Since its inception, the modus operandi of multi-task learning (MTL) has been to minimize the task-wise mean of the empirical risks. We introduce a generalized loss-compositional paradigm for MTL that includes a spectrum of formulations as a subfamily. One endpoint of this spectrum is minimax MTL: a new MTL formulation…
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48 results for “minimax formulation”
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.
Improving Generalization of Reinforcement Learning with Minimax Distributional Soft Actor-Criticcs.LG
Improves RL generalization by minimizing adversarial risk.
problem Overfitting to training environments and poor generalization to unseen scenarios.
method Introduces minimax formulation and distributional framework to RL.
result Trained policy shows improved generalization to different environments.
Paper proposes FR algorithm to solve minimax optimization locally.
problem Gradient descent fails to find local minimax in minimax optimization.
method Follow-the-Ridge (FR) algorithm, addressing rotational behavior of gradient dynamics.
result FR algorithm provably converges to local minimax.
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 …
Paper develops minimax rates for non-exact sparse models in high dimensions.
problem Estimating non-exact sparse models in high-dimensional data.
method Formalizes approximate sparsity, derives minimax rates, proposes an estimator.
result Achieves minimax optimal rates for non-exact sparse models.
The paper addresses learner privacy in convex optimization with feedback.
problem Privacy risks from eavesdropping adversaries observing learner's queries.
method Optimally obfuscating learner's queries to make their learned optimal value hard to estimate.
result Query complexity overhead is additive in in the minimax formulation, multiplicative in in the Bayesian formulation.
Two new methods improve block-sparse signal recovery from noisy data.
problem Recovering block-sparse signals with unknown partitions.
method LogLOP-l2/l1 and AdaLOP-l2/l1 methods using log-sum penalty and MCP.
result Our methods outperform existing techniques in estimation accuracy.
Proposes MGCE for improved classification performance.
problem Optimizing between robustness and optimization difficulty in classification.
method Minimax formulation of GCE leading to convex optimization over margins.
result MGCE achieves strong accuracy and better calibration, especially in noisy labels.
Regularization can improve machine learning models' robustness against poisoning attacks.
problem Poisoning attacks degrade machine learning models' performance by manipulating a fraction of the training data.
method Proposes a novel optimal attack formulation considering the effect of hyperparameters on regularization, leading to better evaluation of robustness.
result Demonstrates that regularization can help mitigate the impact of poisoning attacks.
A new method defends against adversarial examples using minimax optimization.
problem Adversarial examples can fool state-of-the-art classifiers.
method Formulated as a two-player game, proposed minimax optimization algorithm.
result Numerical minimax defense is more robust than non-minimax defenses.
Bayesian neural networks are shown to be minimax and admissible under certain conditions.
problem Optimality of Bayesian neural networks in deep learning models.
method Analysis of decision rules induced by BNNs in the normal location model under quadratic loss.
result A hyperprior on the effective output variance yields a minimax and admissible decision rule.
Paper defines local optimality for sequential nonconvex-nonconcave games.
problem Defining local optimality in sequential nonconvex-nonconcave minimax optimization.
method Proposes local minimax definition and connects to gradient descent ascent.
result Gradient descent ascent stable limit points are local minimax points.
Paper develops a new method for differential privacy sampling using Wasserstein distance.
problem Sampling from distributions under differential privacy constraints with geometric structure consideration.
method Develops a novel framework with Wasserstein Projection Mechanism (WPM) for minimax optimal mechanisms.
result Proposes efficient algorithms for approximate computation of the Wasserstein Projection Mechanism.
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.
A new Dantzig Selector with an optimal denoising matrix for reinforcement learning.
problem Improving Dantzig Selector's performance in sparse signal recovery and reinforcement learning.
method Defining an optimal denoising matrix through minimax optimization and proposing an approximate algorithm to estimate it.
result Empirical validation of the proposed ODDS algorithm's superior performance in reinforcement learning.
Generative Adversarial Privacy (GAP) learns privacy mechanisms from data.
problem Learning optimal privacy mechanisms from data.
method Formulates privacy as a constrained minimax game between privatizer and adversary.
result GAP provides privacy guarantees against strong adversaries.
