We investigate the use of Minimax distances to extract in a nonparametric way the features that capture the unknown underlying patterns and structures in the data. We develop a general-purpose and computationally efficient framework to employ Minimax distances with many machine learning methods that perform on numerica…
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48 results for “minimax objective”
This paper studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.
problem Optimizing an unknown function with limited evaluations.
method Studies continuum-armed bandits under Besov smoothness conditions and derives minimax rates.
result Minimax rates over Besov spaces are identical to those over the smallest Hölder space into which Besov spaces embed.
Proposes a fairness criterion for multi-objective optimization in classification.
problem Ensuring fairness in classification models across different groups.
method Formulates a minimax Pareto fairness criterion and provides an optimization algorithm.
result Demonstrates improved fairness compared to existing methods on various real-world datasets.
Efficient sampling reduces memory usage for Minimax distance analysis.
problem Quadratic memory requirement for existing Minimax distance methods.
method Proposes a novel sampling technique with linear space complexity.
result Demonstrates significant reduction in memory usage for Minimax distances.
ConquerNet smooths quantile regression for deep learning with minimax guarantees.
problem Optimization challenges in quantile regression for deep models.
method ConquerNet uses convolution-smoothed quantile ReLU neural networks.
result ConquerNet provides minimax guarantees and outperforms standard quantile neural networks.
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.
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.
Benchmarking Minimax Linkagestat.ML
Minimax linkage was first introduced by Ao et al. [3] in 2004, as an alternative to standard linkage methods used in hierarchical clustering. Minimax linkage relies on distances to a prototype for each cluster; this prototype can be thought of as a representative object in the cluster, hence improving the interpretabil…
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.
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.
We study the problem of alleviating the instability issue in the GAN training procedure via new architecture design. The discrepancy between the minimax and maximin objective values could serve as a proxy for the difficulties that the alternating gradient descent encounters in the optimization of GANs. In this work, we…
Paper proposes algorithms for solving nonconvex-nonconcave problems with complexity guarantees.
problem Nonconvex-nonconcave minimax problems with PL condition.
method Zeroth-order AGDA and VRAGDA algorithms.
result Iteration complexities for obtaining ε-stationary points.
New findings suggest minimax optimality doesn't guarantee distribution learning for GANs.
problem Understanding when GANs can truly learn the underlying distribution.
method Using cryptographic assumptions and ReLU network generators, the paper shows that achieving minimax optimality is insufficient for distribution learning.
result Achieving minimax optimality is insufficient for distribution learning in the usual statistical sense.
The paper tackles robust policy learning from multiple data sources.
problem Learning a policy that generalizes across diverse settings from multiple heterogeneous data sources.
method Proposes a minimax regret optimization objective and a policy learning algorithm combining doubly robust offline policy evaluation and no-regret learning.
result Achieves minimal worst-case mixture regret up to a moderated vanishing rate of the total data across all sources.
The paper identifies network bottlenecks using minimax paths in stochastic networks.
problem Identifying bottlenecks in networks with stochastic weights.
method Modeling as combinatorial semi-bandit problem, applying combinatorial Thompson Sampling, and approximating the original objective due to computational intractability.
result Established an upper bound on Bayesian regret and evaluated Thompson Sampling performance on real-world networks.
New algorithm solves minimax games with linear constraints.
problem Nonconvex minimax games with coupled linear constraints.
method Primal-dual alternating proximal gradient (PDAPG) algorithm.
result Achieves ε-stationary solution within O(ε^(-2)) iterations for strongly concave settings.
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.
There is a rapidly increasing interest in crowdsourcing for data labeling. By crowdsourcing, a large number of labels can be often quickly gathered at low cost. However, the labels provided by the crowdsourcing workers are usually not of high quality. In this paper, we propose a minimax conditional entropy principle to…
Study minimax regret in sequential probability assignment with and without side information.
problem Minimax regret analysis in sequential probability assignment.
method Upper and lower bounds on minimax regret using square-root entropy.
result Lower bound matches upper bound for Donsker classes, up to log factors.
The paper analyzes the efficiency of unlearning methods and establishes bounds for minimax computation times.
problem Efficiency of removing specific data points from a trained model without full retraining.
method Analysis of unlearning methods and establishment of upper and lower bounds on computation times.
result A phase diagram for the unlearning complexity ratio, revealing three regimes of feasibility.
Recently, researchers have discovered that the state-of-the-art object classifiers can be fooled easily by small perturbations in the input unnoticeable to human eyes. It is also known that an attacker can generate strong adversarial examples if she knows the classifier parameters. Conversely, a defender can robustify …
This paper tackles convex-submodular minimax problems in mixed continuous-discrete domains.
problem Convex-submodular minimax problems in mixed continuous-discrete domains.
method Introduces new notions of optimality and proposes iterative algorithms combining discrete and continuous optimization.
result Characterizes convergence rates, computational complexity, and quality of solutions for convex and monotone-submodular minimax problems.
MRCpy implements minimax risk classifiers with performance guarantees and distribution shift adaptability.
problem Classical risk minimization approaches are not robust to distribution shifts.
method Robust risk minimization approach for minimax risk classifiers.
result MRCs provide performance guarantees and adapt to distribution shifts.
The paper optimizes risk-sensitive RL with CVaR, achieving near-minimax-optimal results.
problem Optimizing risk-sensitive reinforcement learning with CVaR objective.
method Developed algorithms for multi-arm bandits and online RL in MDPs, achieving near-minimax-optimal regret.
result Achieved near-minimax-optimal regret of for constant .
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.
Develops a robust learning method for unknown context distributions.
problem Learning from data in different, unknown contexts.
method Focuses on excess risks, constructs distribution sets with statistical coverage.
result Shows robustness in worst-case scenarios without sacrificing nominal performance.
