To enhance the variational distribution in Variational Search Distributions (VSD), one could explore more sophisticated generative models that can better capture the underlying dependencies and structure of the design space. For instance, employing graph-based models could be beneficial, especially in biological sequence design, where interactions between amino acids or nucleotides can be represented as edges in a graph. This would allow the model to learn complex relationships and dependencies that are not captured by independent or autoregressive formulations.
Additionally, variational autoencoders (VAEs) could be utilized to learn a latent representation of the design space. By training a VAE on the design space, the model can capture intricate patterns and correlations among the designs, leading to a more informed variational distribution. This approach would allow for the generation of diverse and high-quality candidates that are more likely to belong to the desired class.
Another avenue for improvement is the integration of hierarchical models that can capture multi-level structures in the data. For example, a hierarchical Bayesian model could allow for the incorporation of prior knowledge at different levels, such as general properties of sequences at a higher level and specific interactions at a lower level. This would enable the variational distribution to adaptively adjust based on the complexity of the design space.
Lastly, incorporating reinforcement learning techniques could also enhance the variational distribution. By treating the optimization process as a sequential decision-making problem, one could use policy gradients to refine the variational distribution based on feedback from the fitness evaluations, thus improving the exploration of the design space.