Evolutionary optimization algorithms are often derived from loose biological
analogies and struggle to leverage information obtained during the sequential
course of optimization. An alternative promising approach is to leverage data
and directly discover powerful optimization principles via meta-optimization.
In this work, we follow such a paradigm and introduce Evolution Transformer, a
causal Transformer architecture, which can flexibly characterize a family of
Evolution Strategies. Given a trajectory of evaluations and search distribution
statistics, Evolution Transformer outputs a performance-improving update to the
search distribution. The architecture imposes a set of suitable inductive
biases, i.e. the invariance of the distribution update to the order of
population members within a generation and equivariance to the order of the
search dimensions. We train the model weights using Evolutionary Algorithm
Distillation, a technique for supervised optimization of sequence models using
teacher algorithm trajectories. The resulting model exhibits strong in-context
optimization performance and shows strong generalization capabilities to
otherwise challenging neuroevolution tasks. We analyze the resulting properties
of the Evolution Transformer and propose a technique to fully
self-referentially train the Evolution Transformer, starting from a random
initialization and bootstrapping its own learning progress. We provide an open
source implementation under this https URL

通过元优化的方式，引入一种能够灵活表征一系列进化策略的因果 Transformer 架构 ——Evolution Transformer，用于从数据中直接发现强大的优化原理。通过 Evolution Transformer，结合进化算法蒸馏技术进行模型权重训练，我们得到一个在特定上下文中表现良好且能够很好泛化到其他具有挑战性的神经进化任务的模型。此外，我们还分析了 Evolution Transformer 的属性，并提出了一种全自引用训练的技术，从随机初始化开始并引导其自身的学习进程。我们提供了一个开源实现，网址为 https://<URL>

进化变换器：基于上下文的进化优化

Evolution Transformer: In-Context Evolutionary Optimization

Large Transformer models are capable of implementing a plethora of so-called
in-context learning algorithms. These include gradient descent, classification,
sequence completion, transformation, and improvement. In this work, we
investigate whether large language models (LLMs), which never explicitly
encountered the task of black-box optimization, are in principle capable of
implementing evolutionary optimization algorithms. While previous works have
solely focused on language-based task specification, we move forward and focus
on the zero-shot application of LLMs to black-box optimization. We introduce a
novel prompting strategy, consisting of least-to-most sorting of discretized
population members and querying the LLM to propose an improvement to the mean
statistic, i.e. perform a type of black-box recombination operation.
Empirically, we find that our setup allows the user to obtain an LLM-based
evolution strategy, which we call `EvoLLM', that robustly outperforms baseline
algorithms such as random search and Gaussian Hill Climbing on synthetic BBOB
functions as well as small neuroevolution tasks. Hence, LLMs can act as
`plug-in' in-context recombination operators. We provide several comparative
studies of the LLM's model size, prompt strategy, and context construction.
Finally, we show that one can flexibly improve EvoLLM's performance by
providing teacher algorithm information via instruction fine-tuning on
previously collected teacher optimization trajectories.

大型语言模型（LLMs）具备黑箱优化任务的潜力，可以通过 least-to-most 排序的提示策略提供演化优化算法，称为 EvoLLM，从而在合成 BBOB 函数和小规模神经进化任务上稳定优于传统算法。并通过对 LLM 的模型规模、提示策略和上下文构建的比较研究表明，通过对先前收集的教师优化轨迹进行指令微调，能够灵活地提高 EvoLLM 的性能。

大型语言模型作为进化策略

Large Language Models As Evolution Strategies

The performance of individual evolutionary optimization algorithms is mostly
measured in terms of statistics such as mean, median and standard deviation
etc., computed over the best solutions obtained with few trails of the
algorithm. To compare the performance of two algorithms, the values of these
statistics are compared instead of comparing the solutions directly. This kind
of comparison lacks direct comparison of solutions obtained with different
algorithms. For instance, the comparison of best solutions (or worst solution)
of two algorithms simply not possible. Moreover, ranking of algorithms is
mostly done in terms of solution quality only, despite the fact that the
convergence of algorithm is also an important factor. In this paper, a direct
comparison approach is proposed to analyze the performance of evolutionary
optimization algorithms. A direct comparison matrix called \emph{Prasatul
Matrix} is prepared, which accounts direct comparison outcome of best solutions
obtained with two algorithms for a specific number of trials. Five different
performance measures are designed based on the prasatul matrix to evaluate the
performance of algorithms in terms of Optimality and Comparability of
solutions. These scores are utilized to develop a score-driven approach for
comparing performance of multiple algorithms as well as for ranking both in the
grounds of solution quality and convergence analysis. Proposed approach is
analyzed with six evolutionary optimization algorithms on 25 benchmark
functions. A non-parametric statistical analysis, namely Wilcoxon paired
sum-rank test is also performed to verify the outcomes of proposed direct
comparison approach.

该论文提出一种直接比较演化优化算法性能的方法，通过构建名为 Prasatul Matrix 的直接比较矩阵和五种性能评估指标，既可以比较多个算法的性能，也能评估每个算法的优化和可比性解决方案，同时使用 Wilcoxon 配对秩和检验来验证该方法的结果。