33 research outputs found
Computing the channel capacity of a communication system affected by uncertain transition probabilities
We study the problem of computing the capacity of a discrete memoryless
channel under uncertainty affecting the channel law matrix, and possibly with a
constraint on the average cost of the input distribution. The problem has been
formulated in the literature as a max-min problem. We use the robust
optimization methodology to convert the max-min problem to a standard convex
optimization problem. For small-sized problems, and for many types of
uncertainty, such a problem can be solved in principle using interior point
methods (IPM). However, for large-scale problems, IPM are not practical. Here,
we suggest an first-order algorithm based on Nemirovski
(2004) which is applied directly to the max-min problem.Comment: 22 pages, 2 figure
Robust Losses for Decision-Focused Learning
Optimization models used to make discrete decisions often contain uncertain
parameters that are context-dependent and are estimated through prediction. To
account for the quality of the decision made based on the prediction,
decision-focused learning (end-to-end predict-then-optimize) aims at training
the predictive model to minimize regret, i.e., the loss incurred by making a
suboptimal decision. Despite the challenge of this loss function being possibly
non-convex and in general non-differentiable, effective gradient-based learning
approaches have been proposed to minimize the expected loss, using the
empirical loss as a surrogate. However, empirical regret can be an ineffective
surrogate because the uncertainty in the optimization model makes the empirical
regret unequal to the expected regret in expectation. To illustrate the impact
of this inequality, we evaluate the effect of aleatoric and epistemic
uncertainty on the accuracy of empirical regret as a surrogate. Next, we
propose three robust loss functions that more closely approximate expected
regret. Experimental results show that training two state-of-the-art
decision-focused learning approaches using robust regret losses improves
test-sample empirical regret in general while keeping computational time
equivalent relative to the number of training epochs.Comment: 13 pages, 3 figure
Machine Learning for K-adaptability in Two-stage Robust Optimization
Two-stage robust optimization problems constitute one of the hardest
optimization problem classes. One of the solution approaches to this class of
problems is K-adaptability. This approach simultaneously seeks the best
partitioning of the uncertainty set of scenarios into K subsets, and optimizes
decisions corresponding to each of these subsets. In general case, it is solved
using the K-adaptability branch-and-bound algorithm, which requires exploration
of exponentially-growing solution trees. To accelerate finding high-quality
solutions in such trees, we propose a machine learning-based node selection
strategy. In particular, we construct a feature engineering scheme based on
general two-stage robust optimization insights that allows us to train our
machine learning tool on a database of resolved B&B trees, and to apply it
as-is to problems of different sizes and/or types. We experimentally show that
using our learned node selection strategy outperforms a vanilla, random node
selection strategy when tested on problems of the same type as the training
problems, also in case the K-value or the problem size differs from the
training ones
An approximation framework for two-stage ambiguous stochastic integer programs under mean-MAD information
We consider two-stage recourse models in which only limited information is available on the probability distributions of the random parameters in the model. If all decision variables are continuous, then we are able to derive the worst-case and best-case probability distributions under the assumption that only the means and mean absolute deviations of the random parameters are known. Contrary to most existing results in the literature, these probability distributions are the same for every first-stage decision. The ambiguity set that we use in this paper also turns out to be particularly suitable for ambiguous recourse models involving integer decisions variables. For such problems, we develop a general approximation framework and derive error bounds for using these approximatons. We apply this approximation framework to mixed-ambiguous mixed-integer recourse models in which some of the probability distributions of the random parameters are known and others are ambiguous. To illustrate these results we carry out numerical experiments on a surgery block allocation problem. (C) 2018 Elsevier B.V. All rights reserved
Droplet-based digital antibiotic susceptibility screen reveals single-cell clonal heteroresistance in an isogenic bacterial population
Since antibiotic resistance is a major threat to global health, recent observations that the traditional test of minimum inhibitory concentration (MIC) is not informative enough to guide effective antibiotic treatment are alarming. Bacterial heteroresistance, in which seemingly susceptible isogenic bacterial populations contain resistant sub-populations, underlies much of this challenge. To close this gap, here we developed a droplet-based digital MIC screen that constitutes a practical analytical platform for quantifying the single-cell distribution of phenotypic responses to antibiotics, as well as for measuring inoculum effect with high accuracy. We found that antibiotic efficacy is determined by the amount of antibiotic used per bacterial colony forming unit (CFU), not by the absolute antibiotic concentration, as shown by the treatment of beta-lactamase-carrying Escherichia coli with cefotaxime. We also noted that cells exhibited a pronounced clustering phenotype when exposed to near-inhibitory amounts of cefotaxime. Overall, our method facilitates research into the interplay between heteroresistance and antibiotic efficacy, as well as research into the origin and stimulation of heterogeneity by exposure to antibiotics. Due to the absolute bacteria quantification in this digital assay, our method provides a platform for developing reference MIC assays that are robust against inoculum-density variations