We propose an approach to find low-makespan solutions to multi-robot multi-task planning problems in environments where robots block each other from completing tasks simultaneously. We introduce a formulation of the problem that allows for an approach based on greedy descent with random restarts for generation of the task assignment and task sequence. We then use a multi-agent path planner to evaluate the makespan of a given assignment and sequence. The planner decomposes the problem into multiple simple subproblems that only contain a single robots and a single task, and can thus be solved quickly to produce a solution for a fixed task sequence. The solutions to the subproblems are then combined to form a valid solution to the original problem. We showcase the approach on robotic stippling and robotic bin picking with up to 4 robot arms. The makespan of the solutions found by our algorithm are up to 30% lower compared to a greedy approach.

Increasingly, optimization problems in machine learning, especially those arising from high-dimensional statistical estimation, have a large number of variables. Modern statistical estimators developed over the past decade have statistical or sample complexity that depends only weakly on the number of parameters when there is some structure to the problem, such as sparsity. A central question is whether similar advances can be made in their computational complexity as well. In this paper, we propose strategies that indicate that such advances can indeed be made. In particular, we investigate the greedy coordinate descent algorithm, and note that performing the greedy step efficiently weakens the costly dependence on the problem size provided the solution is sparse.

Increasingly, optimization problems in machine learning, especially those arising from high-dimensional statistical estimation, have a large number of variables. Modern statistical estimators developed over the past decade have statistical or sample complexity that depends only weakly on the number of parameters when there is some structure to the problem, such as sparsity. A central question is whether similar advances can be made in their computational complexity as well. In this paper, we propose strategies that indicate that such advances can indeed be made. In particular, we investigate the greedy coordinate descent algorithm, and note that performing the greedy step efficiently weakens the costly dependence on the problem size provided the solution is sparse.