New lower bounds for bilevel optimization with first-order oracles.
problem Complexity of bilevel optimization with first-order oracles.
method Development of hard instances and proof of lower bounds.
result Nontrivial lower bounds for first-order zero-respecting algorithms.
A new method solves complex constrained minimax problems.
problem Solving constrained minimax optimization problems.
method First-order augmented Lagrangian method.
result Established an operation complexity of O ( ε − 4 log ε − 1 ) O(\varepsilon^{-4}\log\varepsilon^{-1}) O ( ε − 4 log ε − 1 ) . Optimal first-order methods are shown to be fundamental limits in functional estimation.
problem Optimal functional estimation under weak conditions.
method Formalization of functional estimation with black-box nuisance function estimates and derivation of minimax lower bounds.
result First-order methods are optimal under weak conditions, but higher-order methods can outperform them when nuisance function structure is known.
We note that known methods achieving the optimal oracle complexity for first order convex optimization require quadratic memory, and ask whether this is necessary, and more broadly seek to characterize the minimax number of first order queries required to optimize a convex Lipschitz function subject to a memory constra…
A new method solves a complex optimization problem efficiently.
problem Nonconvex-strongly-concave constrained minimax optimization.
method First-order augmented Lagrangian method with a first-order subproblem solver.
result Achieves improved operation complexity for finding solutions.
Novel BSG method for efficient stochastic optimization.
problem Efficient optimization of non-convex surfaces in stochastic settings.
method Binary search combined with first order gradient optimization.
result BSG produces more promising results and better generalization than other methods.
New memory-query tradeoffs for convex optimization algorithms.
problem Optimizing memory usage for convex optimization algorithms.
method Analyzing randomized first-order algorithms for minimizing convex functions.
result Cutting plane methods are optimal in terms of memory and query complexity.
A framework for decentralized optimization using first-order methods.
problem Optimization of finite sums over networked nodes.
method Decentralized first-order gradient and stochastic methods.
result General framework for undirected and directed networks.
Unified approach for first-order methods with Markovian noise in stochastic optimization and variational inequalities.
problem Stochastic optimization problems with Markovian noise.
method Unified theoretical analysis of first-order gradient methods using randomized batching and multilevel Monte Carlo.
result Optimal (linear) dependence on the mixing time of the noise sequence, eliminating previous limiting assumptions.
CEFOL uses deep learning for dynamic programming with recursive utility.
problem Challenges in solving dynamic programming problems with recursive utility.
method Introduces a separate neural network for certainty equivalent, uses first-order optimality conditions to learn value and policy functions.
result CEFOL achieves high accuracy in learning value and policy functions, matching VFI benchmarks.
Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces. But unlike convex optimization, geodesically convex (g-convex) optimization is much less developed. In this paper we contribute to the understanding of g-convex optimization by developing iteration complexity analysis for …
OptEx accelerates first-order optimization with parallelized iterations.
problem Inefficiencies in first-order optimization algorithms for complex tasks.
method Approximately parallelized iterations using kernelized gradient estimation.
result OptEx achieves substantial efficiency improvements with an effective acceleration rate of Ω ( N ) Ω(\sqrt{N}) Ω ( N ) . New inequalities help optimize first-order algorithms for statistical risk analysis.
problem Optimizing first-order iterative algorithms for statistical risk analysis.
method Introducing basic inequalities that connect implicit and explicit regularization.
result The basic inequalities translate the number of iterations into an effective regularization coefficient.
New framework tackles bi-level optimization without LLS condition.
problem Bi-level optimization problems without LLS condition.
method Bi-level Descent Aggregation (BDA) framework, proving convergence without LLS condition.
result Proves convergence of BDA without LLS condition.
Optimized method tackles convex optimization with heavy-tailed noise.
problem Convex optimization problems with noisy gradients.
method Vanilla stochastic proximal subgradient method without gradient clipping or normalization.
result Achieves optimal complexity for various convex optimization types under heavy-tailed noise.
