arXiv research

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 …

In many online learning problems the computational bottleneck for gradient-based methods is the projection operation. For this reason, in many problems the most efficient algorithms are based on the Frank-Wolfe method, which replaces projections by linear optimization. In the general case, however, online projection-fr…

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

Paper tackles online learning on curved spaces without projections.

Efficient boosting method for regression with limited feedback.

New algorithm reduces adaptive regret without projections.

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…

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

Improved algorithm reduces communication rounds for distributed online learning.

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

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…

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

A dissertation on scalable projection-free optimization methods.

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

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…

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

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

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

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

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 …

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…

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…

New algorithm solves complex optimization problems without needing projections.

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 …

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…

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 …

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

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 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,…

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

Study on computable online learning with new conditions and complexities.

We propose a fast general projection-free metric learning framework, where the minimization objective $\min_{\textbf{M} \in \mathcal{S}} Q(\textbf{M})$ is a convex differentiable function of the metric matrix $\textbf{M}$, and $\textbf{M}$ resides in the set $\mathcal{S}$ of generalized graph Laplacian matrices for con…

Continuous-time algorithms improve online learning performance.

Improved online classification with accurate predictions.

FedSGM tackles constrained federated learning with unified framework.

This research improves online learning by correcting for target shift in machine learning.

Boosts weak online learners to strong ones with sublinear regret.

Efficient RNN algorithm guarantees convergence in online learning.

Study online learning of quantum processes, showing feasibility for certain types.

Extends quantum learning theory to multiclass and online settings.

New private algorithms for online learning improve regret in high privacy regimes.

Local LMO optimizes constrained problems using local linear minimization.

New framework connects online learning to statistical learning for better generalization bounds.

This work explains why online imitation learning improves faster than theory predicts.

This work establishes always-valid risk bounds for online matrix completion.

Open problem seeks an online learning algorithm for binary classification.

We study the relationship between the notions of differentially private learning and online learning in games. Several recent works have shown that differentially private learning implies online learning, but an open problem of Neel, Roth, and Wu \cite{NeelAaronRoth2018} asks whether this implication is {\it efficient}…

Study online learning with set-valued feedback, showing differences between deterministic and randomized approaches.