洞察 - Algorithms and Data Structures - # Batch Sequential Optimization of Rare Combinatorial Designs

Efficient Batch Optimization of Rare Combinatorial Designs Using Variational Search Distributions

Q: How can the variational distribution in VSD be further improved to better capture the structure of the design space, beyond the simple independent and autoregressive formulations explored in the paper?

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.

Q: What are the limitations of using machine learning oracles as ground truth in the black-box optimization experiments, and how can the evaluation be made more robust to these limitations?

Using machine learning oracles as ground truth in black-box optimization experiments presents several limitations. One significant issue is the overfitting of the oracle to the training data, which can lead to poor generalization when predicting unseen designs. This can result in misleading evaluations of the optimization methods, as the oracle may not accurately reflect the true fitness landscape. Another limitation is the uncertainty in predictions made by the oracle. Machine learning models, especially those trained on limited data, can produce predictions with high variance, leading to unreliable fitness estimates. This uncertainty can skew the optimization process, as methods may converge on suboptimal solutions based on inaccurate fitness evaluations. To make the evaluation more robust, one approach is to use ensemble methods that combine predictions from multiple oracles or models. This can help mitigate the risk of overfitting and provide a more stable estimate of fitness. Additionally, incorporating uncertainty quantification techniques, such as Bayesian neural networks, can provide confidence intervals around predictions, allowing for more informed decision-making during the optimization process. Another strategy is to conduct cross-validation by splitting the available data into training and validation sets, ensuring that the oracle is evaluated on unseen data. This can help assess the generalization capability of the oracle and provide a more accurate measure of its performance. Finally, integrating real experimental data into the evaluation process can provide a reality check against the predictions of the oracle. By periodically validating the oracle's predictions with actual experimental results, one can adjust the optimization strategy to account for discrepancies between the oracle and real-world outcomes.

Q: Can VSD be extended to handle continuous or mixed discrete-continuous design spaces, and how would this affect the optimization and sampling procedures?

Yes, VSD can be extended to handle continuous or mixed discrete-continuous design spaces, which would significantly enhance its applicability in various optimization scenarios. The extension would involve adapting the variational distribution to accommodate continuous variables, which can be achieved through the use of mixture models or hybrid generative models that can represent both discrete and continuous components. In continuous design spaces, the optimization procedure would need to incorporate techniques such as gradient-based optimization methods, which can efficiently navigate the continuous landscape. This could involve using Gaussian processes or neural networks to model the fitness function, allowing for the estimation of gradients and facilitating the optimization of continuous variables. For mixed design spaces, the sampling procedure would require a more sophisticated approach to ensure that both discrete and continuous candidates are generated effectively. One potential method is to use rejection sampling or importance sampling, where candidates are drawn from a joint distribution that accounts for both types of variables. This would ensure that the generated candidates are representative of the entire design space. Additionally, the optimization objective may need to be reformulated to account for the different types of variables. For instance, one could use a multi-objective optimization framework that simultaneously optimizes for both discrete and continuous objectives, allowing for a more holistic approach to the design problem. Overall, extending VSD to handle continuous or mixed discrete-continuous design spaces would enhance its flexibility and effectiveness, enabling it to tackle a broader range of optimization challenges in fields such as bioinformatics, materials science, and engineering design.

核心概念

A method called Variational Search Distributions (VSD) is developed to efficiently find rare, desirable designs in a batch sequential manner with a fixed experimental budget, by formulating the problem as a variational inference task.

摘要

The paper presents Variational Search Distributions (VSD), a method for efficiently finding rare, desirable designs in a batch sequential manner with a fixed experimental budget. The key insights are:

The batch active search problem over an innumerable discrete design space is formulated as an instance of variational inference. This allows VSD to satisfy well-defined requirements and desiderata for the problem, such as using off-the-shelf gradient-based optimization, taking advantage of scalable predictive models, and generating diverse batches of candidates.
VSD uses a reverse Kullback-Leibler (KL) divergence objective, which can be optimized without directly evaluating the intractable posterior distribution over rare, desirable designs. Instead, VSD uses a variational distribution and a class probability estimation (CPE) model.
Experiments on several biological sequence design tasks show that VSD can outperform existing baseline methods, including design by adaptive sampling (DbAS), conditioning by adaptive sampling (CbAS), AdaLead, and proximal exploration (PEX). VSD is particularly effective on higher-dimensional problems.
VSD is also evaluated on the related sequential black-box optimization (BBO) problem, where it demonstrates competitive performance compared to state-of-the-art Bayesian optimization (BO) methods.

