New algorithms solve non-convex isotonic regression problems efficiently.
problem Minimizing submodular functions with ordering constraints.
method Discretization schemes leading to zero-th, first, or higher order oracles for efficient optimization.
result Non-convex loss functions can be robust to outliers and still lead to efficient optimization.
Lower bounds for higher-order methods in non-convex optimization.
problem Proving lower bounds for higher-order methods in smooth non-convex finite-sum optimization.
method Analyzing deterministic and randomized algorithms, proposing a new smoothness assumption.
result Proves optimal lower bounds for simulating pth-order regularized methods on the whole function.
Improved non-smooth optimization methods achieve faster convergence rates.
problem Non-smooth optimization problems, especially in ℓ ∞ \ell_\infty ℓ ∞ and ℓ 1 \ell_1 ℓ 1 -SVM. method Higher-order accelerated methods, leveraging recent advances in smooth convex optimization.
result Achieved O ( ε − 4 / 5 ) O(ε^{-4/5}) O ( ε − 4/5 ) iteration complexity for ℓ ∞ \ell_\infty ℓ ∞ regression, breaking previous barriers. The paper establishes prediction bounds for trend filtering with higher order total variation penalties.
problem Estimating signals with jumps of varying orders using total variation regularization.
method Combining oracle inequalities and interpolating vectors to bound effective sparsity.
result The ℓ 1 \ell_1 ℓ 1 -penalty on ( k − 1 ) e x t t h (k-1)^{ ext{th}} ( k − 1 ) e x t t h order differences allows adaptive estimation for k ∈ { 1 , 2 , 3 , 4 } k \in \{1,2,3,4\} k ∈ { 1 , 2 , 3 , 4 } . The paper analyzes the efficiency of gradient estimation methods in noisy function evaluations.
problem Estimating gradients of smooth functions using noisy function evaluations.
method Information-theoretic lower bounds and finite difference method analysis.
result The finite difference method is not minimax optimal, suggesting room for improvement in gradient estimation.
The study quantifies the information needed for causal queries at different levels of Pearl's hierarchy.
problem How much additional information is needed for interventional and counterfactual queries compared to observational queries?
method Formalized via query-class description length, using Kolmogorov complexity of answer oracles induced by SCMs.
result Binary acyclic SCMs show a quadratic gap between observational and interventional descriptions, and a logarithmic gap between interventional and counterfactual descriptions.
Improved algorithms for convex-concave min-max optimization and monotone variational inequalities.
problem Efficiently solving constrained convex-concave min-max problems and monotone variational inequalities.
method Higher-order methods achieving iteration complexities of O(1/T^{ rac{p+1}{2}}) for p-th order derivatives.
result Achieved improved convergence rates for min-max and monotone variational inequalities.
Rank regression from pairwise comparisons requires many comparisons to accurately learn model parameters.
problem Learning model parameters for rank regression from noisy pairwise comparisons.
method Uniform random pairwise comparisons to estimate model parameters with a given accuracy.
result Learning model parameters requires a number of comparisons proportional to d N log 3 N / ε 2 dN\log^3 N/ε^2 d N log 3 N / ε 2 . New oracle uses uncertainty for active classification with noisy feedback.
problem Improving query complexity in interactive binary classifier learning.
method Proposes a new pairwise comparison oracle that considers uncertainty and an adaptive labeling algorithm.
result Demonstrates improved performance and efficiency compared to existing methods.
Study optimizes zero-order strongly convex function minimization with higher order smoothness.
problem Optimizing a strongly convex function with noisy evaluations.
method Randomized approximation of projected gradient descent with smoothing kernel.
result Upper bounds and minimax lower bounds for the algorithm, showing near-optimality.
Quantum oracles help identify counterfactuals better than classical ones.
problem Identifying unknown causal parameters in causal models.
method Using quantum oracles to query and identify all causal parameters and counterfactuals.
result Quantum oracles enable identification of all two-way joint counterfactuals and tighter bounds on higher-order counterfactuals.
