New single-loop algorithm tackles weakly convex constraints in stochastic optimization.
problem Optimization with weakly convex constraints in machine learning.
method Single-loop penalty-based stochastic algorithm using hinge-based penalty.
result Achieves state-of-the-art complexity for finding approximate KKT solutions.
New algorithms improve convergence of minimax optimization.
problem Minimax optimization convergence issues in nonconvex problems.
method Established new convergence results for two single-loop algorithms.
result Improved convergence rates for minimax optimization.
SLEDGE algorithm reduces gradient computation errors in optimization.
problem Accumulated errors in gradient estimation methods for large-scale optimization.
method Single-loop method for finite-sum nonconvex optimization without periodic gradient refresh.
result Achieves nearly optimal gradient complexity and second-order optimality.
A new algorithm solves bilevel optimization with linear constraints.
problem Solving bilevel optimization problems with coupled linear constraints.
method Penalty and augmented Lagrangian methods reformulate the problem; a single-loop, first-order algorithm proposed.
result Improved convergence rates compared to prior methods.
New algorithms reduce complexity for solving nonconvex optimization problems with stochastic objectives and constraints.
problem Solving nonconvex optimization problems with stochastic objectives and constraints.
method Single-loop quadratic penalty and augmented Lagrangian algorithms with variance reduction techniques.
result Achieved best-known complexity guarantees for solving nonconvex optimization problems with stochastic objectives and constraints.
Paper achieves ε−2 sample complexity for actor-critic methods with minimal assumptions.
problem Achieving ε−2 sample complexity for actor-critic methods under minimal assumptions. method Single-loop, single-timescale implementation; coupled Lyapunov drift framework.
result First ildeO(ε−2) sample complexity guarantee for finding an ε-optimal policy. New algorithm solves complex non-convex problems efficiently.
problem Non-smooth non-convex problems with weakly convex and strongly concave components.
method Stochastic Moreau envelope approximate gradient method (SMAG).
result First single-loop algorithm with state-of-the-art convergence rate.
We introduce a hybrid stochastic estimator to design stochastic gradient algorithms for solving stochastic optimization problems. Such a hybrid estimator is a convex combination of two existing biased and unbiased estimators and leads to some useful property on its variance. We limit our consideration to a hybrid SARAH…
Unified framework for decentralized bilevel optimization with various heterogeneity-correction strategies.
problem Decentralized bilevel optimization with neighborhood communications and data heterogeneity.
method SPARKLE: Single-loop Primal-dual Algorithm for decentralized bilevel optimization, incorporating various heterogeneity-correction techniques.
result Unified convergence analysis for SPARKLE with state-of-the-art convergence rates compared to existing algorithms.
Two single-timescale algorithms improve TD learning with nonlinear approximations.
problem Optimizing TD learning with nonlinear smooth function approximation.
method Proposes two single-timescale single-loop algorithms with momentum and variance reduction.
result Achieves O(ε−4) sample complexity for the first algorithm and O(ε−3) for the second. New algorithms solve nonconvex-concave minimax problems without parameter knowledge.
problem Solving nonconvex-concave minimax problems efficiently.
method Three completely parameter-free single-loop algorithms.
result Achieve optimal iteration complexity for nonconvex-concave minimax problems.
New algorithm solves complex minimax problems efficiently.
problem Minimizing and maximizing bilinearly coupled smooth functions.
method Lifted Primal-Dual (LPD) method that optimally handles both smooth and bilinear terms.
result First optimal algorithm achieving the lower complexity bound for the problem.
Fast algorithm for online optimization on transport polytopes.
problem Optimizing convex objectives on transport polytopes.
method Mirror Sinkhorn algorithm combining Sinkhorn scaling and mirror descent.
result Robust and efficient online optimization for convex objectives.
Efficient federated algorithm for calculating transportation barycenter.
problem Efficiently calculating the free-support transportation barycenter in a federated setting.
method Single-loop dual decomposition algorithm that uses only aggregated information.
result Significantly scalable and low-complexity algorithm for federated computation.
Paper proposes an algorithm to solve complex minimax problems efficiently.
problem Stochastic nonconvex-concave minimax problems in various fields.
method Accelerated first-order regularized momentum descent ascent algorithm (FORMDA).
result Achieves best-known complexity bound of ildeO(ε−6.5) for single-loop algorithms. We introduce several methods to define the self-inductance of a single loop as the regularization of divergent integrals which we obtain by applying Neumann (or Weber) formula for the mutual inductance of a pair of loops to the case when two loops are identical.
