10,012 research outputs found
Analysis of Noisy Evolutionary Optimization When Sampling Fails
In noisy evolutionary optimization, sampling is a common strategy to deal
with noise. By the sampling strategy, the fitness of a solution is evaluated
multiple times (called \emph{sample size}) independently, and its true fitness
is then approximated by the average of these evaluations. Previous studies on
sampling are mainly empirical. In this paper, we first investigate the effect
of sample size from a theoretical perspective. By analyzing the (1+1)-EA on the
noisy LeadingOnes problem, we show that as the sample size increases, the
running time can reduce from exponential to polynomial, but then return to
exponential. This suggests that a proper sample size is crucial in practice.
Then, we investigate what strategies can work when sampling with any fixed
sample size fails. By two illustrative examples, we prove that using parent or
offspring populations can be better. Finally, we construct an artificial noisy
example to show that when using neither sampling nor populations is effective,
adaptive sampling (i.e., sampling with an adaptive sample size) can work. This,
for the first time, provides a theoretical support for the use of adaptive
sampling
Horizon-unbiased Investment with Ambiguity
In the presence of ambiguity on the driving force of market randomness, we
consider the dynamic portfolio choice without any predetermined investment
horizon. The investment criteria is formulated as a robust forward performance
process, reflecting an investor's dynamic preference. We show that the market
risk premium and the utility risk premium jointly determine the investors'
trading direction and the worst-case scenarios of the risky asset's mean return
and volatility. The closed-form formulas for the optimal investment strategies
are given in the special settings of the CRRA preference
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