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Stochastic optimization (SO) are optimization methods that generate and use random variables. For stochastic optimization problems, the objective functions or constraints are random. Stochastic optimization also include methods with random iterates .
Estimation of distribution algorithms (EDAs), sometimes called probabilistic model-building genetic algorithms (PMBGAs), [1] are stochastic optimization methods that guide the search for the optimum by building and sampling explicit probabilistic models of promising candidate solutions. Optimization is viewed as a series of incremental updates ...
In the field of mathematical optimization, stochastic programming is a framework for modeling optimization problems that involve uncertainty. A stochastic program is an optimization problem in which some or all problem parameters are uncertain, but follow known probability distributions .
Stochastic optimization is an umbrella set of methods that includes simulated annealing and numerous other approaches. Particle swarm optimization is an algorithm modeled on swarm intelligence that finds a solution to an optimization problem in a search space, or models and predicts social behavior in the presence of objectives.
Examples of these kinds of methods include tabu search and genetic algorithms. [4] Metamodels enable researchers to obtain reliable approximate model outputs without running expensive and time-consuming computer simulations. Therefore, the process of model optimization can take less computation time and cost. [8]
Stochastic approximation methods are a family of iterative methods typically used for root-finding problems or for optimization problems. The recursive update rules of stochastic approximation methods can be used, among other things, for solving linear systems when the collected data is corrupted by noise, or for approximating extreme values of functions which cannot be computed directly, but ...
In 1997, the practical performance benefits from vectorization achievable with such small batches were first explored, [13] paving the way for efficient optimization in machine learning. As of 2023, this mini-batch approach remains the norm for training neural networks, balancing the benefits of stochastic gradient descent with gradient descent .
A gambler has $2, she is allowed to play a game of chance 4 times and her goal is to maximize her probability of ending up with a least $6. If the gambler bets $ on a play of the game, then with probability 0.4 she wins the game, recoup the initial bet, and she increases her capital position by $; with probability 0.6, she loses the bet amount $; all plays are pairwise independent.