First-order method solves stochastic bilevel optimization with linear constraints.
problem Stochastic bilevel optimization with linear constraints and noise.
method Developed a novel framework using gradient-based techniques and smoothed penalty functions.
result Achieved finite-time convergence guarantees for ( δ , ε ) (δ, ε) ( δ , ε ) -Goldstein stationary points. SGD's performance improves with critical batch size, minimizing SFO complexity.
problem Optimizing SGD's performance with batch size and learning rate.
method Analysis of SGD using constant and decaying learning rates, focusing on batch size effects.
result SGD with critical batch size minimizes SFO complexity.
New methods solve optimization problems with heavy-tailed noise, improving upon existing complexity bounds.
problem Optimization problems with heavy-tailed noise and weakly average smoothness.
method Normalized stochastic first-order methods with Polyak, multi-extrapolated, and recursive momentum.
result First-order oracle complexity results for finding approximate stochastic stationary points under heavy-tailed noise.
DEO uses gradient information to escape saddle points in neural networks.
problem Training deep neural networks struggles with flat regions and saddle points.
method Dimer-Enhanced Optimization (DEO) uses gradient information to estimate curvature and escape saddle points.
result DEO improves training efficiency and performance compared to standard first-order methods.
Study examines how slight model changes affect multi-period optimization outcomes.
problem Effect of small probabilistic model changes on multi-period optimization problems.
method Adapted Wasserstein distance for measuring changes, explicit first-order approximations proved.
result Explicit first-order approximations for multi-period stochastic optimization and optimal stopping problems.
Paper develops fast method for computing optimal transport.
problem Efficient computation of optimal transport distance between distributions.
method Entropy-regularized extragradient method for first-order optimization.
result Achieves state-of-the-art runtime guarantees and good numerical performance.
New algorithms optimize constrained problems faster, avoiding full set optimization.
problem Optimizing constrained problems efficiently and quickly.
method Designing accelerated first-order algorithms that avoid full set optimization.
result Proved convergence to stationary points in nonconvex settings and accelerated rates in convex settings.
BMM algorithm improves convergence for nonconvex optimization problems.
problem Constrained nonsmooth nonconvex optimization problems.
method Block majorization-minimization with diminishing radius.
result Improved convergence rate for nonconvex optimization problems.
New methods reduce constraint violations to certainty in stochastic optimization.
problem Finding a point with certain constraint satisfaction and near-stationarity.
method Single-loop variance-reduced stochastic first-order methods with truncated momentum schemes.
result Achieves strong convergence guarantees for ε ε ε -stochastic stationary points with certain constraint satisfaction. Memory-constrained algorithms need superlinear memory for efficient convex optimization.
problem Efficiently minimizing convex functions with limited memory.
method Analyzing first-order algorithms with superlinear memory constraints.
result Superlinear memory is necessary for optimal performance in convex optimization.
New methods boost first-order optimization with faster rates.
problem Designing efficient first-order methods for convex problems.
method Shifted objective function with interpolation condition.
result New schemes achieve faster convergence rates.
The filtering-clustering models, including trend filtering and convex clustering, have become an important source of ideas and modeling tools in machine learning and related fields. The statistical guarantee of optimal solutions in these models has been extensively studied yet the investigations on the computational as…
New method for tuning Graphical Lasso hyperparameters.
problem Tuning hyperparameters of Graphical Lasso.
method Bilevel optimization with first-order method.
result Derivation of Graphical Lasso Jacobian.
We study an optimal control problem related to swing option pricing in a general non-Markovian setting in continuous time. As a main result we show that the value process solves a first-order non-linear backward stochastic partial differential equation. Based on this result we can characterize the set of optimal contro…
In this paper, we study optimization methods consisting of iteratively minimizing surrogates of an objective function. By proposing several algorithmic variants and simple convergence analyses, we make two main contributions. First, we provide a unified viewpoint for several first-order optimization techniques such as …
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.
New method accelerates steepest descent for convex optimization.
problem Achieving acceleration for general ℓ p \ell_p ℓ p smooth functions. method Primal-dual iterate sequences with differing norms, implicitly determined interpolation parameter.
result Improves iteration complexity to O ( d 1 − 2 p ) O(d^{1-\frac{2}{p}}) O ( d 1 − p 2 ) for ℓ p \ell_p ℓ p norm smooth problems. New algorithm for safer machine learning with different testing and training distributions.
problem Challenges in modern machine learning where training and testing distributions differ.
method First-order optimization algorithm for superquantile-based learning.
result Promising numerical results show the approach's effectiveness.
