Related papers: Entropy Penalized Semidefinite Programming
Maximization of an expensive, unimodal function under random observations has been an important problem in hyperparameter tuning. It features expensive function evaluations (which means small budgets) and a high level of noise. We develop…
Recently, a race towards the simplification of deep networks has begun, showing that it is effectively possible to reduce the size of these models with minimal or no performance loss. However, there is a general lack in understanding why…
In the literature, besides the assumption of strict complementarity, superlinear convergence of implementable polynomial-time interior point algorithms using known search directions, namely, the HKM direction, its dual or the NT direction,…
Statistical inference problems arising within signal processing, data mining, and machine learning naturally give rise to hard combinatorial optimization problems. These problems become intractable when the dimensionality of the data is…
In this paper, we present a cross-entropy optimization method for hyperparameter optimization in stochastic gradient-based approaches to train deep neural networks. The value of a hyperparameter of a learning algorithm often has great…
Previous work on planning as active inference addresses finite horizon problems and solutions valid for online planning. We propose solving the general Stochastic Shortest-Path Markov Decision Process (SSP MDP) as probabilistic inference.…
In many learning tasks, certain requirements on the processing of individual data samples should arguably be formalized as strict constraints in the underlying optimization problem, rather than by means of arbitrary penalties. We show that,…
We introduce a class of specially structured linear programming (LP) problems, which has favorable modeling capability for important application problems in different areas such as optimal transport, discrete tomography and economics. To…
In this paper we consider general rank minimization problems with rank appearing in either objective function or constraint. We first establish that a class of special rank minimization problems has closed-form solutions. Using this result,…
This work is concerned with the issue of applications of the semi-definite programming (SDP) in the field of quantum information science. Our results of the analysis of certain quantum information protocols using this optimization technique…
Memory-Bounded Dynamic Programming (MBDP) has proved extremely effective in solving decentralized POMDPs with large horizons. We generalize the algorithm and improve its scalability by reducing the complexity with respect to the number of…
In several domains obtaining class annotations is expensive while at the same time unlabelled data are abundant. While most semi-supervised approaches enforce restrictive assumptions on the data distribution, recent work has managed to…
The Elementary Shortest-Path Problem(ESPP) seeks a minimum cost path from s to t that visits each vertex at most once. The presence of negative-cost cycles renders the problem NP-hard. We present a probabilistic method for finding…
Semidefinite programming (SDP) is a unifying framework that generalizes both linear programming and quadratically-constrained quadratic programming, while also yielding efficient solvers, both in theory and in practice. However, there exist…
Constraint Programming (CP) is a declarative programming paradigm that allows for modeling and solving combinatorial optimization problems, such as the Job-Shop Scheduling Problem (JSSP). While CP solvers manage to find optimal or…
Suppose that we observe entries or, more generally, linear combinations of entries of an unknown $m\times T$-matrix $A$ corrupted by noise. We are particularly interested in the high-dimensional setting where the number $mT$ of unknown…
We introduce an extension of Stochastic Dual Dynamic Programming (SDDP) to solve stochastic convex dynamic programming equations. This extension applies when some or all primal and dual subproblems to be solved along the forward and…
Tactical selection of experiments to estimate an underlying model is an innate task across various fields. Since each experiment has costs associated with it, selecting statistically significant experiments becomes necessary. Classic linear…
Random projection, a dimensionality reduction technique, has been found useful in recent years for reducing the size of optimization problems. In this paper, we explore the use of sparse sub-gaussian random projections to approximate…
In this paper, we study a class of fractional semi-infinite polynomial programming problems involving s.o.s-convex polynomial functions. For such a problem, by a conic reformulation proposed in our previous work and the quadratic modules…