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In gradient descent, the learning rate, $\eta$, is a critical open-loop control that sets the step size, essential for navigating the loss landscape effectively. While high learning rates can lead to overshooting the optimal point due to rapid convergence, low rates may achieve precision but at the cost of slower progress, potentially trapping the model in local minima. Introducing learning rate decay schedules offers a strategic open-loop adjustment to $\eta$ over time, promoting swift initial progress and transitioning to greater accuracy as the model nears optimal solutions. Unlike adaptive methods like momentum, RMSprop, and Adam that adjust rates per parameter based on feedback mechanisms, decay schedules systematically reduce the learning rate, enhancing the model’s ability to explore broadly initially and then exploit finer details of the loss landscape as it converges.
In the example below, we will see that a linear decay of the learning rate (represented by the green line) results in faster convergence towards the optimum.
The figures illustrate the journey to the minimum point on the loss surface, with each iteration marked by a cross. The schedule featuring decay (green) reaches the optimum in just four iterations, while higher (red) and lower (blue) learning rates require significantly more iterations.
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A high initial learning rate accelerates early progress by making broad sweeps across the loss landscape, transitioning to fine-tuning as the rate decays, which enhances precision and stability, increasing the likelihood of reaching a global minimum. Reducing the learning rate over time mitigates overshoot risks by refining the step size, making movements more deliberate and avoiding bypassing the optimal point.
Decay schedules tailor steps to the terrain, allowing smaller steps in steep areas to prevent reckless moves and longer strides in flatter areas, optimizing the path based on the topography of the error surface. This gradual reduction also prevents hasty convergence to suboptimal local minima, promoting a thorough search essential for robust solutions in complex, high-dimensional spaces.
Implementing a learning rate schedule involves choosing an initial learning rate and a decay function that adjusts the rate based on specific criteria at each iteration or epoch. This choice is crucial and often results from experimentation tailored to the training task's demands. Here are some insights you may want to explore yourself.
Learning Rate Decay Schedules: There are various strategies to adjust the learning rate over time. Each schedule has its distinct approach and benefits, tailored to different training needs and preferences:
Exponential Decay gradually reduces the learning rate, ensuring a smooth transition that's beneficial for models requiring steady refinement.
Step Decay implements abrupt decreases at specific intervals, suitable for scenarios where drastic adjustments are needed to overcome plateaus.
These options allow for flexibility in training dynamics, catering to the diverse landscapes of loss functions and the specific challenges of each training session. By selecting the appropriate decay schedule, one can significantly influence the efficiency and outcome of the model training, aligning the learning rate's behavior with the model's evolving needs.
Impact of Cyclical Learning Rates: Cyclical learning rates vary between a lower and upper bound instead of consistently decreasing, creating a dynamic environment that can enhance the model's ability to navigate complex loss landscapes. This oscillation helps in avoiding premature convergence to suboptimal local minima by periodically increasing the learning rate to encourage exploration. Cyclical rates are particularly beneficial in tasks where the loss landscape is rugged or deceptive, enabling more effective global search strategies.
Warm-up (slow-start) Strategies: Initiating training with a low learning rate that gradually increases, or "warms up," can significantly stabilize the early stages of model training. This approach is essential for complex architectures that might react poorly to aggressive initial updates, risking divergence. Warm-up strategies gently prepare the model for the optimization process, establishing a foundation that supports robust learning when transitioning to higher learning rates.
Choosing the right decay function for the learning rate depends on factors like model complexity, dataset characteristics, and expected training duration. More complex models or larger datasets might benefit from dynamic decay schedules like cosine annealing, allowing for extensive initial exploration and later fine-tuning. Simpler models or shorter trainings could work well with linear decay, ensuring a steady learning pace. Aligning the decay function with the model’s and dataset’s specifics is crucial for efficient, effective training and achieving accurate, generalizable results.