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Predictive-sensitivity for optimization
The objective is to explore the applications of the predictive-sensitivity approach in the field of optimization, in particular, for algorithm that have nested loops on different time-scales.
A classical approach to design controllers for interconnected systems is to assume that the different subsystems operate at different time scales, then design simpler controllers within each time scale, and finally certify stability of the interconnected system via singular perturbation analysis. Alternatively, the recently-proposed predictive-sensitivity approach (https://arxiv.org/pdf/2101.04367.pdf) allows to also separately design the controllers of the individual subsystems, but combine them without the need of time-scale separation. For that, it uses a feed-forward term to modify the dynamics of faster systems and anticipate the dynamics of slower ones. The predictive-sensitivity approach has promising applications in the field of optimization, in particular, for algorithms that have nested loops on different time-scales, like dual ascent, interior point methods, bilevel gradient descent.
A classical approach to design controllers for interconnected systems is to assume that the different subsystems operate at different time scales, then design simpler controllers within each time scale, and finally certify stability of the interconnected system via singular perturbation analysis. Alternatively, the recently-proposed predictive-sensitivity approach (https://arxiv.org/pdf/2101.04367.pdf) allows to also separately design the controllers of the individual subsystems, but combine them without the need of time-scale separation. For that, it uses a feed-forward term to modify the dynamics of faster systems and anticipate the dynamics of slower ones. The predictive-sensitivity approach has promising applications in the field of optimization, in particular, for algorithms that have nested loops on different time-scales, like dual ascent, interior point methods, bilevel gradient descent.
The goal of this project is to explore these potential applications and derive results proving that stability and convergence can be preserved in a single time scale when applying the predictive-sensitivity. The predictive-sensitivity approach is quite novel, hence, promising results can be turned into a publication.
The goal of this project is to explore these potential applications and derive results proving that stability and convergence can be preserved in a single time scale when applying the predictive-sensitivity. The predictive-sensitivity approach is quite novel, hence, promising results can be turned into a publication.