We study online convex optimization under stochastic sub-gradient observation faults, where we introduce adaptive algorithms with minimax optimal regret guarantees. We specifically study scenarios where our sub-gradient observations can be noisy or even completely missing in a stochastic manner. To this end, we propose…
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48 results for “stochastic minimax optimization”
The paper analyzes generalization bounds for NC-SC/NC-C stochastic minimax optimization.
problem Generalization analysis of nonconvex-(strongly)-concave stochastic minimax optimization.
method Established algorithm-agnostic and algorithm-dependent generalization bounds via uniform convergence and stability arguments.
result Sample complexities and generalization bounds for NC-SC and NC-C settings.
New analysis improves understanding of bilevel optimization stability and generalization.
problem Understanding how well bilevel optimization algorithms generalize.
method Algorithmic stability arguments and generalization bounds for three bilevel minimax solvers.
result Precise trade-off between algorithmic stability, generalization gaps, and practical settings.
A new decentralized method solves minimax problems with reduced communication and sample complexity.
problem Solving minimax optimization problems in a distributed setting.
method Decentralized stochastic gradient descent ascent with variance reduction.
result Achieved optimal sample and communication complexities for nonconvex-strongly-concave problems.
Paper proposes ZO-SMD for MERO, achieving optimal convergence rates.
problem Minimizing excess risk across all test distributions.
method Zeroth-order stochastic mirror descent algorithm for both smooth and non-smooth MERO.
result Converges at optimal rates of for estimates and optimization errors.
New algorithm solves federated minimax optimization problems.
problem Federated minimax optimization challenges.
method Federated Stochastic Smoothed Gradient Descent Ascent (FESS-GDA).
result FESS-GDA uniformly solves federated minimax problems.
New algorithm AG-OG optimizes separable convex-concave problems efficiently.
problem Efficiently solving separable convex-concave minimax optimization problems.
method Leverages Nesterov acceleration and optimistic gradient on component and coupling parts of the problem.
result Achieves optimal convergence rate for various settings including bilinearly coupled problems.
New methods solve complex optimization problems without strong convexity assumptions.
problem Complex bilevel optimization problems with minimax lower-level structures.
method Penalty-based first-order methods for bilevel minimax optimization.
result Achieves -KKT point with improved oracle complexity.
New research shows existing information-theoretic methods can't establish minimax rates for gradient descent in stochastic convex optimization.
problem Establishing minimax rates for gradient descent in stochastic convex optimization using information-theoretic methods.
method Examined several information-theoretic frameworks including input-output mutual information bounds, conditional mutual information bounds, PAC-Bayes bounds, and their variants.
result Proved that none of the examined information-theoretic frameworks can establish minimax rates for gradient descent in stochastic convex optimization.
Paper improves risk bounds for nonconvex-strongly-concave minimax problems.
problem Achieving sharper risk bounds for nonconvex-strongly-concave minimax problems.
method Using uniform localized convergence to derive high probability generalization error bounds.
result Derives n times faster excess primal risk bounds for popular algorithms.
This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply characterizing the stationary covariance matrix of this process. The…
Paper explores generalization of minimax learners, proposing a new metric.
problem Understanding how minimax learners perform on unseen data.
method Proposes a new metric, the primal gap, to study generalization of minimax learners.
result Derives generalization error bounds for the primal gap in nonconvex-concave settings.
Study minimax-optimal rates for offline decision-making with function approximation.
problem Statistical complexity of offline decision-making with function approximation.
method Near minimax-optimal rates for stochastic contextual bandits and Markov decision processes, using pseudo-dimension and behavior policy.
result Established performance limits and new characterization of behavior policy.
New framework for DP-SMO with near-optimal privacy-loss trade-off.
problem Optimal trade-off between privacy and population loss in DP-SMO.
method General framework using Phased-ERM method and black-box optimization.
result Near-linear time algorithms with near-optimal guarantees.
We extend the traditional worst-case, minimax analysis of stochastic convex optimization by introducing a localized form of minimax complexity for individual functions. Our main result gives function-specific lower and upper bounds on the number of stochastic subgradient evaluations needed to optimize either the functi…
Optimal algorithm for high-dimensional stochastic linear bandits with sparse parameters.
problem High-dimensional stochastic linear bandits with sparse parameters.
method Three-stage arm selection algorithm using thresholded Lasso for estimation.
result Achieves exact minimax optimality in cumulative regret.