This paper improves convergence bounds for AC and NAC algorithms with function approximation.
problem Improving convergence bounds for actor-critic algorithms with function approximation.
method Non-asymptotic analysis of AC and NAC algorithms with compatible function approximation.
result Eliminates the term ε_critic from the error bounds while maintaining best known sample complexities.
Reciprocal processes are acausal generalizations of Markov processes introduced by Bernstein in 1932. In the literature, a significant amount of attention has been focused on developing dynamical models for reciprocal processes. Recently, probabilistic graphical models for reciprocal processes have been provided. This …
Many machine learning tasks can be formulated in terms of predicting structured outputs. In frameworks such as the structured support vector machine (SVM-Struct) and the structured perceptron, discriminative functions are learned by iteratively applying efficient maximum a posteriori (MAP) decoding. However, maximum li…
New algorithm for solving minimax problems over distributions converges to Nash equilibrium.
problem Solving minimax problems over probability distributions.
method Symmetric Mean-field Langevin Dynamics (MFL-AG and MFL-ABR) with weighted averaging and best response dynamics.
result Converges to mixed Nash equilibrium with average-iterate and last-iterate convergence.
New IRL algorithm identifies optimal reward and policy from expert demonstrations.
problem Understanding reward functions from expert demonstrations with neural networks.
method Two-timescale single-loop IRL algorithm for neural network parameterized rewards.
result First IRL algorithm with non-asymptotic convergence guarantee and global optimality in neural network settings.
New algorithm solves nonconvex-convex minimax problems efficiently.
problem Solving nonconvex-convex minimax problems with nonsmooth, nonconvex, and nonlinearity.
method Hybrid variance-reduced SGD algorithm combining smoothing and biased techniques.
result Achieves O(T^(-2/3)) convergence rate and best oracle complexity.
TiAda adapts adaptive gradient methods for nonconvex minimax optimization.
problem Nonconvex minimax optimization challenges in achieving convergence.
method TiAda is a time-scale adaptive GDA algorithm for nonconvex minimax optimization.
result TiAda achieves near-optimal complexities in deterministic and stochastic settings.
We study online learning when partial feedback information is provided following every action of the learning process, and the learner incurs switching costs for changing his actions. In this setting, the feedback information system can be represented by a graph, and previous works studied the expected regret of the le…
Nesterov's accelerated gradient descent (AGD), an instance of the general family of "momentum methods", provably achieves faster convergence rate than gradient descent (GD) in the convex setting. However, whether these methods are superior to GD in the nonconvex setting remains open. This paper studies a simple variant…
Computing partition function is the most important statistical inference task arising in applications of Graphical Models (GM). Since it is computationally intractable, approximate methods have been used to resolve the issue in practice, where mean-field (MF) and belief propagation (BP) are arguably the most popular an…
AdaSDBO solves decentralized bilevel optimization without problem parameters, achieving competitive performance.
problem Decentralized bilevel optimization problems without known parameters.
method AdaSDBO, a fully problem-parameter-free algorithm with adaptive stepsizes.
result AdaSDBO achieves a convergence rate of $\widetilde{\mathcal{O}}\left(\frac{1}{T}
ight)$, matching state-of-the-art methods up to polylogarithmic factors.
We introduce a new approach to develop stochastic optimization algorithms for a class of stochastic composite and possibly nonconvex optimization problems. The main idea is to combine two stochastic estimators to create a new hybrid one. We first introduce our hybrid estimator and then investigate its fundamental prope…
New algorithms eliminate stepsize tuning for bilevel optimization problems.
problem Bilevel optimization problems with unknown parameters and stepsizes.
method D-TFBO and S-TFBO algorithms with adaptive stepsizes.
result Achieve performance comparable to well-tuned approaches with theoretical guarantees.
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.
A new algorithm speeds up sparse-penalized quantile regression solving non-convex penalties.
problem Sparse-penalized quantile regression with non-convex penalties.
method Single-loop smoothing ADMM (SIAD) algorithm for faster convergence.
result SIAD method outperforms existing approaches in solving sparse-penalized quantile regression.
Two algorithms solve nonconvex minimax problems with linear constraints, achieving complexity guarantees.
problem Nonconvex minimax problems with coupled linear constraints.
method Zeroth-order primal-dual alternating projected gradient (ZO-PDAPG) and zeroth-order regularized momentum primal-dual projected gradient (ZO-RMPDPG) algorithms.
result Iteration complexity guarantees for solving nonconvex-(strongly) concave minimax problems with coupled linear constraints.