New lower bounds for bilevel optimization with first-order oracles.
problem Complexity of bilevel optimization with first-order oracles.
method Development of hard instances and proof of lower bounds.
result Nontrivial lower bounds for first-order zero-respecting algorithms.
Improved estimation of higher order integrals using shrinkage techniques.
problem Estimating higher order Bochner integrals in non-parametric settings.
method Shrinkage of U-statistic towards a target element, considering kernel degeneracy.
result Consistent shrinkage estimators with fast rates of convergence, even for non-degenerate kernels.
New method defends deep nets against large perturbations perceptible to humans.
problem Vulnerability of deep nets to adversarial attacks with perceptible but not changing predictions.
method Oracle-Aligned Adversarial Training (OA-AT) to align network predictions with Oracle's.
result Achieves state-of-the-art performance at large perturbation bounds (L-inf of 16/255 on CIFAR-10).
Study asks if memory constraints affect optimal convex optimization methods.
problem Characterize the minimax number of queries for convex optimization with memory constraints.
method Analyze first order methods under memory limitations.
result Optimal oracle complexity may be achievable with limited memory.
META-DES.Oracle uses meta-learning and feature selection to improve ensemble selection accuracy.
problem Dynamic Ensemble Selection (DES) issues with classifier competence estimation.
method META-DES.Oracle integrates multiple criteria and an Oracle-based meta-feature selection scheme.
result META-DES.Oracle significantly improves classification accuracy compared to previous methods.
Paper tackles sampling from non-log-concave distributions using denoising diffusion.
problem Sampling from non-log-concave distributions efficiently.
method DDMC framework, Zeroth-Order Diffusion Monte Carlo (ZOD-MC) algorithm.
result ZOD-MC achieves inverse polynomial dependence on sampling accuracy, efficient for low dimensions.
A new method for faster optimization of noisy functions.
problem Optimizing noisy functions efficiently.
method A universal and adaptive second-order method for convex functions.
result Achieves O ( σ / T ) O(σ/ \sqrt{T}) O ( σ / T ) convergence for stochastic oracles and O ( 1 / T 3 ) O( 1 / T^3) O ( 1/ T 3 ) for deterministic oracles. Unified theory for UCB policies in total and max bandit problems.
problem Order optimality of UCB policies in max bandit problems.
method Unified definition of UCB policy using oracle quantity and failure count.
result UCB policies are order optimal in both total and max bandit problems.
Improved algorithm finds second-order stationary points in non-convex optimization.
problem Minimizing non-convex objectives while preserving training data privacy.
method SpiderBoost framework with two gradient oracles: precise and less precise.
result Improved rates for finding second-order stationary points.
Improved zeroth-order algorithms tackle nonconvex minimax problems with reduced complexity.
problem Nonconvex minimax optimization problems in machine learning.
method Design and analysis of Zeroth-Order Gradient Descent Ascent ( exttt{ZO-GDA}) and Zeroth-Order Gradient Descent Multi-Step Ascent ( exttt{ZO-GDMSA}) algorithms.
result Oracle complexity improvements for minimax optimization problems.
A new algorithm for solving constrained convex optimization problems efficiently.
problem Constrained convex optimization problems requiring high accuracy solutions.
method Second-Order Conditional Gradient Sliding (SOCGS) algorithm, using projection-free methods to solve quadratic subproblems inexactly.
result Converges quadratically in primal gap after a finite number of linearly convergent iterations.
Piecewise polynomial interpolation-based gradient descent reduces oracle complexity for smooth loss functions.
problem Optimizing empirical risk minimization loss functions
method Piecewise polynomial interpolation-based gradient descent
result Oracle complexity is reduced for smooth loss functions
Develops a new method for solving nonsmooth nonconvex optimization problems.
problem Solving nonsmooth nonconvex composite optimization problems with noisy gradient information.
method Combines stochastic higher order steps and additional stochastic proximal gradient steps.
result Global convergence to stationary points in expectation with favorable performance on large-scale problems.
