Screening for a Reweighted Penalized Conditional Gradient Method

• URL: http://arxiv.org/abs/2107.01106v1
• Date: Fri, 2 Jul 2021 14:37:37 GMT
• Title: Screening for a Reweighted Penalized Conditional Gradient Method
• Abstract summary: The conditional gradient method (CGM) is widely used in large-scale sparse convex optimization. We show how to adjust the sparsity acquiring properties of a general penalized generalizers. In our experiments, we verify the aggressiveness of the screening rule by tuning the concavity of the regularizer.
• Score: 20.62129327196916
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: The conditional gradient method (CGM) is widely used in large-scale sparse convex optimization, having a low per iteration computational cost for structured sparse regularizers and a greedy approach to collecting nonzeros. We explore the sparsity acquiring properties of a general penalized CGM (P-CGM) for convex regularizers and a reweighted penalized CGM (RP-CGM) for nonconvex regularizers, replacing the usual convex constraints with gauge-inspired penalties. This generalization does not increase the per-iteration complexity noticeably. Without assuming bounded iterates or using line search, we show $O(1/t)$ convergence of the gap of each subproblem, which measures distance to a stationary point. We couple this with a screening rule which is safe in the convex case, converging to the true support at a rate $O(1/(\delta^2))$ where $\delta \geq 0$ measures how close the problem is to degeneracy. In the nonconvex case the screening rule converges to the true support in a finite number of iterations, but is not necessarily safe in the intermediate iterates. In our experiments, we verify the consistency of the method and adjust the aggressiveness of the screening rule by tuning the concavity of the regularizer.

Related papers

• Regularized Online RLHF with Generalized Bilinear Preferences [68.44113000390544]
  We consider the problem of contextual online RLHF with general preferences.<n>We adopt the Generalized Bilinear Preference Model to capture preferences via low-rank, skew-symmetric matrices.<n>We prove that the dual gap of the greedy policy is bounded by the square of the estimation error.
  arXiv  Detail & Related papers  (2026-02-26T15:27:53Z)
• Bayesian Risk-Sensitive Policy Optimization For MDPs With General Loss Functions [8.16996766356341]
  We consider Markov decision processes (MDPs) with a general loss function and unknown parameters.<n>We take a Bayesian approach to estimate the parameters from data and impose a coherent risk functional on the loss.<n>We propose a policy gradient optimization method, leveraging the dual representation of coherent risk measures.
  arXiv  Detail & Related papers  (2025-09-19T01:16:59Z)
• Revisiting Convergence: Shuffling Complexity Beyond Lipschitz Smoothness [50.78508362183774]
  Shuffling-type gradient methods are favored in practice for their simplicity and rapid empirical performance.<n>Most require the Lipschitz condition, which is often not met in common machine learning schemes.
  arXiv  Detail & Related papers  (2025-07-11T15:36:48Z)
• A Stochastic Proximal Method for Nonsmooth Regularized Finite Sum Optimization [7.014966911550542]
  We consider the problem of training a deep neural network with nonsmooth regularization to retrieve a sparse sub-structure. We derive a new solver, called SR2, whose convergence and worst-case complexity are established without knowledge or approximation of the gradient's Lipschitz constant. Experiments on network instances trained on CIFAR-10 and CIFAR-100 show that SR2 consistently achieves higher sparsity and accuracy than related methods such as ProxGEN and ProxSGD.
  arXiv  Detail & Related papers  (2022-06-14T00:28:44Z)
• Benign Underfitting of Stochastic Gradient Descent [72.38051710389732]
  We study to what extent may gradient descent (SGD) be understood as a "conventional" learning rule that achieves generalization performance by obtaining a good fit training data. We analyze the closely related with-replacement SGD, for which an analogous phenomenon does not occur and prove that its population risk does in fact converge at the optimal rate.
  arXiv  Detail & Related papers  (2022-02-27T13:25:01Z)
• Faster One-Sample Stochastic Conditional Gradient Method for Composite Convex Minimization [61.26619639722804]
  We propose a conditional gradient method (CGM) for minimizing convex finite-sum objectives formed as a sum of smooth and non-smooth terms. The proposed method, equipped with an average gradient (SAG) estimator, requires only one sample per iteration. Nevertheless, it guarantees fast convergence rates on par with more sophisticated variance reduction techniques.
  arXiv  Detail & Related papers  (2022-02-26T19:10:48Z)
• Fast Global Convergence of Policy Optimization for Constrained MDPs [17.825031573375725]
  We show that gradient-based methods can achieve an $mathcalO(log(T)/T)$ global convergence rate both for the optimality gap and the constraint violation. When Slater's condition is satisfied and known a priori, zero constraint violation can be further guaranteed for a sufficiently large $T$.
  arXiv  Detail & Related papers  (2021-10-31T17:46:26Z)
• High-probability Bounds for Non-Convex Stochastic Optimization with Heavy Tails [55.561406656549686]
  We consider non- Hilbert optimization using first-order algorithms for which the gradient estimates may have tails. We show that a combination of gradient, momentum, and normalized gradient descent convergence to critical points in high-probability with best-known iteration for smooth losses.
  arXiv  Detail & Related papers  (2021-06-28T00:17:01Z)
• Benign Overfitting of Constant-Stepsize SGD for Linear Regression [122.70478935214128]
  inductive biases are central in preventing overfitting empirically. This work considers this issue in arguably the most basic setting: constant-stepsize SGD for linear regression. We reflect on a number of notable differences between the algorithmic regularization afforded by (unregularized) SGD in comparison to ordinary least squares.
  arXiv  Detail & Related papers  (2021-03-23T17:15:53Z)
• Private Stochastic Non-Convex Optimization: Adaptive Algorithms and Tighter Generalization Bounds [72.63031036770425]
  We propose differentially private (DP) algorithms for bound non-dimensional optimization. We demonstrate two popular deep learning methods on the empirical advantages over standard gradient methods.
  arXiv  Detail & Related papers  (2020-06-24T06:01:24Z)
• On the Almost Sure Convergence of Stochastic Gradient Descent in Non-Convex Problems [75.58134963501094]
  This paper analyzes the trajectories of gradient descent (SGD) We show that SGD avoids saddle points/manifolds with $1$ for strict step-size policies.
  arXiv  Detail & Related papers  (2020-06-19T14:11:26Z)
• Variance reduction for Random Coordinate Descent-Langevin Monte Carlo [7.464874233755718]
  Langevin Monte Carlo (LMC) that provides fast convergence requires computation of gradient approximations. In practice one uses finite-differencing approximations as surrogates, and the method is expensive in high-dimensions. We introduce a new variance reduction approach, termed Coordinates Averaging Descent (RCAD), and incorporate it with both overdamped and underdamped LMC.
  arXiv  Detail & Related papers  (2020-06-10T21:08:38Z)
• Explicit Regularization of Stochastic Gradient Methods through Duality [9.131027490864938]
  We propose randomized Dykstra-style algorithms based on randomized dual coordinate ascent. For accelerated coordinate descent, we obtain a new algorithm that has better convergence properties than existing gradient methods in the interpolating regime.
  arXiv  Detail & Related papers  (2020-03-30T20:44:56Z)
• Safe Screening for the Generalized Conditional Gradient Method [2.806911268410107]
  We explore the sparsity acquiring properties of a generalized conditional gradient method (gCGM) We show that the gCGM for modified penalties have similar feature selection properties as common penalties.
  arXiv  Detail & Related papers  (2020-02-22T15:07:20Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.