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.
New algorithm solves structured nonconvex-nonconcave min-max problems.
problem Min-max optimization challenges in deep learning.
method Generalized extragradient algorithm for structured nonconvex-nonconcave problems.
result Algorithm converges to stationary points in Euclidean and ℓp spaces. DS-GDA solves nonconvex-nonconcave problems without regularity conditions.
problem Nonconvex-nonconcave minimax optimization challenges.
method Doubly smoothed gradient descent ascent method (DS-GDA).
result Achieves convergence on various nonconvex-nonconcave problems.
Study on robust utility maximization with nonconcave utility functions under projective determinacy.
problem Investor's optimal investment strategy under model ambiguity and nonconcave utility.
method Projective functions of the path and sets of priors, upper-semicontinuous utility.
result Existence of optimal investment strategy under PD.
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.
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.
Study nonconcave portfolio choice with smooth ambiguity and Bayesian learning.
problem Nonconcave portfolio choice under smooth ambiguity and Bayesian learning.
method Developed a general framework for dynamic, non-concave asset allocation.
result Dynamic consistency achieved through a robust representation.
New method tackles nonconvex-nonconcave problems with local KL condition.
problem Nonconvex-nonconcave minimax problems under varying KL conditions.
method Inexact proximal gradient method for KL-structured subproblems.
result Complexity guarantees for approximate stationary points.
New algorithm converges to equilibrium in nonconvex-nonconcave optimization problems without dimension dependence.
problem Min-max optimization in nonconvex-nonconcave landscapes.
method Convergent algorithm with greedy max-player updates and proposal distribution for min-player.
result Algorithm converges to equilibrium in non-dependent iterations, suitable for GAN training.
Paper proves Sion's theorem in geodesic spaces and develops a Riemannian extragradient method.
problem Understanding saddle points in nonconvex-nonconcave minimax problems.
method Geodesic metric space version of Sion's theorem and Riemannian extragradient method.
result Developed a Riemannian extragradient algorithm for smooth minimax problems.
New method solves complex constrained optimization problems.
problem Constrained nonconvex-nonconcave minimax optimization problems.
method Inexact proximal gradient method using sequential convex programming.
result Established complexity guarantees for approximate stationary points.
High throughput genetic sequencing arrays with thousands of measurements per sample and a great amount of related censored clinical data have increased demanding need for better measurement specific model selection. In this paper we establish strong oracle properties of nonconcave penalized methods for nonpolynomial (N…
Adversarial training, a special case of multi-objective optimization, is an increasingly prevalent machine learning technique: some of its most notable applications include GAN-based generative modeling and self-play techniques in reinforcement learning which have been applied to complex games such as Go or Poker. In p…
Minimax optimization has found extensive applications in modern machine learning, in settings such as generative adversarial networks (GANs), adversarial training and multi-agent reinforcement learning. As most of these applications involve continuous nonconvex-nonconcave formulations, a very basic question arises---"w…
Proposes an efficient alternative to nonconvex-nonconcave min-max optimization.
problem Min-max optimization challenges in nonconvex-nonconcave settings.
method Introduces ε-greedy adversarial equilibrium model and proves its existence.
result Existence of ε-greedy adversarial equilibrium for smooth bounded functions.
Study finds non-monotonic Value of Information in dynamic multi-market monopoly.
problem Investigates non-monotonicity in Value of Information for a price-setting monopolist.
method Uses a Bayesian inverse problem with Kalman-Bucy-Stratonovich filter in a dynamic discrete model.
result Non-monotonic relationship between signal variance and Value of Information.
Paper analyzes convergence of GDA for nonconvex-nonconcave minimax problems.
problem Understanding convergence of GDA for nonconvex-nonconcave minimax problems.
method Local convergence analysis of GDA with stepsize ratio Θ(κ).
result Stepsize ratio of Θ(κ) is necessary and sufficient for local convergence of GDA to a Stackelberg Equilibrium.
We establish C2,α estimates for PDE of the form convex + a sum of weakly concave functions of the Hessian, thus generalising a recent result of Collins which is in turn inspired by a theorem of Caffarelli and Yuan. Independently, we also prove an existence result for a certain generalised Monge-Ampère PDE.
New algorithms solve nonconvex-nonconcave minimax optimization problems.
problem Solving minimax optimization problems in machine learning.
method Two novel Newton-type algorithms for nonconvex-nonconcave minimax optimization.
result Proved local convergence at strict local minimax points.
