Online Linear

Online linear optimization (OLO) focuses on making sequential decisions to minimize cumulative losses in scenarios where information is revealed incrementally. Current research emphasizes developing algorithms that achieve logarithmic regret (optimal performance) under various conditions, including adversarial settings, bandit feedback, and non-stationary environments, often employing techniques like online mirror descent, coin betting, and Frank-Wolfe methods. These advancements are significant for improving efficiency in applications such as online resource allocation, revenue management, and machine learning, where adapting to changing data streams is crucial. The field is also exploring ways to leverage side information and reduce computational complexity, particularly in high-dimensional problems.