The greedy strategy is an approximation algorithm to solve optimization problems arising in decision making with multiple actions. How good is the greedy strategy compared to the optimal solution? In this survey, we mainly consider two classes of optimization problems where the objective function is submodular. The first is set submodular optimization, which is to choose a set of actions to optimize a set submodular objective function, and the second is string submodular optimization, which is to choose an ordered set of actions to optimize a string submodular function. Our emphasis here is on performance bounds for the greedy strategy in submodular optimization problems. Specifically, we review performance bounds for the greedy strategy, more general and improved bounds in terms of curvature, performance bounds for the batched greedy strategy, and performance bounds for Nash equilibria.

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子模块优化问题和贪婪策略：一项调查

贪心策略是一种近似算法，用于解决多动作决策中出现的优化问题。贪心策略与最优解相比有多好？在本次调查中，我们主要考虑目标函数是子模的两类优化问题。第一个是集合子模块优化，即选择一组动作来优化一个集合子模块目标函数，第二个是字符串子模块优化，即选择一组有序的动作来优化一个字符串子模块函数。我们这里的重点是在子模块优化问题中贪婪策略的性能界限。具体来说，我们回顾了贪婪策略的性能界限，更一般和改进的曲率界限，批量贪婪策略的性能界限，