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. This unification requires carefully partitioning 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, however, any bookkeeping choices which satisfy this relation will result in 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, Natural Gradient Descent, and the Damped Newton's method among many others. 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格科学模拟。然而，现代算法常常为了受物理学启发的启发式方法或肤浅的生物学隐喻而放弃进化保真度。本文直接从进化第一原理推导出一系列先进的基于梯度的优化算法。我们引入达尔文谱系模拟（DLS）来证明，在无性繁殖背景下，Fisher和Wright历史上对立的进化观点实际上是形式等价的。这种统一需要仔细地将Fisher确定性地演化的总种群划分为Wright随机漂移的子种群。我们证明，正确的簿记需要引入一种特定类型的结构化噪声（DLS噪声关系）。然而，关键在于，任何满足此关系的簿记选择都将产生对进化的忠实模拟。利用这一巨大的表示自由度，我们证明了一系列久经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、自然梯度下降、阻尼牛顿法等。通过简单地添加DLS噪声（即进化忠实的遗传漂变），这些算法成为达尔文进化在硅模拟中的科学有效工具。最后，我们证明，即使是当前最先进的Adam优化器，也可以通过一次微小的数学手术实现进化合规。