Paper establishes tight lower bounds for minimizing certain smooth and convex functions.
problem Minimizing high-order Hölder smooth and uniformly convex functions.
method Analyzes two asymmetric cases of q > p + ν q > p + ν q > p + ν and q < p + ν q < p + ν q < p + ν using worst-case oracle complexities. result Establishes worst-case oracle complexities for reaching an ε-approximate solution.
New method improves CATE model selection with optimal regret rates.
problem Nontrivial task of selecting accurate CATE models.
method Causal Q-aggregation using doubly robust loss.
result Achieves optimal oracle model selection regret rates of log(M)/n.
New algorithms optimize convex functions with high-order derivatives.
problem Optimizing convex functions with high-order derivatives under various norms.
method Developed a non-Euclidean inexact accelerated proximal point method using an inexact uniformly convex regularizer.
result Showed nearly optimal algorithms for high dimensions in the black-box oracle model for ℓ p \ell_p ℓ p -settings and all q ≥ 1 q \geq 1 q ≥ 1 . New algorithm tackles stochastic bilevel optimization under relaxed smoothness conditions.
problem Optimal algorithms for stochastic bilevel optimization under relaxed smoothness conditions.
method Introduces a novel fully single-loop and Hessian-inversion-free algorithmic framework for stochastic bilevel optimization.
result Demonstrates state-of-the-art oracle complexity results for multi-objective robust bilevel optimization.
New method finds stationary points in bilevel optimization problems.
problem Solving nonconvex-strongly-convex bilevel optimization problems.
method Restarted Accelerated HyperGradient Descent (RAHGD) method.
result Achieves best-known theoretical guarantees for finding stationary points in bilevel optimization.
Extracts fairness truth from classifiers using an oracle.
problem Fairness in classification algorithms without context.
method Uses fairness oracle to learn underlying fairness truth.
result Extracts metric fairness from classifiers.
We investigate properties of estimators obtained by minimization of U-processes with the Lasso penalty in high-dimensional settings. Our attention is focused on the ranking problem that is popular in machine learning. It is related to guessing the ordering between objects on the basis of their observed predictors. We p…
New analysis shows Thompson Sampling can work with greedy approximations in combinatorial bandits.
problem Thompson Sampling's theoretical limits with greedy approximations in combinatorial semi-bandits.
method Study with greedy oracle, providing lower and upper bounds on regret.
result First theoretical results showing TS can work with greedy approximations, breaking misconceptions.
Study on gradient complexity of private optimization with private oracles.
problem Analyzing the efficiency of differentially private optimization algorithms.
method Lower bounds on the number of first-order oracle queries for private optimization.
result Lower bounds on the number of queries for private optimization algorithms, showing a dimension-dependent runtime penalty.
Propose an XMSE-aware mixed estimator for EB that interpolates between ML and EB shrinkage.
problem Kernel-based EB estimation may be worse than ML when the kernel is poorly aligned with the true parameter.
method An XMSE-aware mixed estimator that interpolates between ML and EB shrinkage.
result Fixed-weight XMSE is a scalar quadratic, yielding a closed-form oracle mixing weight that is no worse than both ML and the base EB estimator at the XMSE scale.
Improved stochastic approximation method reduces residual error.
problem Reducing residual error in stochastic approximation algorithms.
method Fixed-schedule one-quarter barrier and bias-corrected acceleration.
result Achieves T − 1 / 2 + o ( 1 ) T^{-1/2+o(1)} T − 1/2 + o ( 1 ) residual reduction with O ( 1 ) O(1) O ( 1 ) primitive samples. New algorithms reduce reinforcement learning regret in factored MDPs.
problem Optimizing reinforcement learning in non-episodic factored MDPs.
method Proposed two near-optimal and oracle-efficient algorithms for FMDPs.
result Oracle-efficient algorithms achieve near-optimal regret bounds of O ( D S A T ) O(DS\sqrt{AT}) O ( D S A T ) . Study improves CTS's approximation regret for combinatorial bandits.
