In gradient descent, what direction does the algorithm move to minimize a function?

In gradient descent, the algorithm aims to minimize a function by taking steps proportional to the negative of the gradient of the function at the current point. The gradient provides the direction of the steepest increase of the function, so moving in the opposite direction of the gradient leads the algorithm towards the steepest descent. This approach effectively reduces the function's value with each iteration.

Choosing the direction of the steepest descent is crucial because it ensures that the algorithm is making the most efficient progress towards finding the minimum. It allows for systematic adjustments to the parameters being optimized, hitting closer to the optimal solution.

The other options do not describe the core mechanism of gradient descent. Consulting historical data may provide insights but does not dictate the directional movement of the algorithm. Moving along the axis of maximum variance relates more to techniques like Principal Component Analysis rather than minimization. Following a random path lacks the systematic approach and efficiency necessary for convergence to the minimum value of a function.