arXiv research

AI models solved the Kaczmarz algorithm's worst-case complexity.

In three-dimensional computational topology, the theory of normal surfaces is a tool of great theoretical and practical significance. Although this theory typically leads to exponential time algorithms, very little is known about how these algorithms perform in "typical" scenarios, or how far the best known theoretical…

New framework improves worst-case generalization bounds for stochastic optimization.

In this paper we prove the probabilistic continuous complexity conjecture. In continuous complexity theory, this states that the complexity of solving a continuous problem with probability approaching 1 converges (in this limit) to the complexity of solving the same problem in its worst case. We prove the conjecture ho…

New method for identifying best designs in vector optimization with uncertain feedback.

Study on proper learning under relaxed worst-case robust loss for VC classes.

Hardness proof for agnostically learning halfspaces from worst-case lattice problems.

Proposes a new framework for balancing average- and worst-case performance in machine learning.

The study assesses ML model robustness under worst-case subpopulations.

Majorizing measures control sequential complexities for online learning.

This article contains detailed proofs and additional examples related to the UAI-2013 submission `Learning Sparse Causal Models is not NP-hard'. It describes the FCI+ algorithm: a method for sound and complete causal model discovery in the presence of latent confounders and/or selection bias, that has worst case polyno…

New algorithm reduces worst-case sample complexity for learning best arm.

We study a recent model of collaborative PAC learning where $k$ players with $k$ different tasks collaborate to learn a single classifier that works for all tasks. Previous work showed that when there is a classifier that has very small error on all tasks, there is a collaborative algorithm that finds a single classifi…

We study the complexity of the entire regularization path for least squares regression with 1-norm penalty, known as the Lasso. Every regression parameter in the Lasso changes linearly as a function of the regularization value. The number of changes is regarded as the Lasso's complexity. Experimental results using exac…

New theory explains why normalization is preferred in SGD under heavy-tailed noise.

RH-UCRL combines pessimism and optimism for robust RL.

It is well known that Sparse PCA (Sparse Principal Component Analysis) is NP-hard to solve exactly on worst-case instances. What is the complexity of solving Sparse PCA approximately? Our contributions include: 1) a simple and efficient algorithm that achieves an $n^{-1/3}$-approximation; 2) NP-hardness of approximatio…

Improved bounds for function approximation in nonlinear sets.

Worst-Case Sensitivity measures model sensitivity to uncertainty set size.

We analyze the computational complexity of Quantum Sparse Support Vector Machine, a linear classifier that minimizes the hinge loss and the $L_1$ norm of the feature weights vector and relies on a quantum linear programming solver instead of a classical solver. Sparse SVM leads to sparse models that use only a small fr…

Worst-case risk measures refer to the calculation of the largest value for risk measures when only partial information of the underlying distribution is available. For the popular risk measures such as Value-at-Risk (VaR) and Conditional Value-at-Risk (CVaR), it is now known that their worst-case counterparts can be ev…

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

New reinforcement learning algorithm achieves instance-optimal sample complexity.

An algorithm solves optimization problems with large sample sets, improving worst-case complexity.

The book explores alternatives to worst-case analysis for algorithm performance.

Optimizes bond portfolios to avoid worst-case losses.

In this paper we study stochastic quasi-Newton methods for nonconvex stochastic optimization, where we assume that noisy information about the gradients of the objective function is available via a stochastic first-order oracle (SFO). We propose a general framework for such methods, for which we prove almost sure conve…

Swapping debt contracts can mitigate risk in financial networks.

This paper calculates worst-case target semi-variances for uncertain losses.

The goal of regression and classification methods in supervised learning is to minimize the empirical risk, that is, the expectation of some loss function quantifying the prediction error under the empirical distribution. When facing scarce training data, overfitting is typically mitigated by adding regularization term…

Algorithm extsc{Pedel} learns near-optimal policies efficiently on specific problems.

New framework identifies worst-case shifts for predictive resource allocation models.

Study approximates worst-case stock trading under uncertainty, quantifying sensitivity.

New algorithms test independence with fewer samples by using predictive information.

UCB algorithm's arm-sampling behavior is revealed, leading to new insights and proofs.

EKM solves the K-medoids problem in polynomial time.

Framework for worst-case generation using Wasserstein space optimization.

We consider the problem of learning a dictionary matrix from a number of observed signals, which are assumed to be generated via a linear model with a common underlying dictionary. In particular, we derive lower bounds on the minimum achievable worst case mean squared error (MSE), regardless of computational complexity…

Neural networks are part of many contemporary NLP systems, yet their empirical successes come at the price of vulnerability to adversarial attacks. Previous work has used adversarial training and data augmentation to partially mitigate such brittleness, but these are unlikely to find worst-case adversaries due to the c…

Develops wcPCA for better low-rank approximations in heterogeneous domains.

Three new efficient algorithms project vectors onto weighted l1 ball.

In this paper we describe a new algorithm called Fast Adaptive Sequencing Technique (FAST) for maximizing a monotone submodular function under a cardinality constraint $k$ whose approximation ratio is arbitrarily close to $1-1/e$, is $O(\log(n) \log^2(\log k))$ adaptive, and uses a total of $O(n \log\log(k))$ queries. …

The paper analyzes worst-case distortion risk metrics and weighted entropy under partial information.

A new algorithm avoids worst-case outcomes in risky contexts.

New analysis shows halting time is predictable for large models, improving optimization efficiency.

Improves neural network performance by enriching training dataset.

New solver SR2 tackles deep neural network training with nonsmooth regularization.

The study assesses how financial networks resist simultaneous price shocks and calculates the worst-case loss.