problem Improving CTS's performance on non-exact oracles.
method Develops a new O ( log ( T ) / Δ ) \mathcal{O}(\log(T)/Δ) O ( log ( T ) /Δ ) upper bound for CTS under specific conditions. result First O ( log ( T ) / Δ ) \mathcal{O}(\log(T)/Δ) O ( log ( T ) /Δ ) approximation regret upper bound for CTS. Algorithm tackles large-scale portfolio optimization with higher moments, improving computational efficiency.
problem Optimizing portfolios with higher moments (variance, skewness, kurtosis) for large asset universes is computationally infeasible.
method Developed a structure-exploiting algorithm based on Yau's affine-normal descent, working directly with return matrix.
result Algorithm avoids explicit higher-order tensors and exploits quartic structure for efficient computation.
New algorithm solves complex optimization problems without needing projections.
problem Optimizing nested functions under convex constraints with noisy evaluations.
method Projection-free conditional gradient-type algorithm for smooth stochastic multi-level composition optimization.
result The algorithm achieves ε ε ε -stationary solutions with complexity bounds independent of ε ε ε and T T T . Proposes using oracle feedback to predict and prevent errors in RL agents.
problem Mismatches between simulated and real-world environments lead to errors in reinforcement learning.
method Formalizes the problem as a noisy supervised learning task, combines techniques for label aggregation, calibration, and supervised learning.
result Achieves higher predictive performance than baseline methods and can prevent errors by selectively querying an oracle.
Paper develops a TR-SSQP method for noisy optimization with heavy-tailed noise.
problem Optimization problems with stochastic objectives and heavy-tailed noise.
method Trust-Region Stochastic Sequential Quadratic Programming (TR-SSQP) method.
result Achieves high-probability first-order and second-order stationarity bounds for heavy-tailed noise.
Proposes a new model to generate informative samples for image classification without querying an oracle.
problem Expensive and difficult labeling of data for machine learning models.
method Integrates active learning with a conditional GAN to generate samples with high uncertainty for a specific label.
result Generated samples improve image classification performance without querying an oracle.
Improved method reduces projection calls for nonsmooth convex optimization.
problem Optimizing nonsmooth convex functions with convex constraints.
method MOPES and MOLES methods combining Moreau-Yosida smoothing and accelerated first-order schemes.
result Achieves ε ε ε -suboptimality with significantly fewer projection calls. New algorithm optimizes convex functions with noisy evaluations in one dimension.
problem Optimizing convex functions with noisy zero-order evaluations in one dimension.
method Proposed a computationally efficient algorithm achieving O ( 1 / T ) O(1/\sqrt{T}) O ( 1/ T ) convergence rate. result Achieved the optimal O ( 1 / T ) O(1/\sqrt{T}) O ( 1/ T ) convergence rate, closing the gap in one dimension. Study on tradeoffs between mistakes and ERM oracle calls in online and transductive learning.
problem Analyzing online and transductive learning with limited ERM and weak consistency oracle access.
method Proves lower bounds and upper bounds on mistakes and oracle calls, considering realizable and agnostic cases.
result Achieves optimal mistake bounds with weak consistency queries for certain concept classes.
Paper introduces structured sparsity estimators for Generalized Linear Models.
problem Estimating structured sparsity in GLMs with debiased estimators.
method Extends Stucky and van de Geer's results to GLMs with structured sparsity.
result Proves oracle inequalities for structured sparsity estimators in GLMs.
Representation learning systems typically rely on massive amounts of labeled data in order to be trained to high accuracy. Recently, high-dimensional parametric models like neural networks have succeeded in building rich representations using either compressive, reconstructive or supervised criteria. However, the seman…
New methods solve optimization problems with heavy-tailed noise, improving upon existing complexity bounds.
problem Optimization problems with heavy-tailed noise and weakly average smoothness.
method Normalized stochastic first-order methods with Polyak, multi-extrapolated, and recursive momentum.
result First-order oracle complexity results for finding approximate stochastic stationary points under heavy-tailed noise.