We propose the kl-UCB ++ algorithm for regret minimization in stochastic bandit models with exponential families of distributions. We prove that it is simultaneously asymptotically optimal (in the sense of Lai and Robbins' lower bound) and minimax optimal. This is the first algorithm proved to enjoy these two propertie…
We study computational and statistical consequences of problem geometry in stochastic and online optimization. By focusing on constraint set and gradient geometry, we characterize the problem families for which stochastic- and adaptive-gradient methods are (minimax) optimal and, conversely, when nonlinear updates -- su…
Stochastic Optimization in Semi-Discrete Optimal Transport: Convergence Analysis and Minimax Ratemath.ST
Stochastic optimization improves semi-discrete OT map estimation with a minimax rate.
problem Empirical success of SGD in semi-discrete OT, but lack of theoretical guarantees.
method Averaged projected SGD with a minimax convergence rate of O(1/√n).
result SGD methods can estimate the OT map with a minimax convergence rate of O(1/√n).
In this paper, we study zeroth-order algorithms for minimax optimization problems that are nonconvex in one variable and strongly-concave in the other variable. Such minimax optimization problems have attracted significant attention lately due to their applications in modern machine learning tasks. We first consider a …
Optimal Guarantees for Algorithmic Reproducibility and Gradient Complexity in Convex Optimizationcs.LG
New algorithms ensure reproducibility and optimal convergence in convex optimization.
problem Trade-off between reproducibility and convergence rate in convex optimization.
method Regularization-based algorithms for smooth convex minimization and minimax optimization.
result Achieves optimal reproducibility and near-optimal gradient complexity for various oracle settings.
Paper tackles gradient-free minimax optimization with variance reduction for faster convergence.
problem Gradient-free minimax optimization problems in machine learning.
method Variance reduction technique to design a novel zeroth-order gradient descent ascent algorithm.
result Achieves the best known query complexity of O(κ(d₁ + d₂)ε⁻³), outperforming previous methods.
This paper analyzes neural networks for solving complex optimization problems.
problem Minimax optimization problems in infinite-dimensional function spaces.
method Mean-field analysis of stochastic gradient descent-ascent in neural networks.
result The algorithm converges to a stationary point at a sublinear rate.
We consider the mixed regression problem with two components, under adversarial and stochastic noise. We give a convex optimization formulation that provably recovers the true solution, and provide upper bounds on the recovery errors for both arbitrary noise and stochastic noise settings. We also give matching minimax …
Implicit Finite-Horizon Approximation and Efficient Optimal Algorithms for Stochastic Shortest Pathcs.LG
New algorithms minimize regret in SSP with optimal sparse updates.
problem Minimizing regret in Stochastic Shortest Path models.
method Implicit finite-horizon approximation for analysis, model-free and model-based algorithms developed.
result Minimax optimal regret for both model-free and model-based algorithms.
VRPG algorithm optimizes convex constraints with non-asymptotic guarantees.
problem Stochastic convex optimization under convex constraints.
method Natural variance reduced proximal gradient (VRPG) algorithm.
result VRPG achieves local minimax lower bound up to constants and log factor of .
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.
Despite remarkable empirical success, the training dynamics of generative adversarial networks (GAN), which involves solving a minimax game using stochastic gradients, is still poorly understood. In this work, we analyze last-iterate convergence of simultaneous gradient descent (simGD) and its variants under the assump…
Study finds optimal regret bound for multi-armed bandit problem with expert advice.
problem Optimizing decision-making in a multi-armed bandit problem with expert advice.
method Proved a tight lower bound matching the upper bound of Kale (2014) for minimax expected regret.
result The minimax optimal expected regret is Θ(√(T K log (N/K))) for the problem.
In this paper, we study the minimax optimization problem in the smooth and strongly convex-strongly concave setting when we have access to noisy estimates of gradients. In particular, we first analyze the stochastic Gradient Descent Ascent (GDA) method with constant stepsize, and show that it converges to a neighborhoo…
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 for single-loop algorithms.
Kernel estimator optimally recovers function from noisy exponential Radon transform.
problem Inverting noisy exponential Radon transform of a function.
method Proposed a kernel estimator to estimate the true function.
result The estimator converges to the true function at minimax optimal rate.
