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Found 102 papers, 16 papers with code
Learning Adversarial Markov Decision Processes with Bandit Feedback and Unknown Transition
We consider the task of learning in episodic finite-horizon Markov decision processes with an unknown transition function, bandit feedback, and adversarial losses.
Complexity of Finding Stationary Points of Nonconvex Nonsmooth Functions
Therefore, we introduce the notion of (delta, epsilon)-stationarity, a generalization that allows for a point to be within distance delta of an epsilon-stationary point and reduces to epsilon-stationarity for smooth functions.
Graph Transformers Dream of Electric Flow
We show theoretically and empirically that the linear Transformer, when applied to graph data, can implement algorithms that solve canonical problems such as electric flow and eigenvector decomposition.
Memory-augmented Transformers can implement Linear First-Order Optimization Methods
We show that memory-augmented Transformers (Memformers) can implement linear first-order optimization methods such as conjugate gradient descent, momentum methods, and more generally, methods that linearly combine past gradients.
First-Order Methods for Linearly Constrained Bilevel Optimization
For linear equality constraints, we attain $\epsilon$-stationarity in $\widetilde{O}(\epsilon^{-2})$ gradient oracle calls, which is nearly-optimal.
Efficient Sampling on Riemannian Manifolds via Langevin MCMC
We study the task of efficiently sampling from a Gibbs distribution $d \pi^* = e^{-h} d {vol}_g$ over a Riemannian manifold $M$ via (geometric) Langevin MCMC; this algorithm involves computing exponential maps in random Gaussian directions and is efficiently implementable in practice.
Transformers Implement Functional Gradient Descent to Learn Non-Linear Functions In Context
Many neural network architectures are known to be Turing Complete, and can thus, in principle implement arbitrary algorithms.
Linear attention is (maybe) all you need (to understand transformer optimization)
Transformer training is notoriously difficult, requiring a careful design of optimizers and use of various heuristics.
Invex Programs: First Order Algorithms and Their Convergence
Invex programs are a special kind of non-convex problems which attain global minima at every stationary point.
How to escape sharp minima with random perturbations
Under this notion, we then analyze algorithms that find approximate flat minima efficiently.
On the Training Instability of Shuffling SGD with Batch Normalization
We uncover how SGD interacts with batch normalization and can exhibit undesirable training dynamics such as divergence.
Can Direct Latent Model Learning Solve Linear Quadratic Gaussian Control?
We study the task of learning state representations from potentially high-dimensional observations, with the goal of controlling an unknown partially observable system.
On a class of geodesically convex optimization problems solved via Euclidean MM methods
We study geodesically convex (g-convex) problems that can be written as a difference of Euclidean convex functions.
Understanding the unstable convergence of gradient descent
Most existing analyses of (stochastic) gradient descent rely on the condition that for $L$-smooth costs, the step size is less than $2/L$.
Sign and Basis Invariant Networks for Spectral Graph Representation Learning
We introduce SignNet and BasisNet -- new neural architectures that are invariant to two key symmetries displayed by eigenvectors: (i) sign flips, since if $v$ is an eigenvector then so is $-v$; and (ii) more general basis symmetries, which occur in higher dimensional eigenspaces with infinitely many choices of basis eigenvectors.
Ranked #12 on
Graph Regression
on ZINC-500k
Sion's Minimax Theorem in Geodesic Metric Spaces and a Riemannian Extragradient Algorithm
Deciding whether saddle points exist or are approximable for nonconvex-nonconcave problems is usually intractable.
Time varying regression with hidden linear dynamics
We revisit a model for time-varying linear regression that assumes the unknown parameters evolve according to a linear dynamical system.
Max-Margin Contrastive Learning
Standard contrastive learning approaches usually require a large number of negatives for effective unsupervised learning and often exhibit slow convergence.
Ranked #116 on
Self-Supervised Image Classification
on ImageNet
Understanding Riemannian Acceleration via a Proximal Extragradient Framework
We contribute to advancing the understanding of Riemannian accelerated gradient methods.
