Short note on soft-max and policy gradients in bandit problems using Lyapunov functions.
problem Analyzing soft-max and policy gradient methods in bandit problems.
method Lyapunov function argument for soft-max and differential equations for policy gradient algorithms.
result Regret bounds for soft-max and a different policy gradient algorithm in bandit problems.
New methods using natural gradient for structured optimization.
problem Structured optimization problems.
method Structured second-order methods via natural gradient descent.
result Efficiency demonstrated on non-convex and deep learning problems.
Policy gradients methods apply to complex, poorly understood, control problems by performing stochastic gradient descent over a parameterized class of polices. Unfortunately, even for simple control problems solvable by standard dynamic programming techniques, policy gradient algorithms face non-convex optimization pro…
FGD reduces noisy gradient variance in SGD for neural networks.
problem Noisy and unreliable gradient estimation in SGD for deep learning.
method Solves an adaptive filtering problem to consistently estimate the local gradient.
result Significantly reduces gradient variance and accelerates convergence.
Paper analyzes convergence of dynamic policy gradient for MDPs, improving performance in finite-time problems.
problem Optimal policies in finite-time MDPs are not stationary and require epoch-specific training.
method Introduces dynamic policy gradient combining dynamic programming and policy gradient, analyzes convergence for softmax parametrisation.
result Dynamic policy gradient training exploits finite-time structure, leading to better convergence bounds.
New method uses diffusion models to solve inverse problems.
problem Solving ill-posed inverse problems with powerful priors.
method Formulate posterior sampling as a regularized Wasserstein gradient flow in latent space.
result Demonstrates improved performance on standard benchmarks.
Gradient descent and SGD solve nonlinear inverse problems efficiently.
problem Solving nonlinear inverse problems with random design.
method Gradient descent and SGD with mini-batching, under classical assumptions.
result Achieves optimal convergence rates in RKHS framework.
Stochastic gradient algorithms estimate the gradient based on only one or a few samples and enjoy low computational cost per iteration. They have been widely used in large-scale optimization problems. However, stochastic gradient algorithms are usually slow to converge and achieve sub-linear convergence rates, due to t…
New method for RL with general utilities using variational policy gradient.
problem Optimizing policies with general concave utility functions in RL.
method Derives Variational Policy Gradient Theorem, develops variational Monte Carlo gradient estimation algorithm.
result Global convergence to optimal policy for general objectives, exponential convergence under strong convexity.
In this paper we consider solving saddle point problems using two variants of Gradient Descent-Ascent algorithms, Extra-gradient (EG) and Optimistic Gradient Descent Ascent (OGDA) methods. We show that both of these algorithms admit a unified analysis as approximations of the classical proximal point method for solving…
Improved complexity for smooth nonconvex optimization using quasi-Newton methods.
problem Finding ε-first-order stationary points of smooth functions with gradient information only.
method Two-level online learning approach involving quasi-Newton methods.
result Gradient complexity improved to O(d^(1/4)ε^(-13/8)) for d = O(ε^(-1/2)).
New framework for policy gradient methods in continuous time reinforcement learning.
problem Addressing policy gradient methods for continuous time reinforcement learning.
method Control randomisation technique to derive policy gradient representation for various Markovian control problems.
result Demonstrated application to optimal switching problems in the energy sector.
Multi-subject fMRI data analysis is an interesting and challenging problem in human brain decoding studies. The inherent anatomical and functional variability across subjects make it necessary to do both anatomical and functional alignment before classification analysis. Besides, when it comes to big data, time complex…
Introduces new gradient-based methods for machine learning problems.
problem New challenges in machine learning due to decision-making and multi-agent problems.
method Gradient-based optimization and variational inequalities.
result Shifts focus from pattern recognition to decision-making and multi-agent problems.