Develops a new robust hypothesis testing framework using Wasserstein uncertainty sets.
problem Improving robustness in hypothesis testing under uncertainty.
method Data-driven uncertainty sets based on Wasserstein metric, convex safe approximation, and tractable reformulation.
result Demonstrates nearly-optimal performance in hypothesis testing.
Study minimax robustness in statistical estimation under Wasserstein contamination.
problem Adversarial perturbations in statistical data.
method Developed minimax theory for losses under Wasserstein- contaminations.
result Exact minimax risk identified for joint contaminations in location estimation and prediction in linear regression.
MOPI optimizes flexible set-valued mappings to achieve superior shape adaptivity in conformal prediction.
problem Challenges in achieving valid conditional coverage in conformal prediction.
method Minimax Optimization Predictive Inference (MOPI) framework that optimizes over a flexible class of set-valued mappings.
result MOPI achieves superior shape adaptivity and maintains a principled connection to mean squared coverage error.
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.
New approach estimates personalized treatment effects using surrogate losses.
problem Estimating personalized treatment effects with binary outcomes and limited data.
method Proposes surrogate loss functions that incorporate both treatment and control data.
result Minimax support vector machine formulation yields tighter bounds.
Optimizes link prediction using matrix logistic regression.
problem Predicting links in networks with limited data.
method Formulated as matrix logistic regression, analyzed in high dimensions, combinatorial estimator with penalized maximum likelihood.
result Achieves minimax rate for Frobenius-norm risk, cannot be computed efficiently.
We formulate statistical watermarking as hypothesis testing and establish near-optimal bounds.
problem Statistical watermarking in the context of hypothesis testing.
method Formulated as a hypothesis testing problem, using coupling of output tokens and rejection regions.
result Established nearly matching upper and lower bounds on the number of i.i.d. tokens required for small Type I and Type II errors.
New ranking system balances fairness and user utility.
problem Achieving group fairness in ranking systems.
method Formulated a minimax game between a ranking player and an adversary.
result Better utility for highly fair rankings.
This research deconstructs GANs into formulation, generalization, and optimization components.
problem Improving the performance and stability of GANs.
method Proposes a perturbation view of GANs, introduces Cascade GANs, and develops principles for GAN generalization and optimization.
result Demonstrates a fundamental trade-off in GAN approximation and statistical errors, and proposes a new GAN architecture with zero minimax duality gap.
This work optimizes mean estimation under varying privacy constraints.
problem Mean estimation with heterogeneous privacy constraints.
method Proposes an algorithm for mean estimation under different privacy levels for users.
result Shows a saturation phenomenon in performance as privacy levels are relaxed.
We formulate the notion of minimax estimation under storage or communication constraints, and prove an extension to Pinsker's theorem for nonparametric estimation over Sobolev ellipsoids. Placing limits on the number of bits used to encode any estimator, we give tight lower and upper bounds on the excess risk due to qu…
A new algorithm calculates optimal strategies for two-player zero-sum games.
problem Computing the optimal strategies for two-player zero-sum games.
method Extending successive relaxation to two-player zero-sum games and developing a generalized minimax Q-learning algorithm.
result The proposed algorithm converges and effectively computes optimal strategies.
New method for clustering large multi-view data.
problem Handling large multi-view data efficiently.
method Incremental minimax optimization based fuzzy clustering (IminimaxFCM).
result IminimaxFCM outperforms related methods in clustering accuracy.
NS-GAN mode collapse due to sample weighting inversion, solved with MM-nsat.
problem Mode collapse in GANs due to sample weighting inversion.
method Preserves MM-GAN sample weighting while avoiding saturation by rescaling gradients.
result MM-nsat improves mode coverage, stability, and FID on MNIST and CIFAR-10.
Designs efficient algorithms for optimizing functions with known Lipschitz constants.
problem Optimizing unknown functions with a finite Lipschitz constant.
method Develops sequential algorithms, proves consistency and minimax rates, introduces adaptive versions.
result Theoretical guarantees for LIPO and adaptive LIPO algorithms, demonstrated through numerical examples.
New approach transfers rewards learned in one environment to reinforcement learning in a new environment.
problem Transfer of rewards learned using inverse reinforcement learning from one environment to a new, different environment.
method Formulate the problem as a joint system of Bellman equations, develop minimax estimators for the target soft--function, solve the source and target system of equations jointly.
result The coupled approach removes the first-order influence of source Bellman residual error compared to the sequential approach.
