Sequential Randomized Algorithms for Robust Optimization

Distributionally Robust Optimization for Sequential Decision Making

The distributionally robust Markov Decision Process approach has been proposed in the literature, where the goal is to seek a distributionally robust policy that achieves the maximal expected total reward under the most adversarial joint distribution of uncertain parameters. In this paper, we study distributionally robust MDP where ambiguity sets for uncertain parameters are of a format that ca...

Thrifty Algorithms for Multistage Robust Optimization

We consider a class of multi-stage robust covering problems, where additional information is revealed about the problem instance in each stage, but the cost of taking actions increases. The dilemma for the decision-maker is whether to wait for additional information and risk the inflation, or to take early actions to hedge against rising costs. We study the “k-robust” uncertainty model: in each...

Randomized Algorithms in Robust Control

The probabilistic approach to analysis and design of robust control systems is an emerging philosophy that gained increasing interest in recent years, see e.g. the book [24]. Opposed to the so-far dominating paradigm of deterministic worst-case robustness, the probabilistic approach presents itself as a natural tool to deal with the random character of uncertainties affecting control systems. I...

Randomized Algorithms for Geometric Optimization Problems

This chapter reviews randomization algorithms developed in the last few years to solve a wide range of geometric optimization problems. We review a number of general techniques, including randomized binary search, randomized linear-programming algorithms, and random sampling. Next, we describe several applications of these techniques, including facility location, proximity problems, nearest nei...

Randomized Algorithms for Geometri Optimization Problems