This paper tackles Sinkhorn DRO by reformulating it as a bilevel program and proposes sampling-based algorithms.
problem Distributionally robust optimization with ambiguity sets defined via the Sinkhorn discrepancy.
method Primal perspective reformulation as a bilevel program, double-loop and single-loop sampling-based algorithms.
result Simultaneously obtain the optimal robust decision and the worst-case distribution.
New algorithm optimizes stochastic optimization with circular dependency.
problem Circular dependency between decision variable and importance sampling.
method Single-loop stochastic approximation algorithm based on Nesterov's dual averaging.
result Achieves minimal asymptotic variance and resolves circular optimization challenge.
Paper tackles multi-block min-max optimization with applications in deep AUC maximization.
problem Multi-block min-max bilevel optimization with non-convex strongly-concave upper level and strongly convex lower level.
method Single-loop randomized stochastic algorithm for constant number of blocks per iteration.
result Sample complexity of O(1/ε^4) for finding ε-stationary point, matching optimal complexity.
New algorithm reduces MFGs with common noise complexity.
problem Prohibitive computational cost in solving MFGs with common noise.
method Signatured deep fictitious play based on rough path theory.
result Significantly reduced computational complexity and improved efficiency.
Novel algorithm reduces computational burden in IRL with finite-time guarantees.
problem Efficiently recover reward function and optimal policy from expert behavior.
method Single-loop algorithm that maximizes likelihood after each policy improvement step.
result Algorithm provably converges to a stationary solution with finite-time guarantees.
Expanding FCCO to non-smooth weakly-convex problems, improving deep learning performance.
problem Addressing the limitations of current FCCO methods by tackling non-smooth weakly-convex problems.
method Developed a single-loop algorithm for non-smooth weakly-convex FCCO and extended it to tri-level problems.
result Established the complexity for finding ε-stationary points in the Moreau envelop of the objective function.
This paper considers inference over distributed linear Gaussian models using factor graphs and Gaussian belief propagation (BP). The distributed inference algorithm involves only local computation of the information matrix and of the mean vector, and message passing between neighbors. Under broad conditions, it is show…
Algorithm estimates human decision-making in high-dimensional states with finite-time guarantees.
problem Estimating optimal policies and measures of fit in dynamic decision models with high-dimensional state spaces.
method Single-loop estimation algorithm with stochastic gradient steps for reward maximization.
result Algorithm converges to a stationary solution with finite-time guarantees and approximates maximum likelihood sublinearly.
New proof of Haken's Lemma and Scharlemann's theorem using thin position.
problem Proving Haken's Lemma and Scharlemann's theorem about Heegaard surfaces in 3-manifolds.
method Using thin position of Heegaard splittings.
result A new proof of Haken's Lemma and Scharlemann's theorem.
BADR framework optimizes fairness metrics efficiently.
problem Fairness-inefficient models in machine learning.
method Bilevel Adaptive Rescalarisation procedure.
result BADR framework recovers optimal Pareto-efficient models.
Develops a new method for efficient stochastic bilevel optimization.
problem Stochastic bilevel optimization problems in machine learning applications.
method Single-Timescale stochAstic BiLevEl optimization (STABLE) method.
result Achieves the same order of sample complexity as stochastic gradient descent for single-level optimization.
A new method reduces the complexity of decentralized optimization.
problem Decentralized stochastic non-convex optimization over a network.
method GT-HSGD, a hybrid variance-reduced method.
result Achieves an oracle complexity of O(n^(-1)ε^(-3)) for small ε.
We characterize a certain neck-pinching degeneration of (marked) CP1- structures on a closed oriented surface S of genus at least two. Namely, we consider a path Ct of CP1-structures on S leaving every compact subset in the deformation space of (marked) CP1-structures on S, such that its holonomy converges …
New method solves root-finding problems with faster convergence.
problem Finite-sum co-coercive equations
method Variance-reduced Krasnoselkii--Mann methods
result Achieves both O(1/k2) and o(1/k2) convergence rates Improved penalty-based methods for bilevel optimization with reduced complexity.
problem Suboptimal complexity in solving bilevel optimization problems with large penalty terms.
method Novel penalty reformulation that decouples upper and lower-level variables, enabling larger step sizes and reduced iteration complexity.
result PBGD-Free algorithm that avoids inner loops for coupled constraint BLO problems, with reduced iteration complexity.
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) residual reduction with O(1) primitive samples.