Search Results for author:
Found 99 papers, 16 papers with code
Provable Length Generalization in Sequence Prediction via Spectral Filtering
We consider the problem of length generalization in sequence prediction.
FutureFill: Fast Generation from Convolutional Sequence Models
We address the challenge of efficient auto-regressive generation in sequence prediction models by introducing FutureFill - a method for fast generation that applies to any sequence prediction algorithm based on convolutional operators.
Flash STU: Fast Spectral Transform Units
This paper describes an efficient, open source PyTorch implementation of the Spectral Transform Unit.
Online Control in Population Dynamics
The study of population dynamics originated with early sociological works but has since extended into many fields, including biology, epidemiology, evolutionary game theory, and economics.
Second Order Methods for Bandit Optimization and Control
We show that our algorithm achieves optimal (in terms of horizon) regret bounds for a large class of convex functions that we call $\kappa$-convex.
Adaptive Regret for Bandits Made Possible: Two Queries Suffice
In this paper, we give query and regret optimal bandit algorithms under the strict notion of strongly adaptive regret, which measures the maximum regret over any contiguous interval $I$.
Chain of LoRA: Efficient Fine-tuning of Language Models via Residual Learning
Fine-tuning is the primary methodology for tailoring pre-trained large language models to specific tasks.
Spectral State Space Models
This paper studies sequence modeling for prediction tasks with long range dependencies.
Playing Large Games with Oracles and AI Debate
We give a novel efficient algorithm for simultaneous external and internal regret minimization whose regret depends logarithmically on the number of actions.
An Efficient Interior-Point Method for Online Convex Optimization
A new algorithm for regret minimization in online convex optimization is described.
A Nonstochastic Control Approach to Optimization
Selecting the best hyperparameters for a particular optimization instance, such as the learning rate and momentum, is an important but nonconvex problem.
Projection-free Adaptive Regret with Membership Oracles
The most common approach is based on the Frank-Wolfe method, that uses linear optimization computation in lieu of projections.
Best of Both Worlds in Online Control: Competitive Ratio and Policy Regret
We consider the fundamental problem of online control of a linear dynamical system from two different viewpoints: regret minimization and competitive analysis.
Introduction to Online Nonstochastic Control
In online nonstochastic control, both the cost functions as well as the perturbations from the assumed dynamical model are chosen by an adversary.
Partial Matrix Completion
This work establishes a new framework of partial matrix completion, where the goal is to identify a large subset of the entries that can be completed with high confidence.
On the Computational Efficiency of Adaptive and Dynamic Regret Minimization
In online convex optimization, the player aims to minimize regret, or the difference between her loss and that of the best fixed decision in hindsight over the entire repeated game.
Adaptive Online Learning of Quantum States
The problem of efficient quantum state learning, also called shadow tomography, aims to comprehend an unknown $d$-dimensional quantum state through POVMs.
Non-convex online learning via algorithmic equivalence
We prove an $O(T^{\frac{2}{3}})$ regret bound for non-convex online gradient descent in this setting, answering this open problem.
Adaptive Gradient Methods with Local Guarantees
Adaptive gradient methods are the method of choice for optimization in machine learning and used to train the largest deep models.
Online Control of Unknown Time-Varying Dynamical Systems
On the positive side, we give an efficient algorithm that attains a sublinear regret bound against the class of Disturbance Response policies up to the aforementioned system variability term.
A Regret Minimization Approach to Multi-Agent Control
We study the problem of multi-agent control of a dynamical system with known dynamics and adversarial disturbances.
Multiclass Boosting and the Cost of Weak Learning
Here, we focus on an especially natural formulation in which the weak hypotheses are assumed to belong to an ''easy-to-learn'' base class, and the weak learner is an agnostic PAC learner for that class with respect to the standard classification loss.
Machine Learning for Mechanical Ventilation Control (Extended Abstract)
Mechanical ventilation is one of the most widely used therapies in the ICU.
Provable Regret Bounds for Deep Online Learning and Control
The theory of deep learning focuses almost exclusively on supervised learning, non-convex optimization using stochastic gradient descent, and overparametrized neural networks.
Learning Rate Grafting: Transferability of Optimizer Tuning
In the empirical science of training large neural networks, the learning rate schedule is a notoriously challenging-to-tune hyperparameter, which can depend on all other properties (architecture, optimizer, batch size, dataset, regularization, ...) of the problem.
A Boosting Approach to Reinforcement Learning
Reducing reinforcement learning to supervised learning is a well-studied and effective approach that leverages the benefits of compact function approximation to deal with large-scale Markov decision processes.
