Final answer:
We need to update theta_0 and theta_1 simultaneously in gradient descent to minimize the cost function efficiently and to avoid biasing the descent trajectory, ensuring a more direct path to the global minimum.
Step-by-step explanation:
The necessity for simultaneous computation and update of theta_0 and theta_1 in gradient descent arises from the algorithm's objective, which is to minimize the cost function over both parameters simultaneously to find the optimal model. Gradient descent updates parameters in a direction where the cost function decreases most rapidly. By adjusting theta_0 and theta_1 at the same time, it avoids the risk of creating a bias in the descent trajectory that would arise if one updated first before the other.
This process is akin to finding the lowest point in a valley, where each theta represents a coordinate in the landscape. If one were to adjust the position in only one direction at a time, it would take longer to reach the bottom and might even lead to suboptimal convergence. Hence, simultaneous updates can lead to a more direct and efficient path to the global minimum.