17,048 research outputs found
Convex Optimal Uncertainty Quantification
Optimal uncertainty quantification (OUQ) is a framework for numerical
extreme-case analysis of stochastic systems with imperfect knowledge of the
underlying probability distribution. This paper presents sufficient conditions
under which an OUQ problem can be reformulated as a finite-dimensional convex
optimization problem, for which efficient numerical solutions can be obtained.
The sufficient conditions include that the objective function is piecewise
concave and the constraints are piecewise convex. In particular, we show that
piecewise concave objective functions may appear in applications where the
objective is defined by the optimal value of a parameterized linear program.Comment: Accepted for publication in SIAM Journal on Optimizatio
Submodular relaxation for inference in Markov random fields
In this paper we address the problem of finding the most probable state of a
discrete Markov random field (MRF), also known as the MRF energy minimization
problem. The task is known to be NP-hard in general and its practical
importance motivates numerous approximate algorithms. We propose a submodular
relaxation approach (SMR) based on a Lagrangian relaxation of the initial
problem. Unlike the dual decomposition approach of Komodakis et al., 2011 SMR
does not decompose the graph structure of the initial problem but constructs a
submodular energy that is minimized within the Lagrangian relaxation. Our
approach is applicable to both pairwise and high-order MRFs and allows to take
into account global potentials of certain types. We study theoretical
properties of the proposed approach and evaluate it experimentally.Comment: This paper is accepted for publication in IEEE Transactions on
Pattern Analysis and Machine Intelligenc
Continuous Multiclass Labeling Approaches and Algorithms
We study convex relaxations of the image labeling problem on a continuous
domain with regularizers based on metric interaction potentials. The generic
framework ensures existence of minimizers and covers a wide range of
relaxations of the originally combinatorial problem. We focus on two specific
relaxations that differ in flexibility and simplicity -- one can be used to
tightly relax any metric interaction potential, while the other one only covers
Euclidean metrics but requires less computational effort. For solving the
nonsmooth discretized problem, we propose a globally convergent
Douglas-Rachford scheme, and show that a sequence of dual iterates can be
recovered in order to provide a posteriori optimality bounds. In a quantitative
comparison to two other first-order methods, the approach shows competitive
performance on synthetical and real-world images. By combining the method with
an improved binarization technique for nonstandard potentials, we were able to
routinely recover discrete solutions within 1%--5% of the global optimum for
the combinatorial image labeling problem
Difference of Convex Functions Programming Applied to Control with Expert Data
This paper reports applications of Difference of Convex functions (DC)
programming to Learning from Demonstrations (LfD) and Reinforcement Learning
(RL) with expert data. This is made possible because the norm of the Optimal
Bellman Residual (OBR), which is at the heart of many RL and LfD algorithms, is
DC. Improvement in performance is demonstrated on two specific algorithms,
namely Reward-regularized Classification for Apprenticeship Learning (RCAL) and
Reinforcement Learning with Expert Demonstrations (RLED), through experiments
on generic Markov Decision Processes (MDP), called Garnets
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