AGDA and variance-reduced methods solve nonconvex-nonconcave minimax problems globally and faster.
problem Solving nonconvex-nonconcave minimax problems in machine learning.
method Global convergence of AGDA and variance-reduced algorithms.
result AGDA and variance-reduced methods achieve global convergence and faster rates.
Score attack method provides a lower bound on privacy-constrained minimax risk.
problem Characterizing the optimality of privacy-constrained statistical models.
method Score attack based on tracing attack concept.
result Optimally lower bounds the minimax risk of estimating unknown model parameters.
Several problems such as network intrusion, community detection, and disease outbreak can be described by observations attributed to nodes or edges of a graph. In these applications presence of intrusion, community or disease outbreak is characterized by novel observations on some unknown connected subgraph. These prob…
The paper tackles minimax optimality in continuum contextual bandits with Hölder continuity.
problem Minimizing regret in a continuum of contexts with Hölder continuity.
method Proves a static-to-contextual regret conversion theorem and analyzes various dependency cases.
result Achieves minimax optimal contextual regret for convex and strongly convex bandits.
Efficient algorithm for global optimization of multivariate Lipschitz functions.
problem Global optimization of multivariate Lipschitz continuous functions.
method Proposes an efficient minimax optimal algorithm using a predetermined query creation rule.
result Achieves an average regret bound of , minimax optimal.
Negative momentum accelerates convergence in minimax games but at a suboptimal rate.
problem The convergence rate of negative momentum in minimax games is suboptimal.
method Extending variational inequality formulation, connecting momentum method with Chebyshev polynomials.
result Negative momentum accelerates convergence locally but at a suboptimal rate.
New methods estimate transport-growth pairs in unbalanced optimal transport.
problem Statistical guarantees for Monge-type estimation in unbalanced optimal transport remain limited.
method Developed two estimators for transport-growth pairs under different setups.
result Achieved minimax optimal rate for estimation of transport-growth pairs.
A federated minimax framework for heterogeneous clients.
problem Training with edge devices having different datasets and capabilities.
method Proposes a federated minimax optimization framework with normalized updates.
result Improves convergence and communication complexity for nonconvex functions.
Novel methods for accelerating optimization in complex bilevel and minimax problems.
problem Optimization challenges in bilevel and minimax problems, especially when strong convexity assumptions are not met.
method Accelerated fully first-order methods for Bilevel Optimization (BLO) and Minimax Optimization (NCSC).
result State-of-the-art complexity for finding approximate second-order stationary points in BLO and NCSC.
Paper proposes SMO for solving bilevel optimization problems efficiently.
problem Solving bilevel optimization problems with nonsmooth convex lower-level and nonconvex upper-level objectives.
method Sequential minimax optimization (SMO) method using modified augmented Lagrangian and penalty schemes.
result Improves operation complexity for finding -KKT solutions.
Subspace Perspective on Canonical Correlation Analysis: Dimension Reduction and Minimax Ratesmath.ST
Canonical correlation analysis (CCA) is a fundamental statistical tool for exploring the correlation structure between two sets of random variables. In this paper, motivated by recent success of applying CCA to learn low dimensional representations of high dimensional objects, we propose to quantify the estimation loss…
This work optimizes identifying good arms in nonparametric multi-armed bandits.
problem Efficiently identifying arms with high means in nonparametric settings.
method Combining reward-maximizing sampling with a nonparametric sequential test for anytime-valid labeling.
result Achieves minimax optimal stopping times for identifying arms above a threshold.
The paper analyzes PPM for nonconvex-nonconcave problems, identifying three regions with varying convergence guarantees.
problem Challenges in nonconvex-nonconcave minimax optimization.
method Classic proximal point method with insights from the Moreau envelope.
result Identification of three regions with varying convergence guarantees for PPM.
GL-LowPopArt improves minimax-optimal estimation for trace regression.
problem Minimizing estimation error in generalized low-rank trace regression.
method Two-stage approach: nuclear norm regularization followed by matrix Catoni estimation.
result Achieves instance-wise optimal error bounds up to condition number.
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).
Study optimizes portfolio allocation policies using off-policy data and constraints.
problem Optimizing portfolio allocation policies under constraints using off-policy data.
method Solves a minimax objective with off-policy estimators and online learning to control constraint violations.
result Constructs near-optimal allocation policies for various regimes of operation and constraints.
Study detects boundaries in unlabeled noisy images without labels.
problem Detecting boundaries in unlabeled noisy images without labels.
method Proposed a continuous hinge-type surrogate loss for boundary detection, combined with deep neural networks.
result Deep neural network achieves minimax-optimal boundary recovery rate under piecewise smooth boundary model.
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.
SATL adapts to varying smoothness in hypothesis transfer learning.
problem Fixed kernel regularization fails in varying smoothness settings.
method Proposes SATL, a two-phase KRR algorithm with adaptive Gaussian kernels.
result SATL achieves minimax optimality with matching upper and lower bounds.
Combinatorial optimization problems for clustering are known to be NP-hard. Most optimization methods are not able to find the global optimum solution for all datasets. To solve this problem, we propose a global optimal path-based clustering (GOPC) algorithm in this paper. The GOPC algorithm is based on two facts: (1) …
Optimal algorithm for identifying best-arm with minimal regret.
problem Identifying the best arm in two treatments with limited budget.
method Neyman allocation based on outcome standard deviations.
result Neyman allocation is minimax optimal for simple regret.
Optimizes variational inference for dynamic network models.
problem Estimating pairwise inner products and intercepts in dynamic latent space models.
method Structured mean-field variational inference with block coordinate ascent algorithm.
result Variational risk attains minimax optimal rate with logarithmic factor under certain conditions.