NHGD solves bilevel optimization problems with reduced computational time.
problem Solving bilevel optimization problems with high computational cost.
method Exploits statistical structure of inner optimization to use empirical Fisher matrix as Hessian surrogate, enabling parallel optimization and approximation.
result NHGD achieves error bounds and sample complexity guarantees matching state-of-the-art methods, with significantly reduced computational time.
New method finds stationary points in bilevel optimization problems.
problem Solving nonconvex-strongly-convex bilevel optimization problems.
method Restarted Accelerated HyperGradient Descent (RAHGD) method.
result Achieves best-known theoretical guarantees for finding stationary points in bilevel optimization.
Framework solves bilevel optimization on manifolds.
problem Solving bilevel optimization problems with manifold constraints.
method Hypergradient estimation strategies on manifolds, convergence and complexity analyses.
result Efficacy demonstrated through various applications.
We introduce a general method for improving the convergence rate of gradient-based optimizers that is easy to implement and works well in practice. We demonstrate the effectiveness of the method in a range of optimization problems by applying it to stochastic gradient descent, stochastic gradient descent with Nesterov …
Proposes glocal hypergradient estimation for hyperparameter optimization.
problem Combining reliability and efficiency in hyperparameter optimization.
method Uses Koopman operator theory to approximate global hypergradients from local ones.
result Achieves both reliability and efficiency in hyperparameter optimization.
Standard gradient descent methods are susceptible to a range of issues that can impede training, such as high correlations and different scaling in parameter space.These difficulties can be addressed by second-order approaches that apply a pre-conditioning matrix to the gradient to improve convergence. Unfortunately, s…
Working with any gradient-based machine learning algorithm involves the tedious task of tuning the optimizer's hyperparameters, such as its step size. Recent work has shown how the step size can itself be optimized alongside the model parameters by manually deriving expressions for "hypergradients" ahead of time. We sh…
OSGM uses online learning to adapt stepsize for faster convergence.
problem Improving convergence rates of first-order methods.
method OSGM combines online learning and feedback functions to adjust stepsize.
result OSGM achieves convergence rates asymptotically no worse than optimal.
ROBOT framework solves regression without correspondence for large data and complex models.
problem Regression without known correspondence in large datasets.
method ROBOT framework reformulates regression as a continuous optimization problem and uses hypergradient approach.
result ROBOT achieves better performance than existing methods in linear and nonlinear regression tasks.
Study on stochastic hypergradient computation for machine learning problems.
problem Efficient computation of hypergradients in machine learning models.
method Stochastic approximation schemes for hypergradient computation, focusing on empirical risk minimization.
result Bounds for the mean square error of hypergradient approximation under contraction assumptions.
Paper proposes AggITD for efficient federated hypergradient computation.
problem Computing hypergradient in federated settings is challenging due to distributed and nonlinear construction of global Hessian matrices.
method AggITD: a novel communication-efficient federated hypergradient estimator via aggregated iterative differentiation.
result AggITD achieves the same sample complexity as AID-based approaches but with fewer communication rounds, especially in heterogeneous data environments.
Study compares methods for computing hypergradients in machine learning problems.
problem Computing exact hypergradients in machine learning is difficult.
method Investigates reverse mode iterative differentiation and approximate implicit differentiation methods.
result Unified analysis provides iteration complexity bounds and hierarchy of methods.
Semiparametric method removes bias in functional bilevel gradient estimation.
problem First-order bias in plug-in hypergradient when lower-level problem is nonparametric.
method Semiparametric debiasing theory based on efficient influence function leads to cross-fitted orthogonal hypergradient estimator.
result Asymptotic normality and uniform control over outer parameter established for the estimator.
We study the problem of fitting task-specific learning rate schedules from the perspective of hyperparameter optimization, aiming at good generalization. We describe the structure of the gradient of a validation error w.r.t. the learning rate schedule -- the hypergradient. Based on this, we introduce MARTHE, a novel on…
La-MAML improves fast online continual learning with a look-ahead approach.
problem Fast online continual learning with limited model capacity.
method Optimisation-based meta-learning with look-ahead and episodic memory.
result Superior performance on visual classification benchmarks.
One-pass optimisation for high-dimensional hyperparameters.
problem Efficient optimisation of hyperparameters in machine learning models.
method Approximate hypergradient-based optimisation for any continuous hyperparameter, requiring only one training episode.
result Competitive performance on various datasets without hyperparameter restarts.