Paper presents an efficient algorithm for learning minimax risk classifiers with large-scale data.
problem Efficient learning of minimax risk classifiers for large-scale data with multiple classes.
method Combination of constraint and column generation for efficient learning.
result 10x speedup for general large-scale data and 100x speedup with many classes.
The paper analyzes how optimization algorithms affect the generalization of minimax models.
problem The generalization performance of minimax models trained with different optimization algorithms.
method Analysis of gradient descent ascent (GDA) and proximal point method (PPM) algorithms under convex concave and non-convex non-concave settings.
result The PPM algorithm ensures a bounded excess risk in convex concave problems, while GDA's generalization depends on solving subproblems simultaneously.
New random forest variants achieve optimal performance in high dimensions.
problem Handling dependencies between features in high-dimensional data.
method Using oblique splits in random forests with general split directions.
result Achieved minimax optimal convergence rates in arbitrary dimension.
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.
Sampling without replacement speeds up optimization in minimax problems.
problem Optimizing minimax problems with faster convergence rates.
method Analysis of gradient descent ascent and proximal point method with two sampling strategies.
result Sampling without replacement leads to faster convergence rates in minimax optimization.
New algorithms achieve optimal robustness in stochastic convex optimization under contamination.
problem Determining optimal rates for robust stochastic convex optimization under -contamination.
method Developed novel algorithms achieving minimax-optimal excess risk under -contamination model without stringent assumptions.
result Achieved minimax-optimal excess risk (up to logarithmic factors) under -contamination model.
New RL algorithm minimizes distributional learning error.
problem Improving distributional reinforcement learning for better error minimization.
method Proposes a new model-based algorithm with theoretical minimax optimality.
result Proves minimax optimality for approximating return distributions.
We consider nonconvex-concave minimax optimization problems of the form , where is strongly-concave in but possibly nonconvex in and is a convex and compact set. We focus on the stochastic setting, where we can only access an…
Paper develops efficient algorithms for robust optimization across multiple groups.
problem Minimizing maximal empirical risk across distinct groups in robust optimization.
method Develops ALEG and ALEM algorithms for two-level finite-sum convex-concave minimax optimization.
result Achieves ε-accuracy with complexity O(m√(nlnm/ε)) and outperforms state-of-the-art methods.
Paper analyzes nonconvex bandit problems with improved adaptive methods.
problem Continuous armed bandit problems for nonconvex cost functions.
method Simple and adaptive bin splitting methods.
result Adaptive method achieves locally minimax optimal expected cumulative regret.
Study optimizes financial strategies in markets with uncertain drift.
problem Optimizing portfolios in markets with unpredictable drift.
method Combines worst-case optimization with filtering techniques to define uncertainty sets.
result Proves minimax theorem and derives optimal strategies for continuous updates.
New analysis of stochastic approximation with non-expansive mappings.
problem Finite-time analysis of two-time-scale stochastic approximation with non-expansive mappings.
method Studied two-time-scale stochastic approximation algorithms with non-expansive mappings and projection steps.
result Last-iterate mean square residual error decays at a rate .
Paper introduces SGD for nonparametric additive models with optimal risk.
problem Training nonparametric additive models efficiently and accurately.
method Iterative algorithm based on stochastic gradient descent for truncated basis expansions.
result Estimator achieves minimax optimal risk in well-specified settings.
New SGDA method speeds up nonconvex minimax optimization.
problem Improving convergence of nonconvex minimax optimization.
method SGDA with random reshuffling for nonconvex-PŁ objectives.
result Convergence rates faster than with-replacement SGDA.
Optimal algorithm for linear bandits on ellipsoids with minimax regret bound.
problem Linear stochastic bandits on ellipsoids.
method Novel sequential procedure to estimate norm of parameters, followed by an explore-and-commit strategy.
result Regret bound matches minimax lower bound with multiplicative constant.
Algorithm for bandits with switching costs achieves optimal regret bounds.
problem Optimal regret bounds for stochastic and adversarial bandits with switching costs.
method Adaptation of Tsallis-INF algorithm with no prior knowledge of regime or time horizon.
result Achieves minimax optimal regret bounds in various settings.