We develop a worst-case analysis of aggregation of classifier ensembles for binary classification. The task of predicting to minimize error is formulated as a game played over a given set of unlabeled data (a transductive setting), where prior label information is encoded as constraints on the game. The minimax solutio…
This paper analyzes the trade-off between accuracy and communication in personalized federated learning.
problem The accuracy-communication trade-off in personalized federated learning.
method The paper provides a quantitative characterization of the personalization degree on the trade-off, establishing minimax optimality.
result The paper offers theoretical insights for choosing the personalization degree and validates the results on synthetic and real-world datasets.
Novel quasi-Bayesian method for IV regression using machine learning models.
problem Uncertainty quantification in IV regression with machine learning models.
method Quasi-Bayesian procedure based on kernelized IV models and dual formulation.
result Established minimax optimal contraction rates and scalable inference algorithm.
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 Cost of Privacy: Optimal Rates of Convergence for Parameter Estimation with Differential Privacystat.ML
The paper explores how to maintain privacy while estimating parameters accurately.
problem Balancing privacy and accuracy in statistical estimation.
method Developed new technical tools to establish minimax optimality for differential privacy constraints.
result Found that classical lower bound arguments are insufficient for high-dimensional settings and proposed new algorithms that achieve minimax lower bounds.
Causal Inference Under Unmeasured Confounding With Negative Controls: A Minimax Learning Approachstat.ML
New approach uses negative controls to estimate causal parameters without completeness conditions.
problem Estimating causal parameters when not all confounders are observed.
method Identification strategy based on minimax learning formulations for general function classes.
result Avoids completeness conditions and uniqueness assumptions on bridge functions.
Understanding Expert Structures on Minimax Parameter Estimation in Contaminated Mixture of Expertscs.LG
Study analyzes convergence of parameter estimation in contaminated mixture of experts.
problem Challenges in learning from prompts in large-scale models.
method Convergence analysis, distinguishability condition, partial differential equations.
result Comprehensive convergence rates and minimax lower bounds for parameter estimation.
Bayesian deconditioning improves downscaling of spatial fields.
problem Challenges in refining low-resolution spatial fields with high-resolution information.
method Proposes a Bayesian formulation of deconditioning to solve the inverse problem of conditional expectation.
result Shows substantial improvements in atmospheric field downscaling over existing methods.
Proposes MinimaxFCM for multi-view clustering of data from multiple sources.
problem Clustering data from multiple heterogeneous views.
method Minimax optimization-based fuzzy c means clustering.
result MinimaxFCM outperforms other multi-view clustering methods.
Study on -function estimation for continuous state-action MDPs, deriving rates and conditions.
problem Estimating -function in off-policy evaluation for continuous state-action Markov decision processes.
method Reformulated as nonparametric instrumental variables (NPIV) problem, derived minimax lower bounds, proposed sieve two-stage least squares estimator.
result First minimax lower bounds for -function and its derivatives in sup-norm and -norm, same as classical nonparametric regression.
Paper improves adversarial training using a learned optimizer.
problem Improving robustness of deep learning models against adversarial attacks.
method Empirically identified PGD attack's limitations and used a learning-to-learn framework to train an adaptive inner optimizer.
result The proposed framework consistently improves model robustness over traditional adversarial training methods.
Develops a hypothesis testing framework for generalized Thurstone models.
problem Determining whether pairwise comparison data fits a generalized Thurstone model.
method Introduces separation distance and derives upper and lower bounds for testing.
result Critical threshold for testing depends on observation graph topology and scales as for complete graphs.
Develops new tests for high-dimensional models with mixed signal strengths.
problem Challenges in testing models with many signals and high-dimensional data.
method Moment matching formulation for developing new tests.
result Demonstrates optimality of GRIP test for various model types.
Proposes MRO to achieve uniformly low regret in distributionally robust learning.
problem Learning under unknown test distributions (distribution shift).
method Minimax Regret Optimization (MRO) for robust machine learning.
result MRO achieves uniformly low regret across all test distributions.
SREDA optimizes complex machine learning problems with fewer evaluations.
problem Finding an optimal point in nonconvex-strongly-concave minimax problems.
method Stochastic Recursive Gradient Descent Ascent (SREDA) with variance reduction.
result Achieves optimal stochastic gradient complexity of O(κ^3ε^-3).