Many machine learning, statistical inference, and portfolio optimization problems require minimization of a composition of expected value functions (CEVF). Of particular interest is the finite-sum versions of such compositional optimization problems (FS-CEVF). Compositional stochastic variance reduced gradient (C-SVRG)…
Log-density gradient estimation is a fundamental statistical problem and possesses various practical applications such as clustering and measuring non-Gaussianity. A naive two-step approach of first estimating the density and then taking its log-gradient is unreliable because an accurate density estimate does not neces…
This paper is a broad and accessible survey of the methods we have at our disposal for Monte Carlo gradient estimation in machine learning and across the statistical sciences: the problem of computing the gradient of an expectation of a function with respect to parameters defining the distribution that is integrated; t…
In machine learning research, the proximal gradient methods are popular for solving various optimization problems with non-smooth regularization. Inexact proximal gradient methods are extremely important when exactly solving the proximal operator is time-consuming, or the proximal operator does not have an analytic sol…
Optimal neural network approximation for Wasserstein gradient direction via convex optimization.
problem Approximating Wasserstein gradient direction with limited data.
method Two-layer networks with squared-ReLU activations, SDP relaxation.
result Optimal approximation of Wasserstein gradient direction in two-layer networks.
New approach improves model generalization through distributionally robust learning.
problem Improving model generalization in machine learning.
method Stochastic gradient descent applied to the outer minimization problem, with gradient estimation through multi-level Monte Carlo randomization.
result Our approach yields significant benefits over previous work in numerical experiments.
New framework analyzes effectiveness of neural network-based combinatorial problem solvers.
problem Analyzing neural network-based methods for combinatorial optimization problems.
method Introducing a theoretical framework to assess the effectiveness of solution-samplers using policy-gradient methods.
result Positive theoretical answer to the existence of expressive, tractable, and benign optimization landscapes for combinatorial problems.
This paper analyzes adaptive gradient algorithms for better performance in ill-conditioned problems.
problem Poor performance of standard stochastic gradient algorithms in ill-conditioned problems.
method Non-asymptotic analysis of adaptive gradient algorithms (Adagrad and Stochastic Newton) for strongly convex objectives.
result Theoretical analysis and adaptation to practical applications like linear regression and regularized GLM.
Analytical method approximates ELBO gradient in clutter problem.
problem Clutter problem in Bayesian networks with Gaussian likelihood.
method Reparameterization trick, local approximation of likelihood factors.
result Good accuracy and linear computational complexity compared to classical methods.
Paper proposes a pre-conditioning technique to speed up gradient-descent convergence in distributed linear least-squares problems.
problem Expediting convergence of gradient-descent method for ill-conditioned distributed linear least-squares problems.
method Iterative pre-conditioning technique to improve convergence rate of gradient-descent method.
result Pre-conditioned gradient-descent achieves superlinear convergence for unique solutions and improved linear convergence otherwise.
Improves deep learning models by blending gradients from training loss and auxiliary objective.
problem Minimizing a single training loss while encouraging desirable model properties.
method Solves a bilevel optimization problem by combining training loss gradients and orthogonal projections of auxiliary gradients.
result Bloop method leads to better performance than other gradient surgery methods without EMA.
Paper introduces a new multi-kernel algorithm for better gradient approximation.
problem Improving gradient approximation in high-dimensional problems.
method Develops a multi-kernel passive stochastic gradient algorithm with variance reduction.
result The multi-kernel algorithm performs better in high-dimensional problems.
Paper uses SGD for solving linear inverse problems, improving empirical performance.
problem Solving statistical inverse problems in science and engineering.
method Stochastic Gradient Descent (SGD) for linear inverse problems, with smoothing techniques.
result Consistency and finite sample bounds for excess risk demonstrated.
Paper finds unique solutions for curved surfaces with specific gradient.
problem Existence of curved surfaces with specific gradient.
method Second boundary value problem of constant mean curvature equations.
result Unique convex solutions for constant mean curvature equations.
A long-standing obstacle to progress in deep learning is the problem of vanishing and exploding gradients. Although, the problem has largely been overcome via carefully constructed initializations and batch normalization, architectures incorporating skip-connections such as highway and resnets perform much better than …
Enhances SGLD for log-concave posteriors with asynchronous computation.
problem Sampling log-concave posterior distributions efficiently.
method Integrates asynchronous computation into SGLD with delayed gradients.
result Convergence in measure is not significantly affected by delayed gradient information.
AdaX improves Adam by exponentially accumulating past gradients, leading to better performance in machine learning tasks.
problem Adam's fast convergence can lead to local minimums in non-convex problems.
method AdaX exponentially accumulates past gradients to adaptively tune the learning rate.
result AdaX outperforms Adam in various machine learning tasks, including computer vision and natural language processing.