This work speeds up hyperparameter selection for non-smooth convex models using implicit differentiation.
problem Optimizing hyperparameters of non-smooth convex models.
method Implicit differentiation of proximal gradient and coordinate descent methods.
result Implicit differentiation can speed up hyperparameter optimization, especially for non-smooth problems.
CB-RL solves complex decision-making problems with contextual information and exogenous events.
problem Optimal policy in strategic decision-making problems that depend on environmental configuration and exogenous events.
method Contextual Bilevel Reinforcement Learning (CB-RL) with a stochastic Hyper Policy Gradient Descent (HPGD) algorithm.
result Demonstrated convergence and performance of the HPGD algorithm for reward shaping and tax design.
EvoGrad improves efficiency in meta-learning and hyperparameter optimization.
problem Efficiently compute hypergradients for larger network architectures.
method Uses evolutionary techniques to estimate hypergradients without second-order derivatives or longer computational graphs.
result Significant improvements in efficiency, enabling scaling to bigger architectures.
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)-Goldstein stationary points. Solving a bilevel optimization problem is at the core of several machine learning problems such as hyperparameter tuning, data denoising, meta- and few-shot learning, and training-data poisoning. Different from simultaneous or multi-objective optimization, the steepest descent direction for minimizing the upper-level c…
New methods solve complex optimization problems in machine learning.
problem Challenges in stochastic bilevel optimization with constraints and high variables.
method Inexact bilevel stochastic gradient methods for constrained and unconstrained lower-level problems.
result Comprehensive convergence theory for both unconstrained and constrained cases.
New algorithm achieves linear speedup in non-i.i.d. federated bilevel learning.
problem Linear speedup in convergence for non-i.i.d. datasets in federated bilevel optimization.
method Proposes FedMBO with a novel client sampling scheme for non-i.i.d. datasets.
result Achieves a convergence rate of O(1/√(nK) + 1/K + √n/K³/²).
A new method solves bilevel optimization problems in competitive Markov games.
problem Capturing competitive structures in RL with multiple interacting policies.
method Penalty-augmented Nikaido-Isoda descent-ascent (PANDA) method.
result PANDA converges to stationary points without convexity assumptions.
New algorithm tackles stochastic bilevel optimization under relaxed smoothness conditions.
problem Optimal algorithms for stochastic bilevel optimization under relaxed smoothness conditions.
method Introduces a novel fully single-loop and Hessian-inversion-free algorithmic framework for stochastic bilevel optimization.
result Demonstrates state-of-the-art oracle complexity results for multi-objective robust bilevel optimization.
New Hessian-free method improves bilevel optimization for meta-learning.
problem Efficiently solving bilevel optimization problems with limited second-order information.
method Proposes a new Hessian-free method that approximates the response Jacobian matrix via optimization path differences.
result Demonstrates superior performance on meta-learning tasks compared to baseline methods.
SmoothFBO tackles non-stationary functional bilevel optimization.
problem Current FBO methods are limited to static offline settings and perform poorly in online, non-stationary scenarios.
method SmoothFBO introduces a time-smoothed stochastic hypergradient estimator with a window parameter to handle non-stationarity.
result SmoothFBO achieves sublinear regret and outperforms existing methods in non-stationary hyperparameter optimization and model-based reinforcement learning.
New method optimizes fairness in predictive models for continuous sensitive attributes.
problem Enforcing full statistical independence on continuous sensitive attributes is too restrictive.
method Functional bilevel optimization (FBO) and ITD algorithms.
result Achieves lowest or near-lowest fairness-accuracy regret on synthetic and real datasets.
The paper analyzes convergence rates of bilevel optimization algorithms and introduces a new stochastic algorithm.
problem Nonconvex-strongly-convex bilevel optimization problems in machine learning.
method Comprehensive convergence rate analysis for deterministic bilevel optimization using AID and ITD, and a novel stochastic algorithm stocBiO.
result Theoretical convergence rates for AID and ITD methods, and stocBiO's superior performance.
Fewer data weight updates lead to faster convergence in machine learning models.
problem Improving robustness of machine learning models through data mixing.
method Analyzing convergence behavior of data mixing with a finite number of inner steps.
result The optimal number of inner steps scales with the budget and type of gradients used.
Paper tackles bilevel optimization problems using penalty methods.
problem Unconstrained and constrained bilevel optimization problems with nonsmooth lower levels.
method Introduces first-order penalty methods and O(ε−4logε−1) and O(ε−7logε−1) operation complexities. result Establishes operation complexities for finding ε-KKT solutions. Blind Descent avoids gradient issues, using a different learning approach.
problem Gradient issues like exploding and vanishing gradients.
method Does not use gradients to guide learning; instead, it is a more fundamental learning process.
result Gradient descent is a specific case of Blind Descent.
