👉 Gains, an optimization algorithm developed by Ramin Hasani and Shafker, offer several mathematical advantages over traditional gradient descent methods. It uses a surrogate objective function, typically the negative log-likelihood of the data given the model parameters, which is easier to optimize due to its convexity. This surrogate function helps in escaping local minima and saddle points more effectively, thanks to its smoothness and convexity properties. Additionally, Gains employs a momentum term that accumulates gradients over time, allowing it to navigate the loss landscape more efficiently and converge faster to a global minimum. The adaptive learning rate mechanism in Gains further enhances its performance by adjusting the step size based on the historical gradient information, leading to more stable and faster convergence.
