Mirror descent and nonlinear projected subgradient methods for convex optimization

Beck, Amir; Teboulle, Marc

doi:10.1016/s0167-6377(02)00231-6

Cited by 872 publications

(900 citation statements)

References 10 publications

Supporting

Mentioning

895

Contrasting

Order By: Relevance

“…Time-varying regularizers were analyzed in [24] and the analysis tightened in [27]. MD was originally proposed in [18] and later analyzed in [30] for convex optimization. In the online learning literature it makes its first appearance, with a different name, in [15].…”

Section: Previous Resultsmentioning

confidence: 99%

Scale-free online learning

Orabona

Pál

2018

Theoretical Computer Science

View full text Add to dashboard Cite

We design and analyze algorithms for online linear optimization that have optimal regret and at the same time do not need to know any upper or lower bounds on the norm of the loss vectors. Our algorithms are instances of the Follow the Regularized Leader (FTRL) and Mirror Descent (MD) meta-algorithms. We achieve adaptiveness to the norms of the loss vectors by scale invariance, i.e., our algorithms make exactly the same decisions if the sequence of loss vectors is multiplied by any positive constant. The algorithm based on FTRL works for any decision set, bounded or unbounded. For unbounded decisions sets, this is the first adaptive algorithm for online linear optimization with a non-vacuous regret bound. In contrast, we show lower bounds on scale-free algorithms based on MD on unbounded domains.

show abstract

Section: Previous Resultsmentioning

confidence: 99%

Scale-free online learning

Orabona

Pál

2018

Theoretical Computer Science

View full text Add to dashboard Cite

show abstract

“…In these papers the authors adopted the presentation suggested by Beck and Teboulle [6], which corresponds to a Follow-the-Regularized-Leader (FTRL) type strategy. There the focus was on F being strongly convex with respect to some norm.…”

Section: Figurementioning

confidence: 99%

Regret in Online Combinatorial Optimization

2014

View full text Add to dashboard Cite

We address online linear optimization problems when the possible actions of the decision maker are represented by binary vectors. The regret of the decision maker is the difference between her realized loss and the minimal loss she would have achieved by picking, in hindsight, the best possible action. Our goal is to understand the magnitude of the best possible (minimax) regret. We study the problem under three different assumptions for the feedback the decision maker receives: full information, and the partial information models of the socalled "semi-bandit" and "bandit" problems. In the full information case we show that the standard exponentially weighted average forecaster is a provably suboptimal strategy. For the semi-bandit model, by combining the Mirror Descent algorithm and the INF (Implicitely Normalized Forecaster) strategy, we are able to prove the first optimal bounds. Finally, in the bandit case we discuss existing results in light of a new lower bound, and suggest a conjecture on the optimal regret in that case.

show abstract

“…In particular, online convex programming methods [4,7,14,23] rely on the gradient of the instantaneous loss of a predictor to update the prediction for the next data point. The aim of these methods is to ensure that the per-round performance approaches that of the best offline method with access to the entire data sequence.…”

Section: Relationship Between Program Outcomes and Previous State-of-mentioning

confidence: 99%

Photon-limited Sensing and Surveillance

Calderbank¹,

Willett²

2015

View full text Add to dashboard Cite

Public reporting burden for this collection of information is estimated to average 1 hour per response, including the time for reviewing instructions, searching existing data sources, gathering and maintaining the data needed, and completing and reviewing this collection of information. Send comments regarding this burden estimate or any other aspect of this collection of information, including suggestions for reducing this burden to Department of Defense, Washington Headquarters Services, Directorate for Information The goal of this work was to learn and exploit unknown spatio-temporal structure in online photon-limited sensing and surveillance data. Photon-limited imaging arises in a wide variety of applications of interest to the Air Force, including night vision, space weather, imaging through fog, and spectral imaging. The photon-limited video reconstruction problem is particularly challenging because (a) the limited number of available photons introduces intensity-dependent Poisson statistics which require specialized algorithms and analysis for optimal performance, (b) vast quantities of video data will be collected sequentially, necessitating fast online algorithms, and (c) unknown and changing environmental dynamics preclude classical methods based on known dynamical models. Many current systems sidestep photon limitations by artificially restricting the frame rate and resolution of the video, but sophisticated statistical methods allow dramatic increases in resolution and improved object identification and detection capabilities.

show abstract

Mirror descent and nonlinear projected subgradient methods for convex optimization

Cited by 872 publications

References 10 publications

Scale-free online learning

Scale-free online learning

Regret in Online Combinatorial Optimization

Photon-limited Sensing and Surveillance

Contact Info

Product

Resources

About