Minibatch vs Local SGD with Shuffling: Tight Convergence Bounds and Beyond
In distributed learning, local SGD (also known as federated averaging) and its simple baseline minibatch SGD are widely studied optimization methods.
Neural Network Weights Do Not Converge to Stationary Points: An Invariant Measure Perspective
This work examines the deep disconnect between existing theoretical analyses of gradient-based algorithms and the practice of training deep neural networks.
Can contrastive learning avoid shortcut solutions?
However, we observe that the contrastive loss does not always sufficiently guide which features are extracted, a behavior that can negatively impact the performance on downstream tasks via "shortcuts", i. e., by inadvertently suppressing important predictive features.
Can Single-Shuffle SGD be Better than Reshuffling SGD and GD?
We propose matrix norm inequalities that extend the Recht-R\'e (2012) conjecture on a noncommutative AM-GM inequality by supplementing it with another inequality that accounts for single-shuffle, which is a widely used without-replacement sampling scheme that shuffles only once in the beginning and is overlooked in the Recht-R\'e conjecture.
Provably Efficient Algorithms for Multi-Objective Competitive RL
To our knowledge, this work provides the first provably efficient algorithms for vector-valued Markov games and our theoretical guarantees are near-optimal.
Stochastic Optimization with Non-stationary Noise: The Power of Moment Estimation
In particular, standard results on optimal convergence rates for stochastic optimization assume either there exists a uniform bound on the moments of the gradient noise, or that the noise decays as the algorithm progresses.
Why do classifier accuracies show linear trends under distribution shift?
Recent studies of generalization in deep learning have observed a puzzling trend: accuracies of models on one data distribution are approximately linear functions of the accuracies on another distribution.
Online Learning in Unknown Markov Games
We study online learning in unknown Markov games, a problem that arises in episodic multi-agent reinforcement learning where the actions of the opponents are unobservable.
Coping with Label Shift via Distributionally Robust Optimisation
The label shift problem refers to the supervised learning setting where the train and test label distributions do not match.
Contrastive Learning with Hard Negative Samples
How can you sample good negative examples for contrastive learning?
Towards Minimax Optimal Reinforcement Learning in Factored Markov Decision Processes
We study minimax optimal reinforcement learning in episodic factored Markov decision processes (FMDPs), which are MDPs with conditionally independent transition components.
SGD with shuffling: optimal rates without component convexity and large epoch requirements
We study without-replacement SGD for solving finite-sum optimization problems.
Beyond Worst-Case Analysis in Stochastic Approximation: Moment Estimation Improves Instance Complexity
We study oracle complexity of gradient based methods for stochastic approximation problems.
Understanding Nesterov's Acceleration via Proximal Point Method
The proximal point method (PPM) is a fundamental method in optimization that is often used as a building block for designing optimization algorithms.
On Tight Convergence Rates of Without-replacement SGD
For solving finite-sum optimization problems, SGD without replacement sampling is empirically shown to outperform SGD.
Strength from Weakness: Fast Learning Using Weak Supervision
Our theoretical results are reflected empirically across a range of tasks and illustrate how weak labels speed up learning on the strong task.
Complexity of Finding Stationary Points of Nonsmooth Nonconvex Functions
In particular, we study the class of Hadamard semi-differentiable functions, perhaps the largest class of nonsmooth functions for which the chain rule of calculus holds.
From Nesterov's Estimate Sequence to Riemannian Acceleration
We control this distortion by developing a novel geometric inequality, which permits us to propose and analyze a Riemannian counterpart to Nesterov's accelerated gradient method.
Why are Adaptive Methods Good for Attention Models?
While stochastic gradient descent (SGD) is still the \emph{de facto} algorithm in deep learning, adaptive methods like Clipped SGD/Adam have been observed to outperform SGD across important tasks, such as attention models.
