Cameron Smith, M.D., Ph.D., is a Postdoctoral Scholar Postdoctoral Fellow at

Posts

Discrete-Continuous Variational Optimization with Local Gradients

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Variational optimization (VO) offers a general approach for handling objectives which may involve discontinuities, or whose gradients are difficult to calculate. By introducing a variational distribution over the parameter space, such objectives are smoothed, and rendered amenable to VO methods. Local gradient information, though, may be available in certain problems, which is neglected by such an approach. We therefore consider a general method for incorporating local information via an augmented VO objective function to accelerate convergence and improve accuracy. We show how our augmented objective can be viewed as an instance of multilevel optimization. Finally, we show our method can train a genetic algorithm simulator, using a recursive Wasserstein distance objective

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Variational methods for Learning Multilevel Genetic Algorithms using the Kantorovich Monad

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Levels of selection and multilevel evolutionary processes are essential concepts in evolutionary theory, and yet there is a lack of common mathematical models for these core ideas. Here, we propose a unified mathematical framework for formulating and optimizing multilevel evolutionary processes and genetic algorithms over arbitrarily many levels based on concepts from category theory and population genetics. We formulate a multilevel version of the Wright-Fisher process using this approach, and we show that this model can be analyzed to clarify key features of multilevel selection. Particularly, we derive an extended multilevel probabilistic version of Price’s Equation via the Kantorovich Monad, and we use this to characterize regimes of parameter space within which selection acts antagonistically or cooperatively across levels. Finally, we show how our framework can provide a unified setting for learning genetic algorithms (GAs), and we show how we can use a Variational Optimization and a multi-level analogue of coalescent analysis to fit multilevel GAs to simulated data.

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