ACCPM — A library for convex optimization based on an analytic center cutting plane method

Gondzio, Jacek; Merle, O. du; Sarkissian, Robert; Vial, Jean–Philippe

doi:10.1016/0377-2217(96)00169-5

Cited by 47 publications

(25 citation statements)

References 8 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…As recalled by Blondel and Tsitsiklis in a recent survey of computational complexity results in control [6] . [12], [13], [14], [15]. In this paper we exploit the structured LP formulation proposed in [9] and ACCPM to provide an efficient algorithm for solving ergodic MDPs with strong and weak interactions.…”

Section: Markov Decision Processes (Mdps) or Their Control Counterparmentioning

confidence: 99%

See 1 more Smart Citation

Two-Time Scale Controlled Markov Chains: A Decomposition and Parallel Processing Approach

Haurie

Moresino

2007

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

This paper deals with a class of ergodic control problems for systems described by Markov chains with strong and weak interactions. These systems are composed of a set of m subchains that are weakly coupled. Using results already available in the literature one formulates a limit control problem the solution of which can be obtained via an associated nondifferentiable convex programming (NDCP) problem. The technique used to solve the NDCP problem is the Analytic Center Cutting Plane Method (ACCPM) which implements a dialogue between, on one hand, a master program computing the analytical center of a localization set containing the solution and, on the other hand, an oracle proposing cutting planes that reduce the size of the localization set at each main iteration. The interesting aspect of this implementation comes from two characteristics: (i) the oracle proposes cutting planes by solving reduced sized Markov Decision Problems (MDP) via a linear programm (LP) or a policy iteration method; (ii) several cutting planes can be proposed simultaneously through a parallel implementation on m processors. The paper concentrates on these two aspects and shows, on a large scale MDP obtained from the numerical approximation "à la Kushner-Dupuis" of a singularly perturbed hybrid stochastic control problem, the important computational speed-up obtained.

show abstract

Section: Markov Decision Processes (Mdps) or Their Control Counterparmentioning

confidence: 99%

“…where χ(ψ) is the convex function defined as χ(ψ) = max i∈I χ i (ψ) and χ i (ψ) is the optimal value obtained for the problem (15). We notice here that, each problem (15) , a procedure called oracle generates a subgradient X(ψ) ∈ ∂χ atψ with the property…”

Section: A Decoupling the Mdpsmentioning

confidence: 99%

Two-Time Scale Controlled Markov Chains: A Decomposition and Parallel Processing Approach

Haurie

Moresino

2007

IEEE Trans. Automat. Contr.

View full text Add to dashboard Cite

show abstract

“…Interior-point methods in decomposition are based on the use of centers, which was introduced by Huard [6] for convex constrained sets and by Sonnevend [12] for polytopes. Goffin et al [3] developed the idea to Lagrangian relaxation by using the 'separating hyperplane oracle' and 'analytic center cutting plane method', which have been implemented by Goffin and Vial and their coauthors [2,5]. See also a survey paper [4].…”

Section: Introductionmentioning

confidence: 97%

An interior-point smoothing technique for Lagrangian relaxation in large-scale convex programming†

Shida

2008

Optimization

View full text Add to dashboard Cite

An interior-point smoothing technique for Lagrangian relaxation in large-scale convex programming is discussed. We consider the general convex program formulated in the conic form. For the problem, we define the perturbed Lagrangian relaxation by using the self-concordant barriers, and show the basic properties of the perturbed problems. Based on the properties, we present a conceptual method which numerically traces the trajectory that leads to the optimal solution of the original problem.

show abstract

“…The problem (19) has only Y (the number of labels) variables. Hence it can be approached by generic convex solvers like the Analytic Center Cutting Plane algorithm (Gondzio et al 1996). …”

Section: The Problem (19) Providing B(w) Which Is Required To Computementioning

confidence: 99%

“…To solve internal problem (19) we used the Oracle Based Optimization Engine (OBOE) implementation of the Analytic Center Cutting Plane algorithm being a part of COmputational INfrastructure for Operations Research project (COIN-OR) (Gondzio et al 1996).…”

Section: Databases and Implementation Detailsmentioning

confidence: 99%

V-shaped interval insensitive loss for ordinal classification

Antoniuk

Hlaváăź

2016

Mach Learn

View full text Add to dashboard Cite

We address a problem of learning ordinal classifiers from partially annotated examples. We introduce a V-shaped interval-insensitive loss function to measure discrepancy between predictions of an ordinal classifier and a partial annotation provided in the form of intervals of candidate labels. We show that under reasonable assumptions on the annotation process the Bayes risk of the ordinal classifier can be bounded by the expectation of an associated interval-insensitive loss. We propose several convex surrogates of the interval-insensitive loss which are used to formulate convex learning problems. We described a variant of the cutting plane method which can solve large instances of the learning problems. Experiments on a real-life application of human age estimation show that the ordinal classifier learned from cheap partially annotated examples can achieve accuracy matching the results of the so-far used supervised methods which require expensive precisely annotated examples.

show abstract

ACCPM — A library for convex optimization based on an analytic center cutting plane method

Cited by 47 publications

References 8 publications

Two-Time Scale Controlled Markov Chains: A Decomposition and Parallel Processing Approach

Two-Time Scale Controlled Markov Chains: A Decomposition and Parallel Processing Approach

An interior-point smoothing technique for Lagrangian relaxation in large-scale convex programming†

V-shaped interval insensitive loss for ordinal classification

Contact Info

Product

Resources

About