Recent work in ML applies genetic algorithms at inference time to iteratively improve solutions to optimization problems. The basic mutation and recombination operators involved are qualitatively different from those studied classically. Mutations are no longer random; an ML algorithm mutates a solution with the goal of improving an objective. Similarly, recombination is not based on random collages of parent solutions. Instead, it is an ML optimization-based operator whose goal is to synthesize improved solutions from its inputs. Thus, these mutation and recombination operators are more likely to improve the objective, but their computational cost is much higher. We introduce a general model of genetic algorithms and formulating optimization in this model as a query-complexity problem, using the language of reinforcement learning. We then study specialized models. We show that some optimization problems require generation, mutation, and recombination to be solved. We then obtain qualitatively tight algorithms for a family of problems within this framework that captures the nontrivial role of diversity in the solution pool, a key feature of practical ML genetic algorithms.

翻译：近期机器学习领域的工作在推理阶段应用遗传算法，通过迭代改进优化问题的解。其中涉及的变异和重组算子与经典研究存在本质差异：变异不再随机进行，而是由机器学习算法以改进目标为目的对解进行变异；类似地，重组也不再基于父代解的随机组合，而是基于机器学习的优化算子，其目标是从输入中合成改进解。因此，这些变异和重组算子更可能提升目标函数，但其计算代价显著更高。我们引入通用的遗传算法模型，并在此框架中将优化问题形式化为查询复杂度问题，采用强化学习语言进行表述。随后研究特化模型，证明部分优化问题必须通过生成、变异和重组才能求解。在此基础上，我们针对该框架内的一类问题获得定性紧致的算法，这类问题揭示了实践中机器学习遗传算法的关键特征——解池多样性的非平凡作用。