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"The number possible configurations of a single protein is 20^O(100)."
"The DHFR dataset contains 99.7% of the complete combinatorial space of short sequences."
"The TrpB dataset contains 159,129 unique sequences and fitness values."

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"We are interested in this objective for a variety of reasons. For example, we may wish to study the properties of the "fitness landscape" (Papkou et al., 2023) to gain a better scientific understanding of a phenomenon such as natural evolution."
"Importantly, this posterior can be used for generating new designs."

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Variational Search Distributions

by Daniel M. St... 在 arxiv.org 09-11-2024

https://arxiv.org/pdf/2409.06142.pdf

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How can the variational distribution in VSD be further improved to better capture the structure of the design space, beyond the simple independent and autoregressive formulations explored in the paper?

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.

What are the limitations of using machine learning oracles as ground truth in the black-box optimization experiments, and how can the evaluation be made more robust to these limitations?

Using machine learning oracles as ground truth in black-box optimization experiments presents several limitations. One significant issue is the overfitting of the oracle to the training data, which can lead to poor generalization when predicting unseen designs. This can result in misleading evaluations of the optimization methods, as the oracle may not accurately reflect the true fitness landscape.
Another limitation is the uncertainty in predictions made by the oracle. Machine learning models, especially those trained on limited data, can produce predictions with high variance, leading to unreliable fitness estimates. This uncertainty can skew the optimization process, as methods may converge on suboptimal solutions based on inaccurate fitness evaluations.
To make the evaluation more robust, one approach is to use ensemble methods that combine predictions from multiple oracles or models. This can help mitigate the risk of overfitting and provide a more stable estimate of fitness. Additionally, incorporating uncertainty quantification techniques, such as Bayesian neural networks, can provide confidence intervals around predictions, allowing for more informed decision-making during the optimization process.
Another strategy is to conduct cross-validation by splitting the available data into training and validation sets, ensuring that the oracle is evaluated on unseen data. This can help assess the generalization capability of the oracle and provide a more accurate measure of its performance.
Finally, integrating real experimental data into the evaluation process can provide a reality check against the predictions of the oracle. By periodically validating the oracle's predictions with actual experimental results, one can adjust the optimization strategy to account for discrepancies between the oracle and real-world outcomes.

Can VSD be extended to handle continuous or mixed discrete-continuous design spaces, and how would this affect the optimization and sampling procedures?

Yes, VSD can be extended to handle continuous or mixed discrete-continuous design spaces, which would significantly enhance its applicability in various optimization scenarios. The extension would involve adapting the variational distribution to accommodate continuous variables, which can be achieved through the use of mixture models or hybrid generative models that can represent both discrete and continuous components.
In continuous design spaces, the optimization procedure would need to incorporate techniques such as gradient-based optimization methods, which can efficiently navigate the continuous landscape. This could involve using Gaussian processes or neural networks to model the fitness function, allowing for the estimation of gradients and facilitating the optimization of continuous variables.
For mixed design spaces, the sampling procedure would require a more sophisticated approach to ensure that both discrete and continuous candidates are generated effectively. One potential method is to use rejection sampling or importance sampling, where candidates are drawn from a joint distribution that accounts for both types of variables. This would ensure that the generated candidates are representative of the entire design space.
Additionally, the optimization objective may need to be reformulated to account for the different types of variables. For instance, one could use a multi-objective optimization framework that simultaneously optimizes for both discrete and continuous objectives, allowing for a more holistic approach to the design problem.
Overall, extending VSD to handle continuous or mixed discrete-continuous design spaces would enhance its flexibility and effectiveness, enabling it to tackle a broader range of optimization challenges in fields such as bioinformatics, materials science, and engineering design.