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. 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.
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.
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.
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.
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.
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.
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.
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 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.
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.
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 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.
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.
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…
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.
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. 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.
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.
Bayesian optimization reduces computational effort in aircraft design optimization.
problem High computational cost in industrial aircraft design optimization.
method Constrained Bayesian optimization (Super Efficient Global Optimization with Mixture of Experts)
result Significant computational efficiency improvements over existing Isight optimizers.
Bayesian optimization method tackles combinatorial spaces, scalable for large data.
problem Optimization over combinatorial categorical spaces in natural sciences.
method Combines variational optimization and continuous relaxations for gradient-based optimization.
result Method performs comparably to state-of-the-art methods while scaling well.
New algorithm solves complex stopping problems with robust optimization.
problem Solving complex stochastic optimal stopping problems.
method Simulation-based robust optimization with exact reformulation as a zero-one bilinear program.
result Developed polynomial-time heuristics and algorithms for practical solution.
L2O uses ML to optimize traditional optimization techniques.
problem Real-world optimization problems with shared structures.
method Exploiting shared structures to enhance optimization techniques.
result Better or faster solutions through machine learning integration.
A novel neural network approach for optimization problems.
problem Constrained optimization problems.
method Neural Optimization Machine (NOM) using a specially designed NN architecture and training procedure.
result Solves optimization problems efficiently, especially in high-dimensional spaces.
Meta algorithm solves multivariate optimization using univariate optimizers.
problem Multivariate global optimization problems.
method Meta algorithm combining univariate global optimizers.
result Meta algorithm provides robust regret guarantees.
When hyperparameter optimization of a machine learning algorithm is repeated for multiple datasets it is possible to transfer knowledge to an optimization run on a new dataset. We develop a new hyperparameter-free ensemble model for Bayesian optimization that is a generalization of two existing transfer learning extens…
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.
New algorithm selects robust martingale for optimal stopping problems.
problem Optimal stopping problems in stochastic processes.
method Randomized dual martingale minimization algorithm.
result Efficiently selects Doob martingale as close as possible.
Numerical optimization is an important tool in the field of computational physics in general and in nano-optics in specific. It has attracted attention with the increase in complexity of structures that can be realized with nowadays nano-fabrication technologies for which a rational design is no longer feasible. Also, …
This paper shows how to combine optimal tests into log-optimal processes.
problem How to combine optimal sequential tests into log-optimal processes.
method Using a new class of WAIT e-processes, the paper aggregates asymptotically optimal sequential tests into asymptotically log-optimal processes.
result It is possible to aggregate asymptotically optimal sequential tests into asymptotically log-optimal e-processes.
Learning optimal feedback control laws capable of executing optimal trajectories is essential for many robotic applications. Such policies can be learned using reinforcement learning or planned using optimal control. While reinforcement learning is sample inefficient, optimal control only plans an optimal trajectory fr…
Paper studies optimal control for a specific geometric problem.
problem Optimal control problem associated with the Paneitz obstacle problem.
method Existence and regularity results for optimal controls.
result Existence of optimal controls and their properties.
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.
Adapts Bayesian optimization for mixed constraints in aircraft design.
problem Optimizing expensive black box functions with mixed constraints.
method Super efficient global optimization with upper trust bound for constraints, Gaussian process uncertainty, refinement procedure.
result Superior performance on aircraft design problem compared to state-of-the-art solvers.
Adam optimizer converges to zeros of a new vector field, not just gradient zeros.
problem Prove convergence rates for Adam optimizer in simple quadratic optimization problems.
method Introduced Adam vector field to analyze Adam optimizer's convergence.
result Established optimal convergence rates for Adam optimizer.
Optimal crypto asset routing with CFMMs, including fixed costs.
problem Optimizing order execution on a network of CFMMs with fixed costs.
method Convex optimization for no fixed costs, mixed-integer convex for fixed costs, heuristics for approximate solutions.
result Approximate solutions to optimal routing and arbitrage certification problems.
BOSH optimizes functions with stochastic evaluations more efficiently and precisely.
problem Optimizing functions with noisy evaluations can lead to suboptimal solutions.
method BOSH uses a hierarchical Gaussian process to generate a growing pool of realizations.
result BOSH provides more efficient and higher-precision optimization than standard BO.
VeLO learns versatile optimizers from deep learning tasks.
problem Training deep learning models with hand-designed optimizers.
method Meta-training a neural network optimizer on a wide variety of optimization tasks.
result The learned optimizer automatically adapts to different optimization tasks without hyperparameter tuning.
New learned optimizers outperform baselines by incorporating known and novel mechanisms.
problem Understanding how learned optimizers outperform traditional ones.
method Careful analysis and visualization of learned optimizers trained on various tasks.
result Learned optimizers incorporate known techniques like momentum and gradient clipping, as well as new forms of learning rate adaptation.
A new method learns DAGs from data using permutation optimization.
problem Discovering latent DAGs from observational data.
method Optimizes over the Permutahedron to learn topological orderings and edges.
result Our method optimizes exact DAGs, is modular, and performs well on real-world data.
PAGE optimizes nonconvex problems with optimal convergence rates.
problem Nonconvex optimization problems.
method PAGE algorithm for achieving optimal convergence rates.
result PAGE achieves optimal convergence rates for nonconvex optimization.
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.
Enhanced ROOT-SGD optimizes stochastic optimization with diminishing stepsizes.
problem Improving statistical efficiency in stochastic optimization.
method Integrates a diminishing stepsize strategy into ROOT-SGD.
result Achieves optimal convergence rates with improved stability and precision.