Learning Adversarial MDPs with Bandit Feedback and Unknown Transition
We consider the problem of learning in episodic finite-horizon Markov decision processes with an unknown transition function, bandit feedback, and adversarial losses.
Projection-free nonconvex stochastic optimization on Riemannian manifolds
We present algorithms for both purely stochastic optimization and finite-sum problems.
Why ADAM Beats SGD for Attention Models
While stochastic gradient descent (SGD) is still the de facto algorithm in deep learning, adaptive methods like Adam have been observed to outperform SGD across important tasks, such as attention models.
Efficient Policy Learning for Non-Stationary MDPs under Adversarial Manipulation
A Markov Decision Process (MDP) is a popular model for reinforcement learning.
Are deep ResNets provably better than linear predictors?
Recent results in the literature indicate that a residual network (ResNet) composed of a single residual block outperforms linear predictors, in the sense that all local minima in its optimization landscape are at least as good as the best linear predictor.
Near Optimal Stratified Sampling
The performance of a machine learning system is usually evaluated by using i. i. d.\ observations with true labels.
Flexible Modeling of Diversity with Strongly Log-Concave Distributions
We propose SLC as the right extension of SR that enables easier, more intuitive control over diversity, illustrating this via examples of practical importance.
Why gradient clipping accelerates training: A theoretical justification for adaptivity
We provide a theoretical explanation for the effectiveness of gradient clipping in training deep neural networks.
Escaping Saddle Points with Adaptive Gradient Methods
Adaptive methods such as Adam and RMSProp are widely used in deep learning but are not well understood.
Deep-RBF Networks Revisited: Robust Classification with Rejection
On the other hand, deep-RBF networks assign high confidence only to the regions containing enough feature points, but they have been discounted due to the widely-held belief that they have the vanishing gradient problem.
Exponentiated Strongly Rayleigh Distributions
Strongly Rayleigh (SR) measures are discrete probability distributions over the subsets of a ground set.
R-SPIDER: A Fast Riemannian Stochastic Optimization Algorithm with Curvature Independent Rate
We study smooth stochastic optimization problems on Riemannian manifolds.
Small ReLU networks are powerful memorizers: a tight analysis of memorization capacity
We also prove that width $\Theta(\sqrt{N})$ is necessary and sufficient for memorizing $N$ data points, proving tight bounds on memorization capacity.
Efficiently testing local optimality and escaping saddles for ReLU networks
In the benign case, we solve one equality constrained QP, and we prove that projected gradient descent solves it exponentially fast.
Random Shuffling Beats SGD after Finite Epochs
We present the first (to our knowledge) non-asymptotic solution to this problem, which shows that after a "reasonable" number of epochs RandomShuffle indeed converges faster than SGD.
Towards Riemannian Accelerated Gradient Methods
We propose a Riemannian version of Nesterov's Accelerated Gradient algorithm (RAGD), and show that for geodesically smooth and strongly convex problems, within a neighborhood of the minimizer whose radius depends on the condition number as well as the sectional curvature of the manifold, RAGD converges to the minimizer with acceleration.
Direct Runge-Kutta Discretization Achieves Acceleration
We study gradient-based optimization methods obtained by directly discretizing a second-order ordinary differential equation (ODE) related to the continuous limit of Nesterov's accelerated gradient method.
Non-Linear Temporal Subspace Representations for Activity Recognition
As these features are often non-linear, we propose a novel pooling method, kernelized rank pooling, that represents a given sequence compactly as the pre-image of the parameters of a hyperplane in a reproducing kernel Hilbert space, projections of data onto which captures their temporal order.
Learning Determinantal Point Processes by Corrective Negative Sampling
To address this issue, which reduces the quality of the learned model, we introduce a novel optimization problem, Contrastive Estimation (CE), which encodes information about "negative" samples into the basic learning model.
Small nonlinearities in activation functions create bad local minima in neural networks
Our results thus indicate that in general "no spurious local minima" is a property limited to deep linear networks, and insights obtained from linear networks may not be robust.
