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Large language models (LLMs) have recently shown significant potential in various biological tasks such as protein engineering and molecule design. These tasks typically involve black-box discrete sequence optimization, where the challenge lies in generating sequences that are not only biologically feasible but also adhere to hard fine-grained constraints. However, LLMs often struggle with such constraints, especially in biological contexts where verifying candidate solutions is costly and time-consuming. In this study, we explore the possibility of employing LLMs as highly-constrained bilevel optimizers through a methodology we refer to as Language Model Optimization with Margin Expectation (LLOME). This approach combines both offline and online optimization, utilizing limited oracle evaluations to iteratively enhance the sequences generated by the LLM. We additionally propose a novel training objective -- Margin-Aligned Expectation (MargE) -- that trains the LLM to smoothly interpolate between the reward and reference distributions. Lastly, we introduce a synthetic test suite that bears strong geometric similarity to real biophysical problems and enables rapid evaluation of LLM optimizers without time-consuming lab validation. Our findings reveal that, in comparison to genetic algorithm baselines, LLMs achieve significantly lower regret solutions while requiring fewer test function evaluations. However, we also observe that LLMs exhibit moderate miscalibration, are susceptible to generator collapse, and have difficulty finding the optimal solution when no explicit ground truth rewards are available., Comment: Supercedes arXiv:2407.00236v1

There is a growing body of work seeking to replicate the success of machine learning (ML) on domains like computer vision (CV) and natural language processing (NLP) to applications involving biophysical data. One of the key ingredients of prior successes in CV and NLP was the broad acceptance of difficult benchmarks that distilled key subproblems into approachable tasks that any junior researcher could investigate, but good benchmarks for biophysical domains are rare. This scarcity is partially due to a narrow focus on benchmarks which simulate biophysical data; we propose instead to carefully abstract biophysical problems into simpler ones with key geometric similarities. In particular we propose a new class of closed-form test functions for biophysical sequence optimization, which we call Ehrlich functions. We provide empirical results demonstrating these functions are interesting objects of study and can be non-trivial to solve with a standard genetic optimization baseline.

As artificial intelligence (AI) / machine learning (ML) gain widespread adoption, practitioners are increasingly seeking means to quantify and control the risk these systems incur. This challenge is especially salient when such systems have autonomy to collect their own data, such as in black-box optimization and active learning, where their actions induce sequential feedback-loop shifts in the data distribution. Conformal prediction is a promising approach to uncertainty and risk quantification, but prior variants' validity guarantees have assumed some form of ``quasi-exchangeability'' on the data distribution, thereby excluding many types of sequential shifts. In this paper we prove that conformal prediction can theoretically be extended to \textit{any} joint data distribution, not just exchangeable or quasi-exchangeable ones. Although the most general case is exceedingly impractical to compute, for concrete practical applications we outline a procedure for deriving specific conformal algorithms for any data distribution, and we use this procedure to derive tractable algorithms for a series of AI/ML-agent-induced covariate shifts. We evaluate the proposed algorithms empirically on synthetic black-box optimization and active learning tasks., Comment: ICML 2024. Code available at https://github.com/drewprinster/conformal-mfcs

A popular approach to protein design is to combine a generative model with a discriminative model for conditional sampling. The generative model samples plausible sequences while the discriminative model guides a search for sequences with high fitness. Given its broad success in conditional sampling, classifier-guided diffusion modeling is a promising foundation for protein design, leading many to develop guided diffusion models for structure with inverse folding to recover sequences. In this work, we propose diffusioN Optimized Sampling (NOS), a guidance method for discrete diffusion models that follows gradients in the hidden states of the denoising network. NOS makes it possible to perform design directly in sequence space, circumventing significant limitations of structure-based methods, including scarce data and challenging inverse design. Moreover, we use NOS to generalize LaMBO, a Bayesian optimization procedure for sequence design that facilitates multiple objectives and edit-based constraints. The resulting method, LaMBO-2, enables discrete diffusions and stronger performance with limited edits through a novel application of saliency maps. We apply LaMBO-2 to a real-world protein design task, optimizing antibodies for higher expression yield and binding affinity to several therapeutic targets under locality and developability constraints, attaining a 99% expression rate and 40% binding rate in exploratory in vitro experiments.

