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Random optimization (RO) is a family of numerical optimization methods that do not require the gradient of the optimization problem and RO can hence be used on functions that are not continuous or differentiable. Such optimization methods are also known as direct-search, derivative-free, or black-box methods.
A randomized algorithm is an algorithm that employs a degree of randomness as part of its logic or procedure. The algorithm typically uses uniformly random bits as an auxiliary input to guide its behavior, in the hope of achieving good performance in the "average case" over all possible choices of random determined by the random bits; thus either the running time, or the output (or both) are ...
Any randomized algorithm may be interpreted as a randomized choice among deterministic algorithms, and thus as a mixed strategy for Alice. Similarly, a non-random algorithm may be thought of as a pure strategy for Alice. In any two-player zero-sum game, if one player chooses a mixed strategy, then the other player has an optimal pure strategy ...
In computer science and operations research, randomized rounding [1] is a widely used approach for designing and analyzing approximation algorithms. [ 2 ] [ 3 ] Many combinatorial optimization problems are computationally intractable to solve exactly (to optimality).
The scenario approach with regularization has also been considered, [5] and handy algorithms with reduced computational complexity are available. [6] Extensions to more complex, non-convex, set-ups are still objects of active investigation. Along the scenario approach, it is also possible to pursue a risk-return trade-off.
Clarkson's primary research interests are in computational geometry.. His most highly cited paper, with Peter Shor, uses random sampling to devise optimal randomized algorithms for several problems of constructing geometric structures, following up on an earlier singly-authored paper by Clarkson on the same subject.
The randomized weighted majority algorithm is an algorithm in machine learning theory for aggregating expert predictions to a series of decision problems. [1] It is a simple and effective method based on weighted voting which improves on the mistake bound of the deterministic weighted majority algorithm. In fact, in the limit, its prediction ...
An optimal decision is a decision that leads to at least as good a known or expected outcome as all other available decision options. It is an important concept in decision theory . In order to compare the different decision outcomes, one commonly assigns a utility value to each of them.