Riemannian Optimization via Frank-Wolfe Methods
Both tasks involve geodesically convex interval constraints, for which we show that the Riemannian "linear" oracle required by RFW admits a closed-form solution; this result may be of independent interest.
A Generic Approach for Escaping Saddle points
A central challenge to using first-order methods for optimizing nonconvex problems is the presence of saddle points.
Global optimality conditions for deep neural networks
We study the error landscape of deep linear and nonlinear neural networks with the squared error loss.
Distributional Adversarial Networks
We propose a framework for adversarial training that relies on a sample rather than a single sample point as the fundamental unit of discrimination.
An Alternative to EM for Gaussian Mixture Models: Batch and Stochastic Riemannian Optimization
This motivates us to take a closer look at the problem geometry, and derive a better formulation that is much more amenable to Riemannian optimization.
Sequence Summarization Using Order-constrained Kernelized Feature Subspaces
As these features are often non-linear, we propose a novel pooling method, kernelized rank pooling, that represents a given sequence compactly as the pre-image of the parameters of a hyperplane in an RKHS, projections of data onto which captures their temporal order.
Polynomial Time Algorithms for Dual Volume Sampling
We study dual volume sampling, a method for selecting k columns from an n x m short and wide matrix (n <= k <= m) such that the probability of selection is proportional to the volume spanned by the rows of the induced submatrix.
Proximal Stochastic Methods for Nonsmooth Nonconvex Finite-Sum Optimization
We analyze stochastic algorithms for optimizing nonconvex, nonsmooth finite-sum problems, where the nonsmooth part is convex.
Fast Mixing Markov Chains for Strongly Rayleigh Measures, DPPs, and Constrained Sampling
We consider the task of rapidly sampling from such constrained measures, and develop fast Markov chain samplers for them.
Stochastic Frank-Wolfe Methods for Nonconvex Optimization
Finally, we show that the faster convergence rates of our variance reduced methods also translate into improved convergence rates for the stochastic setting.
Fast Sampling for Strongly Rayleigh Measures with Application to Determinantal Point Processes
In this note we consider sampling from (non-homogeneous) strongly Rayleigh probability measures.
Kronecker Determinantal Point Processes
Determinantal Point Processes (DPPs) are probabilistic models over all subsets a ground set of $N$ items.
Fast Stochastic Methods for Nonsmooth Nonconvex Optimization
This paper builds upon our recent series of papers on fast stochastic methods for smooth nonconvex optimization [22, 23], with a novel analysis for nonconvex and nonsmooth functions.
Riemannian SVRG: Fast Stochastic Optimization on Riemannian Manifolds
We study optimization of finite sums of geodesically smooth functions on Riemannian manifolds.
Directional Statistics in Machine Learning: a Brief Review
The modern data analyst must cope with data encoded in various forms, vectors, matrices, strings, graphs, or more.
Combinatorial Topic Models using Small-Variance Asymptotics
Topic models have emerged as fundamental tools in unsupervised machine learning.
Fast Incremental Method for Nonconvex Optimization
We analyze a fast incremental aggregated gradient method for optimizing nonconvex problems of the form $\min_x \sum_i f_i(x)$.
Stochastic Variance Reduction for Nonconvex Optimization
We study nonconvex finite-sum problems and analyze stochastic variance reduced gradient (SVRG) methods for them.
Fast DPP Sampling for Nyström with Application to Kernel Methods
Its theoretical guarantees and empirical performance rely critically on the quality of the landmarks selected.
First-order Methods for Geodesically Convex Optimization
Geodesic convexity generalizes the notion of (vector space) convexity to nonlinear metric spaces.
Gauss quadrature for matrix inverse forms with applications
We present a framework for accelerating a spectrum of machine learning algorithms that require computation of bilinear inverse forms $u^\top A^{-1}u$, where $A$ is a positive definite matrix and $u$ a given vector.
