Evolutionary computation has long promised to deliver both high-performance optimization tools as well as rigorous scientific simulations of Darwinian evolution. However, modern algorithms frequently abandon evolutionary fidelity for physics-inspired heuristics or superficial biological metaphors. This paper derives a suite of advanced gradient-based optimization algorithms directly from evolutionary first principles. We introduce Darwinian Lineage Simulations (DLS) to prove that, in an asexual context, Fisher's and Wright's historically opposed views of evolution are actually formally equivalent; One can partition Fisher's deterministically-evolving total population into Wright's randomly-drifting sub-populations. We prove that proper bookkeeping requires introducing a specific kind of structured noise (the DLS noise relation). Crucially, any bookkeeping choices which satisfy this relation will yield a faithful simulation of evolution. Using this vast representational freedom, we prove that a broad family of battle-tested optimization algorithms are already perfectly compatible with evolutionary dynamics. These include: Stochastic Gradient Descent as well as many regularizations/approximations of Newton's method and Natural Gradient Descent. By simply adding DLS noise (i.e., evolutionarily faithful genetic drift), these algorithms become scientifically valid in silico simulations of Darwinian evolution. Finally, we demonstrate that even the state-of-the-art Adam optimizer can be brought into evolutionary compliance through a minor mathematical surgery.

翻译：进化计算长期以来承诺提供高性能优化工具以及达尔文进化的严谨科学模拟。然而，现代算法常为了物理启发的启发式方法或浅显的生物隐喻而牺牲进化保真度。本文直接从进化第一原理导出一系列高级基于梯度的优化算法。我们引入达尔文谱系模拟（Darwinian Lineage Simulations, DLS）来证明，在无性生殖背景下，Fisher与Wright历史上对立的进化观点实际上是形式等价的：可以将Fisher确定性演化的总群体划分为Wright随机漂移的子群体。我们证明，正确的核算需要引入一种特定类型的结构化噪声（DLS噪声关系）。关键是，任何满足此关系的核算选择都能产生对进化的忠实模拟。利用这种巨大的表示自由度，我们证明，一系列经受过实战考验的优化算法已经与进化动力学完美兼容。这些算法包括：随机梯度下降，以及牛顿法和自然梯度下降的多种正则化/近似形式。通过简单添加DLS噪声（即进化上忠实的遗传漂变），这些算法成为科学有效的达尔文进化计算机模拟。最后，我们证明，即使是最先进的Adam优化器，也可以通过一次微小的数学手术实现进化合规。