New method tackles bilevel optimization with polyhedral constraints.
problem Challenges in bilevel optimization with active-set changes and expensive Hessian inversions.
method Logarithmic barrier smoothing and proxy-gradient algorithm for differentiable approximation.
result Stationarity rates of O(K−2/3) in deterministic setting and O(K−2/5) under stochastic noise. Reparameterizes mirror descent as gradient descent for efficient sparse learning.
problem Efficiently training small sparse networks with mirror descent.
method Develops a framework to convert mirror descent updates into gradient descent updates on different parameters.
result Mirror descent can be reparameterized as gradient descent on modified parameters, facilitating standard backpropagation.
Derives Mirror Descent from gradient flow on a Riemannian manifold.
problem No specific problem stated; focuses on derivation.
method Derives Mirror Descent from gradient flow on a Riemannian manifold with a natural discretization.
result Generalizes Mirror Descent to non-Hessian metrics.
Accelerates coordinate descent methods for machine learning problems.
problem Slowness of coordinate descent methods in machine learning.
method Extrapolation-based accelerated coordinate descent.
result Significant speed-up in practice compared to existing methods.
Stochastic gradient descent on manifolds improves low-rank approximation.
problem Efficiently approximate large matrices with lower rank.
method Stochastic gradient descent on a manifold.
result Algorithm outperforms Euclidean space methods on Netflix Prize data.
A new stochastic method tackles bi-level optimization problems in deep learning.
problem Bi-level optimization problems in deep learning, including hyperparameter optimization and meta learning.
method Turning a BLO problem into a stochastic optimization, using SGLD MCMC and a recurrent algorithm to compute MC-estimated hypergradient.
result Our method is more robust to suboptimal inner optimization and non-unique inner minima, leading to more reliable solutions.
In this note, we observe the behavior of gradient flow and discrete and noisy gradient descent in some simple settings. It is commonly noted that addition of noise to gradient descent can affect the trajectory of gradient descent. Here, we run some computer experiments for gradient descent on some simple functions, and…
New analysis shows GMD can converge linearly under PL-like conditions.
problem Establishing linear convergence for generalized mirror descent.
method PL-based analysis for time-dependent mirrors, Taylor-series approach for stochastic GMD.
result Linear convergence of stochastic GMD under PL-like conditions.
A new method improves stochastic gradient descent for faster and more efficient estimation.
problem Efficient and fast parametric estimation methods.
method Projected stochastic gradient descent corrected by Fisher scoring.
result The method is faster and more efficient than traditional methods.
Double descent phenomenon explained in simple terms.
problem Understanding the surprising drop in test error in overparameterized models.
method Informal explanation using linear algebra and probability, visual intuition with polynomial regression, mathematical analysis with ordinary linear regression.
result Three factors create double descent: data undersampling, model size, and parameter count. Ablating any one of these factors prevents double descent.
New adaptive step-size method for convex optimization without tuning.
problem Optimizing convex functions efficiently with stochastic gradients.
method Adapted Adaptive Gradient Descent Without Descent to stochastic setting.
result Stochastic gradient descent converges under various assumptions.
New insights into double descent phenomenon in neural networks.
problem Understanding the double descent behavior in deep learning models.
method Linear teacher-student setup and tools from statistical physics.
result Distinct features are learned at different scales, leading to epoch-wise double descent.
Gradient descent dynamics in nonconvex models explained with universality.
problem Understanding long-time behavior of nonconvex gradient descent.
method Developed a state evolution system for tracking gradient descent iterates.
result Gradient descent iterates are approximately independent of data and strongly incoherent with feature vectors.
Gradient descent variants improve phase retrieval accuracy.
problem Phase retrieval problem in high-dimensional spaces.
method Gradient descent, stochastic gradient descent, Langevin algorithm, dynamical mean-field theory.
result Stochastic variants of gradient descent achieve better generalization in phase retrieval.
The paper connects tempering and entropic mirror descent for sampling.
problem Sampling from a target distribution with known unnormalized density.
method Establishes the connection between tempering SMC and entropic mirror descent, deriving convergence rates and geometric insights.
result Tempering SMC iterates correspond to entropic mirror descent on the reverse KL divergence, providing new optimization perspectives.
We consider the behavior of gradient flow and of discrete and noisy gradient descent. It is commonly noted that the addition of noise to the process of discrete gradient descent can affect the trajectory of gradient descent. In previous work, we observed such effects. There, we considered the case where the minima had …