Matrix Manifold Optimization for Gaussian Mixtures
We take a new look at parameter estimation for Gaussian Mixture Model (GMMs).
Diversity Networks: Neural Network Compression Using Determinantal Point Processes
We introduce Divnet, a flexible technique for learning networks with diverse neurons.
Efficient Sampling for k-Determinantal Point Processes
Our method takes advantage of the diversity property of subsets sampled from a DPP, and proceeds in two stages: first it constructs coresets for the ground set of items; thereafter, it efficiently samples subsets based on the constructed coresets.
AdaDelay: Delay Adaptive Distributed Stochastic Convex Optimization
We study distributed stochastic convex optimization under the delayed gradient model where the server nodes perform parameter updates, while the worker nodes compute stochastic gradients.
Fixed-point algorithms for learning determinantal point processes
Determinantal point processes (DPPs) offer an elegant tool for encoding probabilities over subsets of a ground set.
Riemannian Dictionary Learning and Sparse Coding for Positive Definite Matrices
Inspired by the great success of dictionary learning and sparse coding for vector-valued data, our goal in this paper is to represent data in the form of SPD matrices as sparse conic combinations of SPD atoms from a learned dictionary via a Riemannian geometric approach.
Manifold Optimization for Gaussian Mixture Models
We take a new look at parameter estimation for Gaussian Mixture Models (GMMs).
On Variance Reduction in Stochastic Gradient Descent and its Asynchronous Variants
We demonstrate the empirical performance of our method through a concrete realization of asynchronous SVRG.
Convex Optimization for Parallel Energy Minimization
By exploiting results from convex and submodular theory, we reformulate the quadratic energy minimization problem as a total variation denoising problem, which, when viewed geometrically, enables the use of projection and reflection based convex methods.
Efficient Structured Matrix Rank Minimization
We study the problem of finding structured low-rank matrices using nuclear norm regularization where the structure is encoded by a linear map.
Modular proximal optimization for multidimensional total-variation regularization
We study \emph{TV regularization}, a widely used technique for eliciting structured sparsity.
Ranked #1 on
Microarray Classification
on ArrayCGH
Inference and Mixture Modeling with the Elliptical Gamma Distribution
We study modeling and inference with the Elliptical Gamma Distribution (EGD).
Parallel and Distributed Block-Coordinate Frank-Wolfe Algorithms
We develop parallel and distributed Frank-Wolfe algorithms; the former on shared memory machines with mini-batching, and the latter in a delayed update framework.
Large-scale randomized-coordinate descent methods with non-separable linear constraints
We develop randomized (block) coordinate descent (CD) methods for linearly constrained convex optimization.
Randomized Nonlinear Component Analysis
Although nonlinear variants of PCA and CCA have been proposed, these are computationally prohibitive in the large scale.
Geometric optimisation on positive definite matrices for elliptically contoured distributions
We exploit the remarkable structure of the convex cone of positive definite matrices which allows one to uncover hidden geodesic convexity of objective functions that are nonconvex in the ordinary Euclidean sense.
Statistical estimation for optimization problems on graphs
Large graphs abound in machine learning, data mining, and several related areas.
Reflection methods for user-friendly submodular optimization
A key component of our method is a formulation of the discrete submodular minimization problem as a continuous best approximation problem that is solved through a sequence of reflections, and its solution can be easily thresholded to obtain an optimal discrete solution.
Scalable nonconvex inexact proximal splitting
To our knowledge, our framework is first to develop and analyze incremental \emph{nonconvex} proximal-splitting algorithms, even if we disregard the ability to handle nonvanishing errors.
A new metric on the manifold of kernel matrices with application to matrix geometric means
Symmetric positive definite (spd) matrices are remarkably pervasive in a multitude of scientific disciplines, including machine learning and optimization.
Positive definite matrices and the S-divergence
Positive definite matrices abound in a dazzling variety of applications.
