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Learning to Warm-Start Fixed-Point Optimization Algorithms

Many applications in robotics, signal processing, and machine learning require real-time solutions of optimization problems that are very similar in nature. Most optimization techniques don’t consider the available data from seeing similar optimization problems before and solve each problem independently. We consider the problem of flying a quadcopter to follow a reference trajectory. To do so, we use model predictive control, a popular technique which repeatedly solves new optimization problems. We impose a budget of $15$ fixed-point steps to solve each problem (mimicking a real-time solution requirement). With our learned warm-start approach, we can solve the quadratic programs more accurately than the other initialization techniques which initialize the quadratic program with the nearest neighbor and previous solution.

Nearest neighbor

Previous solution

Learned