulations in ML have caused a resurgence of research interest in differentiable games. Overwhelmingly, that research focuses on methods and upper bounds on their speed of convergence. In this work, we approach the question of fundamental iteration complexity by providing lower boun…

Unified framework for lower bounds in interactive decision making.

In adaptive data analysis, the user makes a sequence of queries on the data, where at each step the choice of query may depend on the results in previous steps. The releases are often randomized in order to reduce overfitting for such adaptively chosen queries. In this paper, we propose a minimax framework for adaptive…

This paper studies the lower bound complexity for the optimization problem whose objective function is the average of $n$ individual smooth convex functions. We consider the algorithm which gets access to gradient and proximal oracle for each individual component. For the strongly-convex case, we prove such an algorith…

Paper establishes lower bounds for finite-sum optimization problems using novel construction methods.

Sharp bounds for curve isoperimetric deficit derived.

Improved Gaussian process regression with tighter log marginal likelihood bounds.

Paper develops a framework to derive lower bounds on FDR and FNR in multiple testing.

The study sets limits on how well nonlinear models can generalize from training data.

Unified framework for expert selection with bandit and lower-bound feedback.

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

Lower bounds for PI on multi-action MDPs are established, showing complexity grows with action count.

We obtain upper bounds for the isoperimetric quotients of extrinsic balls of submanifolds in ambient spaces which have a lower bound on their radial sectional curvatures. The submanifolds are themselves only assumed to have lower bounds on the radial part of the mean curvature vector field and on the radial part of the…

Traditional statistical analysis requires that the analysis process and data are independent. By contrast, the new field of adaptive data analysis hopes to understand and provide algorithms and accuracy guarantees for research as it is commonly performed in practice, as an iterative process of interacting repeatedly wi…

Score attack method provides a lower bound on privacy-constrained minimax risk.

Smooth finite-sum optimization has been widely studied in both convex and nonconvex settings. However, existing lower bounds for finite-sum optimization are mostly limited to the setting where each component function is (strongly) convex, while the lower bounds for nonconvex finite-sum optimization remain largely unsol…

We study the linear contextual bandit problem with finite action sets. When the problem dimension is $d$, the time horizon is $T$, and there are $n \leq 2^{d/2}$ candidate actions per time period, we (1) show that the minimax expected regret is $Ω(\sqrt{dT (\log T) (\log n)})$ for every algorithm, and (2) introduce a V…

Study uses SGD to learn operators in Hilbert spaces with convergence analysis.

Lower bounds and upper bounds on sample complexity for identifying linear dynamical systems.

The main result of this paper shows that "test configurations" give new lower bounds on the $L^{2}$ norm of the scalar curvature on a Kahler manifold. This is closely analogous to the analysis of the Yang-Mills functional over Riemann surfaces by Atiyah and Bott. The proof uses asymptotic approximation by finite-dimens…

In this paper, we obtain fundamental $\mathcal{L}_{p}$ bounds in sequential prediction and recursive algorithms via an entropic analysis. Both classes of problems are examined by investigating the underlying entropic relationships of the data and/or noises involved, and the derived lower bounds may all be quantified in…

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

Local differential privacy (LDP) is a model where users send privatized data to an untrusted central server whose goal it to solve some data analysis task. In the non-interactive version of this model the protocol consists of a single round in which a server sends requests to all users then receives their responses. Th…

Optimal and safe semi-supervised learning estimator for high-dimensional data.

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

Lower bounds on MALA and HMC for well-conditioned distributions.

Sharp bounds on Alexandrov spaces' boundaries with rigidity analysis.