Geometrically reformulates the Laplace method for optimal transport.
problem Approximating integrals using the Laplace method without geometric interpretation.
method Introduces the Kim-McCann Riemannian metric to give a geometric formulation of the Laplace method.
result Expresses the first-order term of the Laplace method using geometric objects.
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 ε \varepsilon ε -KKT solutions. A new method speeds up quantum state estimation.
problem Exponential growth in sample size and dimension for quantum state tomography.
method Stochastic mirror descent with Burg entropy.
result Optimization error vanishes at a O ( ( 1 / t ) d log t ) O (\sqrt{ ( 1 / t ) d \log t }) O ( ( 1/ t ) d log t ) rate. New sampling method guarantees approximate first-order stationary points for non-convex functions.
problem Sampling from non-log-concave densities with non-convex potential functions.
method Averaged Langevin Monte Carlo with complexity analysis.
result Langevin Monte Carlo outputs a sample with ε-relative Fisher information after O(L²d²/ε²) iterations.
Efficient RNN algorithm guarantees convergence in online learning.
problem Online nonlinear regression with RNNs.
method First-order training algorithm with convergence guarantee.
result The algorithm converges to optimum network parameters.
Improved first-order algorithm for entropy regularized OT with faster convergence.
problem Solving entropy regularized optimal transport efficiently.
method Accelerated primal-dual stochastic mirror descent algorithm with variance reduction.
result Improved rate from O ~ ( n 2.5 / ε ) \widetilde{O}({n^{2.5}}/ε) O ( n 2.5 / ε ) to O ~ ( n 2 / ε ) \widetilde{O}({n^2}/ε) O ( n 2 / ε ) . Boosting can efficiently optimize any loss function without requiring first-order information.
problem Boosting's efficiency in optimizing loss functions without first-order information.
method Extending gradient-based optimization to use only zeroth-order information.
result Boosting can optimize any loss function efficiently, including non-convex, non-differentiable, and non-continuous ones.
Quadratic memory is essential for optimal convex optimization queries.
problem Optimal query complexity for convex optimization and feasibility problems.
method Lower bounds on query complexity for convex optimization and feasibility problems.
result Center-of-mass algorithms are Pareto-optimal for both convex optimization and feasibility problems.
In reinforcement learning, an agent attempts to learn high-performing behaviors through interacting with the environment, such behaviors are often quantified in the form of a reward function. However some aspects of behavior-such as ones which are deemed unsafe and to be avoided-are best captured through constraints. W…
The paper studies the First Order BSPDEs (Backward Stochastic Partial Differential Equations) suggested earlier for a case of multidimensional state domain with a boundary. These equations represent analogs of Hamilton-Jacobi-Bellman equations and allow to construct the value function for stochastic optimal control pro…
A new method optimizes diffusion models for fine-tuning tasks efficiently.
problem Optimizing diffusion models for downstream tasks using nested bilevel structures.
method Formalizes the challenge as a generative bilevel optimization problem and introduces a first-order bilevel framework.
result Our method outperforms existing fine-tuning and hyperparameter search baselines.
Computing Nash equilibrium (NE) of multi-player games has witnessed renewed interest due to recent advances in generative adversarial networks. However, computing equilibrium efficiently is challenging. To this end, we introduce the Gradient-based Nikaido-Isoda (GNI) function which serves: (i) as a merit function, vani…
A new algorithm solves bilevel optimization with linear constraints.
problem Solving bilevel optimization problems with coupled linear constraints.
method Penalty and augmented Lagrangian methods reformulate the problem; a single-loop, first-order algorithm proposed.
result Improved convergence rates compared to prior methods.
New method solves saddle-point problems faster than existing methods.
problem Large-scale saddle-point problems in optimization.
method Sequential subspace optimization with proximal regularization.
result Significantly better convergence compared to first-order methods.
New methods for convex optimization with locally Lipschitz gradient, achieving faster convergence.
problem Optimization problems with locally Lipschitz continuous gradient.
method Accelerated proximal gradient (APG) methods and proximal augmented Lagrangian method.
result Achieved faster convergence rates for convex optimization problems with locally Lipschitz gradient.