Recently, the Deep Learning community has become interested in evolutionary optimization (EO) as a means to address hard optimization problems, e.g.

Dynamic programming methods have been shown to scale much better because they exploit the tree structure by solving subtrees as independent subproblems.

Solving optimization problems is the key to decision making in many real-life analytics applications. However, the coefficients of the optimization problems are often uncertain and dependent on external factors, such as future demand or energy or stock prices. Machine learning (ML) models, especially neural networks, are increasingly being used to estimate these coefficients in a data-driven way.

The goal of personalized medicine is to discover a treatment regimen that optimizes a patient's clinical outcome based on their personal genetic and environmental factors. However, candidate treatments cannot be arbitrarily administered to the patient to assess their efficacy; we often instead have access to an in silico surrogate model that approximates the true fitness of a proposed treatment. Unfortunately, such surrogate models have been shown to fail to generalize to previously unseen patient-treatment combinations. We hypothesize that domain-specific prior knowledge - such as medical textbooks and biomedical knowledge graphs - can provide a meaningful alternative signal of the fitness of proposed treatments. To this end, we introduce LLM-based Entropy-guided Optimization with kNowledgeable priors (LEON), a mathematically principled approach to leverage large language models (LLMs) as black-box optimizers without any task-specific fine-tuning, taking advantage of their ability to contextualize unstructured domain knowledge to propose personalized treatment plans in natural language. In practice, we implement LEON via 'optimization by prompting,' which uses LLMs as stochastic engines for proposing treatment designs. Experiments on real-world optimization tasks show LEON outperforms both traditional and LLM-based methods in proposing individualized treatments for patients.