Robust Online Control with Model Misspecification
We study online control of an unknown nonlinear dynamical system that is approximated by a time-invariant linear system with model misspecification.
A Regret Minimization Approach to Iterative Learning Control
We consider the setting of iterative learning control, or model-based policy learning in the presence of uncertain, time-varying dynamics.
Deluca -- A Differentiable Control Library: Environments, Methods, and Benchmarking
We present an open-source library of natively differentiable physics and robotics environments, accompanied by gradient-based control methods and a benchmark-ing suite.
Boosting for Online Convex Optimization
In this access model, we give an efficient boosting algorithm that guarantees near-optimal regret against the convex hull of the base class.
Machine Learning for Mechanical Ventilation Control
We consider the problem of controlling an invasive mechanical ventilator for pressure-controlled ventilation: a controller must let air in and out of a sedated patient's lungs according to a trajectory of airway pressures specified by a clinician.
Generating Adversarial Disturbances for Controller Verification
We consider the problem of generating maximally adversarial disturbances for a given controller assuming only blackbox access to it.
Geometric Exploration for Online Control
We study the control of an \emph{unknown} linear dynamical system under general convex costs.
Non-Stochastic Control with Bandit Feedback
We study the problem of controlling a linear dynamical system with adversarial perturbations where the only feedback available to the controller is the scalar loss, and the loss function itself is unknown.
Online Boosting with Bandit Feedback
We consider the problem of online boosting for regression tasks, when only limited information is available to the learner.
Black-Box Control for Linear Dynamical Systems
To complete the picture, we investigate the complexity of the online black-box control problem, and give a matching lower bound of $2^{\Omega(\mathcal{L})}$ on the regret, showing that the additional exponential cost is inevitable.
Adaptive Regret for Control of Time-Varying Dynamics
Our main contribution is a novel efficient meta-algorithm: it converts a controller with sublinear regret bounds into one with sublinear {\it adaptive regret} bounds in the setting of time-varying linear dynamical systems.
Online Agnostic Boosting via Regret Minimization
Boosting is a widely used machine learning approach based on the idea of aggregating weak learning rules.
Disentangling Adaptive Gradient Methods from Learning Rates
We investigate several confounding factors in the evaluation of optimization algorithms for deep learning.
Boosting Simple Learners
(ii) Expressivity: Which tasks can be learned by boosting weak hypotheses from a bounded VC class?
Faster Projection-free Online Learning
In many online learning problems the computational bottleneck for gradient-based methods is the projection operation.
Improper Learning for Non-Stochastic Control
We consider the problem of controlling a possibly unknown linear dynamical system with adversarial perturbations, adversarially chosen convex loss functions, and partially observed states, known as non-stochastic control.
Revisiting the Generalization of Adaptive Gradient Methods
A commonplace belief in the machine learning community is that using adaptive gradient methods hurts generalization.
The Nonstochastic Control Problem
We consider the problem of controlling an unknown linear dynamical system in the presence of (nonstochastic) adversarial perturbations and adversarial convex loss functions.
The gradient complexity of linear regression
We investigate the computational complexity of several basic linear algebra primitives, including largest eigenvector computation and linear regression, in the computational model that allows access to the data via a matrix-vector product oracle.
Logarithmic Regret for Online Control
We study optimal regret bounds for control in linear dynamical systems under adversarially changing strongly convex cost functions, given the knowledge of transition dynamics.
Lecture Notes: Optimization for Machine Learning
Lecture notes on optimization for machine learning, derived from a course at Princeton University and tutorials given in MLSS, Buenos Aires, as well as Simons Foundation, Berkeley.
Boosting for Control of Dynamical Systems
We study the question of how to aggregate controllers for dynamical systems in order to improve their performance.
Private Learning Implies Online Learning: An Efficient Reduction
We study the relationship between the notions of differentially private learning and online learning in games.
Online Control with Adversarial Disturbances
We study the control of a linear dynamical system with adversarial disturbances (as opposed to statistical noise).
Extreme Tensoring for Low-Memory Preconditioning
State-of-the-art models are now trained with billions of parameters, reaching hardware limits in terms of memory consumption.
Exponentiated Gradient Meets Gradient Descent
The hypentropy has a natural spectral counterpart which we use to derive a family of matrix-based updates that bridge gradient methods and the multiplicative method for matrices.