We study a hybrid conditional gradient - smoothing algorithm (HCGS) for solving composite convex optimization problems which contain several terms over a bounded set. Examples of these include regularization problems with several norms as penalties and a norm constraint. HCGS extends conditional gradient methods to cas…
Optimizes Thompson sampling policies using policy gradient methods.
problem Improving Thompson sampling in bandit problems.
method Applies policy gradient algorithms to optimize Thompson sampling policies.
result Direct policy search on Thompson sampling improves performance.
Normalization layers are widely used in deep neural networks to stabilize training. In this paper, we consider the training of convolutional neural networks with gradient descent on a single training example. This optimization problem arises in recent approaches for solving inverse problems such as the deep image prior…
Sigmoid-type networks avoid vanishing gradients with regularization and rescaling.
problem Vanishing gradients in sigmoid-type networks.
method Mathematical arguments and two remedies: regularization and rescaling.
result Demonstrates effectiveness of regularization and rescaling in practice.
This paper analyzes OGDA and EG methods for nonconvex minimax problems.
problem Theoretical guarantees of OGDA and EG methods in nonconvex settings.
method Unified analysis through single-call extra-gradient methods.
result Established convergence of OGDA and EG methods under NC-SC and NC-C settings.
We conduct mathematical analysis on the effect of batch normalization (BN) on gradient backpropogation in residual network training, which is believed to play a critical role in addressing the gradient vanishing/explosion problem, in this work. By analyzing the mean and variance behavior of the input and the gradient i…
Identifies a gradient flow to solve kernel learning problems with noise reduction.
problem Kernel learning problem with Gaussian noise.
method Riemannian gradient flow with continuous Lyapunov functionals.
result Flow reduces noise and finds stationary points.
This work proposes a new method for variational inference using Wasserstein gradient descent.
problem Optimizing variational parameters to match a true posterior distribution.
method Reinterpreting VI as an optimization problem over a variational parameter space, using Wasserstein gradient descent.
result The proposed Wasserstein gradient descent can be seen as a generalization of existing optimization techniques in VI.
Langevin algorithms enhance training of deep neural networks for stochastic control problems.
problem Training acceleration for deep neural networks in stochastic control problems.
method Application of Langevin algorithms to minimize the loss of deep neural networks in stochastic control problems.
result Langevin algorithms improve training on various stochastic control problems.
We consider nonconvex-concave minimax optimization problems of the form minxmaxy∈Yf(x,y), where f is strongly-concave in y but possibly nonconvex in x and Y is a convex and compact set. We focus on the stochastic setting, where we can only access an…
New DP optimization methods for sparse gradients, improving on existing algorithms.
problem Differentially private optimization with sparse gradients in high-dimensional settings.
method Improved bounds for mean estimation, pure- and approximate-DP algorithms for stochastic convex optimization.
result First nearly dimension-independent rates for DP optimization with sparse gradients.
dboost optimizes prediction models for convex cone problems.
problem Optimizing prediction models for decision-making.
method Gradient boosting with implicit differentiation for convex quadratic cone programming.
result dboost reduces out-of-sample decision regret.
Study on stability of free boundary Willmore problem using new gradient inequality.
problem Stability of free boundary Willmore problem.
method New Łojasiewicz-Simon gradient inequality for functionals on infinite dimensional manifolds.
result Existence and convergence of solutions for the free boundary Willmore flow.
New algorithm improves convergence for non-convex problems with boundaries.
problem Optimizing non-convex problems with constraints.
method Reflected Gradient Langevin Dynamics with probabilistic representation.
result Promising convergence rates, faster than existing methods.
CPS solves inverse problems using forward passes and constrained particle seeking.
problem Solving inverse problems with limited forward observation information.
method Gradient-free approach that reformulates inverse problem as constrained optimization.
result CPS achieves results comparable to gradient-based methods while outperforming alternatives.
Extends dimension reduction to data-driven settings without gradients.
problem Gradient-based dimension reduction limitations in data-driven settings.
method Score ratio matching framework, tailored parameterization, regularization, eigenvalue deflation.
result Outperforms standard score-matching for problems with low-dimensional structure.
Paper proves gradient estimates for Lagrangian mean curvature equation.
problem Proving gradient estimates for Lagrangian mean curvature equation.
method Interior gradient estimates for critical and supercritical Lagrangian mean curvature equation.
result Solves Dirichlet boundary value problem for critical and supercritical Lagrangian mean curvature equation.