Experience shows that typical evolutionary algorithms can cope well with
stochastic disturbances such as noisy function evaluations.
In this first mathematical runtime analysis of the $(1+\lambda)$ and
$(1,\lambda)$ evolutionary algorithms in the presence of prior bit-wise noise,
we show that both algorithms can tolerate constant noise probabilities without
increasing the asymptotic runtime on the OneMax benchmark. For this, a
population size $\lambda$ suffices that is at least logarithmic in the problem
size $n$. The only previous result in this direction regarded the less
realistic one-bit noise model, required a population size super-linear in the
problem size, and proved a runtime guarantee roughly cubic in the noiseless
runtime for the OneMax benchmark. Our significantly stronger results are based
on the novel proof argument that the noiseless offspring can be seen as a
biased uniform crossover between the parent and the noisy offspring. We are
optimistic that the technical lemmas resulting from this insight will find
applications also in future mathematical runtime analyses of evolutionary
algorithms.

基于数学运行时间分析，该研究表明在具有先前的比特噪声的情况下，(1+λ) 和 (1,λ) 进化算法都可以容忍恒定的噪声概率而不增加 OneMax 基准测试的渐近运行时间。

适度数量的种群可证明具有强健的抗噪性

Already Moderate Population Sizes Provably Yield Strong Robustness to  Noise

It is well known that ignoring the presence of stochastic disturbances in the
identification of stochastic Wiener models leads to asymptotically biased
estimators. On the other hand, optimal statistical identification, via
likelihood-based methods, is sensitive to the assumptions on the data
distribution and is usually based on relatively complex sequential Monte Carlo
algorithms. We develop a simple recursive online estimation algorithm based on
an output-error predictor, for the identification of continuous-time stochastic
parametric Wiener models through stochastic approximation. The method is
applicable to generic model parameterizations and, as demonstrated in the
numerical simulation examples, it is robust with respect to the assumptions on
the spectrum of the disturbance process.

通过基于输出误差预测器的简单递归在线估计算法，开发了一种连续时间随机参数 Wiener 模型的鉴定方法，该方法适用于通用模型参数化，并且在光谱扰动过程的假设方面表现出鲁棒性。

基于采样数据的在线随机连续时间 Wiener 模型识别

Online Identification of Stochastic Continuous-Time Wiener Models Using  Sampled Data

We consider the problem of adaptive stabilization for discrete-time,
multi-dimensional linear systems with bounded control input constraints and
unbounded stochastic disturbances, where the parameters of the true system are
unknown. To address this challenge, we propose a certainty-equivalent control
scheme which combines online parameter estimation with saturated linear
control. We establish the existence of a high probability stability bound on
the closed-loop system, under additional assumptions on the system and noise
processes. Finally, numerical examples are presented to illustrate our results.

针对多维线性系统的自适应稳定化问题，该研究提出了一种确知等效控制方案，该方案将在线参数估计与饱和线性控制相结合，证明了在系统及噪声假设条件下，闭环系统具有高概率稳定性界限，并给出了数值实验结果。