Provably Efficient Maximum Entropy Exploration
Suppose an agent is in a (possibly unknown) Markov Decision Process in the absence of a reward signal, what might we hope that an agent can efficiently learn to do?
Learning in Non-convex Games with an Optimization Oracle
We consider online learning in an adversarial, non-convex setting under the assumption that the learner has an access to an offline optimization oracle.
Efficient Full-Matrix Adaptive Regularization
Due to the large number of parameters of machine learning problems, full-matrix preconditioning methods are prohibitively expensive.
Online Improper Learning with an Approximation Oracle
We revisit the question of reducing online learning to approximate optimization of the offline problem.
Online Learning of Quantum States
Even in the "non-realizable" setting---where there could be arbitrary noise in the measurement outcomes---we show how to output hypothesis states that do significantly worse than the best possible states at most $\operatorname{O}\!\left(\sqrt {Tn}\right) $ times on the first $T$ measurements.
On the Optimization of Deep Networks: Implicit Acceleration by Overparameterization
The effect of depth on optimization is decoupled from expressiveness by focusing on settings where additional layers amount to overparameterization - linear neural networks, a well-studied model.
Spectral Filtering for General Linear Dynamical Systems
We give a polynomial-time algorithm for learning latent-state linear dynamical systems without system identification, and without assumptions on the spectral radius of the system's transition matrix.
Towards Provable Control for Unknown Linear Dynamical Systems
We study the control of symmetric linear dynamical systems with unknown dynamics and a hidden state.
Learning Linear Dynamical Systems via Spectral Filtering
We present an efficient and practical algorithm for the online prediction of discrete-time linear dynamical systems with a symmetric transition matrix.
Lower Bounds for Higher-Order Convex Optimization
State-of-the-art methods in convex and non-convex optimization employ higher-order derivative information, either implicitly or explicitly.
Linear Convergence of a Frank-Wolfe Type Algorithm over Trace-Norm Balls
We propose a rank-$k$ variant of the classical Frank-Wolfe algorithm to solve convex optimization over a trace-norm ball.
Efficient Regret Minimization in Non-Convex Games
We consider regret minimization in repeated games with non-convex loss functions.
Hyperparameter Optimization: A Spectral Approach
In particular, we obtain the first quasi-polynomial time algorithm for learning noisy decision trees with polynomial sample complexity.
The Limits of Learning with Missing Data
We study regression and classification in a setting where the learning algorithm is allowed to access only a limited number of attributes per example, known as the limited attribute observation model.
Finding Approximate Local Minima Faster than Gradient Descent
We design a non-convex second-order optimization algorithm that is guaranteed to return an approximate local minimum in time which scales linearly in the underlying dimension and the number of training examples.
A Non-generative Framework and Convex Relaxations for Unsupervised Learning
We give a novel formal theoretical framework for unsupervised learning with two distinctive characteristics.
Faster Eigenvector Computation via Shift-and-Invert Preconditioning
We give faster algorithms and improved sample complexities for estimating the top eigenvector of a matrix $\Sigma$ -- i. e. computing a unit vector $x$ such that $x^T \Sigma x \ge (1-\epsilon)\lambda_1(\Sigma)$: Offline Eigenvector Estimation: Given an explicit $A \in \mathbb{R}^{n \times d}$ with $\Sigma = A^TA$, we show how to compute an $\epsilon$ approximate top eigenvector in time $\tilde O([nnz(A) + \frac{d*sr(A)}{gap^2} ]* \log 1/\epsilon )$ and $\tilde O([\frac{nnz(A)^{3/4} (d*sr(A))^{1/4}}{\sqrt{gap}} ] * \log 1/\epsilon )$.
Online Learning with Low Rank Experts
We consider the problem of prediction with expert advice when the losses of the experts have low-dimensional structure: they are restricted to an unknown $d$-dimensional subspace.
Optimal Black-Box Reductions Between Optimization Objectives
The diverse world of machine learning applications has given rise to a plethora of algorithms and optimization methods, finely tuned to the specific regression or classification task at hand.
Variance Reduction for Faster Non-Convex Optimization
We consider the fundamental problem in non-convex optimization of efficiently reaching a stationary point.
An optimal algorithm for bandit convex optimization
We consider the problem of online convex optimization against an arbitrary adversary with bandit feedback, known as bandit convex optimization.
Second-Order Stochastic Optimization for Machine Learning in Linear Time
First-order stochastic methods are the state-of-the-art in large-scale machine learning optimization owing to efficient per-iteration complexity.
