arXiv research

A dissertation on scalable projection-free optimization methods.

This paper focuses on projection-free methods for solving smooth Online Convex Optimization (OCO) problems. Existing projection-free methods either achieve suboptimal regret bounds or have high per-iteration computational costs. To fill this gap, two efficient projection-free online methods called ORGFW and MORGFW are …

New algorithm reduces adaptive regret without projections.

New algorithm reduces online learning iterations by a factor of T^2/3.

New framework for decentralized optimization of upper-linearizable functions with improved regret and complexity.

We revisit the challenge of designing online algorithms for the bandit convex optimization problem (BCO) which are also scalable to high dimensional problems. Hence, we consider algorithms that are \textit{projection-free}, i.e., based on the conditional gradient method whose only access to the feasible decision set, i…

In this paper, we propose the first computationally efficient projection-free algorithm for bandit convex optimization (BCO). We show that our algorithm achieves a sublinear regret of $O(nT^{4/5})$ (where $T$ is the horizon and $n$ is the dimension) for any bounded convex functions with uniformly bounded gradients. We …

Study efficient algorithms for nonconvex optimization with state-dependent Markov data.

Efficient boosting method for regression with limited feedback.

Paper tackles online learning on curved spaces without projections.

New algorithms optimize actions under time-varying constraints without projecting.

Optimized algorithms for online learning with linear constraints improve performance and provide worst-case analysis.

New algorithm solves complex optimization problems without needing projections.

How can we efficiently mitigate the overhead of gradient communications in distributed optimization? This problem is at the heart of training scalable machine learning models and has been mainly studied in the unconstrained setting. In this paper, we propose Quantized-Frank-Wolfe (QFW), the first projection-free and co…

The Frank-Wolfe (FW) algorithm has been widely used in solving nuclear norm constrained problems, since it does not require projections. However, FW often yields high rank intermediate iterates, which can be very expensive in time and space costs for large problems. To address this issue, we propose a rank-drop method …

Frank-Wolfe algorithm (FW) and its variants have gained a surge of interests in machine learning community due to its projection-free property. Recently people have reduced the gradient evaluation complexity of FW algorithm to $\log(\frac{1}ε)$ for the smooth and strongly convex objective. This complexity result is esp…

In this work we introduce a conditional accelerated lazy stochastic gradient descent algorithm with optimal number of calls to a stochastic first-order oracle and convergence rate $O\left(\frac{1}{\varepsilon^2}\right)$ improving over the projection-free, Online Frank-Wolfe based stochastic gradient descent of Hazan an…

Online optimization has been a successful framework for solving large-scale problems under computational constraints and partial information. Current methods for online convex optimization require either a projection or exact gradient computation at each step, both of which can be prohibitively expensive for large-scal…

Improved online learning with time-varying constraints for complex domains.

Improved algorithm reduces communication rounds for distributed online learning.

Algorithm identifies best arm in combinatorial bandits with semi-bandit feedback.

The move from hand-designed to learned optimizers in machine learning has been quite successful for gradient-based and -free optimizers. When facing a constrained problem, however, maintaining feasibility typically requires a projection step, which might be computationally expensive and not differentiable. We show how …

We produce a new proof and extend results by Harrell and Stubbe for the discrete spectrum of a self-adjoint operator. An abstract approach--based on commutator algebra, the Rayleigh-Ritz principle, and an ``optimal'' usage of the Cauchy-Schwarz inequality--is used to produce ``parameter-free'', ``projection-free'' vers…

We study the problem of learning policy of an infinite-horizon, discounted cost, Markov decision process (MDP) with a large number of states. We compute the actions of a policy that is nearly as good as a policy chosen by a suitable oracle from a given mixture policy class characterized by the convex hull of a set of k…

We study Frank-Wolfe methods for nonconvex stochastic and finite-sum optimization problems. Frank-Wolfe methods (in the convex case) have gained tremendous recent interest in machine learning and optimization communities due to their projection-free property and their ability to exploit structured constraints. However,…

Local LMO optimizes constrained problems using local linear minimization.

Conditional gradients constitute a class of projection-free first-order algorithms for smooth convex optimization. As such, they are frequently used in solving smooth convex optimization problems over polytopes, for which the computational cost of orthogonal projections would be prohibitive. However, they do not enjoy …

Two new Frank-Wolfe algorithms improve convergence for constrained optimization.

A new algorithm for solving constrained convex optimization problems efficiently.

New method tackles online DR-submodular maximization with improved regret guarantees.

New algorithm for online optimization over symmetric cones, unifying previous methods.

PF-LaCG removes the need for knowing smoothness and strong convexity parameters for locally accelerated CG.

A distributed algorithm for online multi-task learning reduces communication and runtime costs.

FedSGM tackles constrained federated learning with unified framework.

A fast metric learning framework using Gershgorin disc alignment.

New methods optimize complex optimization problems with improved efficiency.

This work tackles regression on non-Euclidean spaces, specifically positive-definite matrices with the Bures-Wasserstein metric.

Decentralized optimization algorithms have received much attention due to the recent advances in network information processing. However, conventional decentralized algorithms based on projected gradient descent are incapable of handling high dimensional constrained problems, as the projection step becomes computationa…

Frank-Wolfe (FW) algorithms have been often proposed over the last few years as efficient solvers for a variety of optimization problems arising in the field of Machine Learning. The ability to work with cheap projection-free iterations and the incremental nature of the method make FW a very effective choice for many l…

A new metric learning framework for signed graphs using Gershgorin disc alignment.

Paper develops zeroth and first order stochastic Frank-Wolfe algorithms for constrained optimization.

Improved TD learning with neural nets reduces sample complexity and overparameterization.

Bipartite networks are a common type of network data in which there are two types of vertices, and only vertices of different types can be connected. While bipartite networks exhibit community structure like their unipartite counterparts, existing approaches to bipartite community detection have drawbacks, including im…

Algorithm identifies correct hypothesis from alternatives in bandit problems.

Bregman divergences play a central role in the design and analysis of a range of machine learning algorithms. This paper explores the use of Bregman divergences to establish reductions between such algorithms and their analyses. We present a new scaled isodistortion theorem involving Bregman divergences (scaled Bregman…

Robust CG methods avoid data corruption and solve structured statistical estimation problems.

Bayesian optimization reduces computational effort in aircraft design optimization.

Bayesian optimization method tackles combinatorial spaces, scalable for large data.