We study robust stochastic optimization problems in the quasi-sure setting in discrete-time. The strategies in the multi-period-case are restricted to those taking values in a discrete set. The optimization problems under consideration are not concave. We provide conditions under which a maximizer exists. The class of …
We study the global convergence of policy optimization for finding the Nash equilibria (NE) in zero-sum linear quadratic (LQ) games. To this end, we first investigate the landscape of LQ games, viewing it as a nonconvex-nonconcave saddle-point problem in the policy space. Specifically, we show that despite its nonconve…
New NPG variants ensure parameter convergence in multi-agent learning.
problem Non-convergence of parameters in NPG for multi-agent learning.
method Proposed variants of NPG for multi-agent learning scenarios.
result Global last-iterate parameter convergence guarantees in various multi-agent learning settings.
GAIL with neural networks converges to global optima and has a known rate.
problem Uncertainty about GAIL with neural networks achieving global optimality.
method Gradient-based alternating updates algorithm.
result Established sublinear convergence to globally optimal solution.
Improving the sample efficiency in reinforcement learning has been a long-standing research problem. In this work, we aim to reduce the sample complexity of existing policy gradient methods. We propose a novel policy gradient algorithm called SRVR-PG, which only requires O(1/ε3/2) episodes to find an ε-approxima…
Study optimal reinsurance contracts to prevent moral hazard under non-concave premium principles.
problem Preventing moral hazard in reinsurance contracts under non-concave premium principles.
method Develops optimal reinsurance contracts under a diffusion risk model with incentive compatibility constraints and extended distortion premium principles.
result An optimal reinsurance contract exists and is characterized by solving a double obstacle problem.
In this paper, we consider an ℓ0-norm penalized formulation of the generalized eigenvalue problem (GEP), aimed at extracting the leading sparse generalized eigenvector of a matrix pair. The formulation involves maximization of a discontinuous nonconcave objective function over a nonconvex constraint set, and is…
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.
New algorithms solve stochastic variational inequalities without bounded variance assumption.
problem Solving stochastic variational inequalities without bounded variance assumption.
method Developed algorithms for two classes of problems: monotone and structured nonmonotone VIs.
result Oracle complexity of O(ε^-4) for solving VIs with unbounded domains and possibly unbounded variance.
Study efficient convergence of RL algorithm with function approximation.
problem Convergence of actor-critic algorithm with nonlinear function approximation.
method Stochastic gradient descent ascent with adaptive proximal term, Polyak-Łojasiewicz condition.
result First efficient convergence result with rate of O(sqrt{ln(N d G^2) / N}).
A new method trains physics-constrained neural networks more efficiently.
problem Training machine learning tools with limited data and physical constraints.
method Dual-Dimer method for searching saddle points in nonconvex-nonconcave functions.
result The Dual-Dimer method improves training efficiency and convergence speed.
We consider the problem of sparse estimation in a factor analysis model. A traditional estimation procedure in use is the following two-step approach: the model is estimated by maximum likelihood method and then a rotation technique is utilized to find sparse factor loadings. However, the maximum likelihood estimates c…
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.
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.
Paper develops machine learning algorithms to learn optimal integer weights for clinical risk scores.
problem Deriving optimal integer weights for clinical risk scores without computational burden.
method Flexible greedy optimization strategy to directly optimize a value function.
result Constructed an integer-weighted comorbidity score for measuring post-discharge mortality risk.
Investigates conditions for risk or utility functionals to be sensitive to large losses.
problem Conditions for risk or utility functionals to be sensitive to large losses.
method Analyzes sensitivity to large losses for various risk and utility functionals.
result Value at Risk and Expected Shortfall generally fail to be sensitive to large losses, but expected utility functionals and certain adjusted versions are sensitive.
New method for fair resource allocation in AI-aware networks with unknown utility functions.
problem Fair resource allocation in AI-aware communication networks with unknown utility functions.
method Distributed, data-driven bilevel optimization approach to learn surrogate utility functions.
result The proposed algorithm learns from data to autotune surrogate utility functions for unknown utility functions.
Optimizes solving complex min-max problems with stochastic and nonconvex elements.
problem Min-max problems with stochastic and nonconvex elements.
method Combines conic nonexpansiveness, refined inexact Halpern iteration, and multilevel Monte Carlo estimator.
result Optimal or best-known complexity guarantees for $ρ< rac{1}{L}$, improving previous results.
Improved FTPL algorithm reduces regret in predictable minimax games.
problem Online learning and minimax games with predictable loss sequences.
method Optimistic modification of FTPL with dual regularization view.
result Tighter regret bounds for predictable sequences, O(T−1/2) accuracy.