Variance-Reduced and Projection-Free Stochastic Optimization
The Frank-Wolfe optimization algorithm has recently regained popularity for machine learning applications due to its projection-free property and its ability to handle structured constraints.
Online Learning for Adversaries with Memory: Price of Past Mistakes
In this work we extend the notion of learning with memory to the general Online Convex Optimization (OCO) framework, and present two algorithms that attain low regret.
Fast and Simple PCA via Convex Optimization
The problem of principle component analysis (PCA) is traditionally solved by spectral or algebraic methods.
Faster Convex Optimization: Simulated Annealing with an Efficient Universal Barrier
We show that simulated annealing, a well-studied random walk algorithms, is directly equivalent, in a certain sense, to the central path interior point algorithm for the the entropic universal barrier function.
Beyond Convexity: Stochastic Quasi-Convex Optimization
The Normalized Gradient Descent (NGD) algorithm, is an adaptation of Gradient Descent, which updates according to the direction of the gradients, rather than the gradients themselves.
Online Gradient Boosting
We extend the theory of boosting for regression problems to the online learning setting.
The Computational Power of Optimization in Online Learning
We also give a lower bound showing that this running time cannot be improved (up to log factors) in the oracle model, thereby exhibiting a quadratic speedup as compared to the standard, oracle-free setting where the required time for vanishing regret is $\widetilde{\Theta}(N)$.
On Graduated Optimization for Stochastic Non-Convex Problems
We extend our algorithm and analysis to the setting of stochastic non-convex optimization with noisy gradient feedback, attaining the same convergence rate.
Classification with Low Rank and Missing Data
We consider classification and regression tasks where we have missing data and assume that the (clean) data resides in a low rank subspace.
The Blinded Bandit: Learning with Adaptive Feedback
We study an online learning setting where the player is temporarily deprived of feedback each time it switches to a different action.
Bandit Convex Optimization: Towards Tight Bounds
Bandit Convex Optimization (BCO) is a fundamental framework for decision making under uncertainty, which generalizes many problems from the realm of online and statistical learning.
Faster Rates for the Frank-Wolfe Method over Strongly-Convex Sets
In this paper we consider the special case of optimization over strongly convex sets, for which we prove that the vanila FW method converges at a rate of $\frac{1}{t^2}$.
Logistic Regression: Tight Bounds for Stochastic and Online Optimization
We show that in contrast to known asymptotic bounds, as long as the number of prediction/optimization iterations is sub exponential, the logistic loss provides no improvement over a generic non-smooth loss function such as the hinge loss.
Oracle-Based Robust Optimization via Online Learning
Robust optimization is a common framework in optimization under uncertainty when the problem parameters are not known, but it is rather known that the parameters belong to some given uncertainty set.
Volumetric Spanners: an Efficient Exploration Basis for Learning
Numerous machine learning problems require an exploration basis - a mechanism to explore the action space.
Online Convex Optimization Against Adversaries with Memory and Application to Statistical Arbitrage
The framework of online learning with memory naturally captures learning problems with temporal constraints, and was previously studied for the experts setting.
A Linearly Convergent Conditional Gradient Algorithm with Applications to Online and Stochastic Optimization
In this computational model we give several new results that improve over the previous state-of-the-art.
A Polylog Pivot Steps Simplex Algorithm for Classification
We present a simplex algorithm for linear programming in a linear classification formulation.
Newtron: an Efficient Bandit algorithm for Online Multiclass Prediction
We prove that the regret of \newtron is \(O(\log T)\) when \(\alpha\) is a constant that does not vary with horizon \(T\), and at most \(O(T^{2/3})\) if \(\alpha\) is allowed to increase to infinity with \(T\).
Approximating Semidefinite Programs in Sublinear Time
In recent years semidefinite optimization has become a tool of major importance in various optimization and machine learning problems.
Beating SGD: Learning SVMs in Sublinear Time
We present an optimization approach for linear SVMs based on a stochastic primal-dual approach, where the primal step is akin to an importance-weighted SGD, and the dual step is a stochastic update on the importance weights.
Beyond Convexity: Online Submodular Minimization
We consider an online decision problem over a discrete space in which the loss function is submodular.
On Stochastic and Worst-case Models for Investing
In practice, most investing is done assuming a probabilistic model of stock price returns known as the Geometric Brownian Motion (GBM).
Computational Equivalence of Fixed Points and No Regret Algorithms, and Convergence to Equilibria
We study the relation between notions of game-theoretic equilibria which are based on stability under a set of deviations, and empirical equilibria which are reached by rational players.
