The paper presents a meta-algorithm called the Multiplicative Weights (MW) update method, which unifies and generalizes various algorithms from different fields such as machine learning, optimization, and game theory. The MW method involves maintaining a distribution over a set of decisions and iteratively updating the weights of these decisions using a multiplicative rule. The meta-algorithm is simple and can be derived from the "Hedge" algorithm from learning theory. The paper highlights the commonalities and differences among the algorithms that use the MW method, making it a useful tool for teaching algorithms courses. The MW method is applied to several problems, including learning linear classifiers (Winnow algorithm), solving zero-sum games approximately, and approximately solving packing/covering linear programs (Plotkin-Shmoys-Tardos framework). The analysis of the MW method uses an exponential potential function, and the running time is proportional to \(1/\varepsilon^2\). The paper also discusses the use of exponential factors in the update rule and provides bounds on the performance of the MW algorithm in different scenarios.The paper presents a meta-algorithm called the Multiplicative Weights (MW) update method, which unifies and generalizes various algorithms from different fields such as machine learning, optimization, and game theory. The MW method involves maintaining a distribution over a set of decisions and iteratively updating the weights of these decisions using a multiplicative rule. The meta-algorithm is simple and can be derived from the "Hedge" algorithm from learning theory. The paper highlights the commonalities and differences among the algorithms that use the MW method, making it a useful tool for teaching algorithms courses. The MW method is applied to several problems, including learning linear classifiers (Winnow algorithm), solving zero-sum games approximately, and approximately solving packing/covering linear programs (Plotkin-Shmoys-Tardos framework). The analysis of the MW method uses an exponential potential function, and the running time is proportional to \(1/\varepsilon^2\). The paper also discusses the use of exponential factors in the update rule and provides bounds on the performance of the MW algorithm in different scenarios.