We introduce GAUCHE, a library for GAUssian processes in CHEmistry. Gaussian processes have long been a cornerstone of probabilistic machine learning, affording particular advantages for uncertainty quantification and Bayesian optimisation. Extending Gaussian processes to chemical representations, however, is nontrivial, necessitating kernels defined over structured inputs such as graphs, strings and bit vectors. By defining such kernels in GAUCHE, we seek to open the door to powerful tools for uncertainty quantification and Bayesian optimisation in chemistry. Motivated by scenarios frequently encountered in experimental chemistry, we showcase applications for GAUCHE in molecular discovery and chemical reaction optimisation. The codebase is made available at https://github.com/leojklarner/gauche

Bayesian optimization is a coherent, ubiquitous approach to decision-making under uncertainty, with applications including multi-arm bandits, active learning, and black-box optimization. Bayesian optimization selects decisions (i.e. objective function queries) with maximal expected utility with respect to the posterior distribution of a Bayesian model, which quantifies reducible, epistemic uncertainty about query outcomes. In practice, subjectively implausible outcomes can occur regularly for two reasons: 1) model misspecification and 2) covariate shift. Conformal prediction is an uncertainty quantification method with coverage guarantees even for misspecified models and a simple mechanism to correct for covariate shift. We propose conformal Bayesian optimization, which directs queries towards regions of search space where the model predictions have guaranteed validity, and investigate its behavior on a suite of black-box optimization tasks and tabular ranking tasks. In many cases we find that query coverage can be significantly improved without harming sample-efficiency., Comment: For code, see https://www.github.com/samuelstanton/conformal-bayesopt.git

Bayesian optimization offers a sample-efficient framework for navigating the exploration-exploitation trade-off in the vast design space of biological sequences. Whereas it is possible to optimize the various properties of interest jointly using a multi-objective acquisition function, such as the expected hypervolume improvement (EHVI), this approach does not account for objectives with a hierarchical dependency structure. We consider a common use case where some regions of the Pareto frontier are prioritized over others according to a specified $\textit{partial ordering}$ in the objectives. For instance, when designing antibodies, we would like to maximize the binding affinity to a target antigen only if it can be expressed in live cell culture -- modeling the experimental dependency in which affinity can only be measured for antibodies that can be expressed and thus produced in viable quantities. In general, we may want to confer a partial ordering to the properties such that each property is optimized conditioned on its parent properties satisfying some feasibility condition. To this end, we present PropertyDAG, a framework that operates on top of the traditional multi-objective BO to impose this desired ordering on the objectives, e.g. expression $\rightarrow$ affinity. We demonstrate its performance over multiple simulated active learning iterations on a penicillin production task, toy numerical problem, and a real-world antibody design task., Comment: 9 pages, 7 figures. Submitted to NeurIPS 2022 AI4Science Workshop

Bayesian optimization (BayesOpt) is a gold standard for query-efficient continuous optimization. However, its adoption for drug design has been hindered by the discrete, high-dimensional nature of the decision variables. We develop a new approach (LaMBO) which jointly trains a denoising autoencoder with a discriminative multi-task Gaussian process head, allowing gradient-based optimization of multi-objective acquisition functions in the latent space of the autoencoder. These acquisition functions allow LaMBO to balance the explore-exploit tradeoff over multiple design rounds, and to balance objective tradeoffs by optimizing sequences at many different points on the Pareto frontier. We evaluate LaMBO on two small-molecule design tasks, and introduce new tasks optimizing \emph{in silico} and \emph{in vitro} properties of large-molecule fluorescent proteins. In our experiments LaMBO outperforms genetic optimizers and does not require a large pretraining corpus, demonstrating that BayesOpt is practical and effective for biological sequence design., Comment: ICML 2022. Code available at https://github.com/samuelstanton/lambo

Physics-inspired neural networks (NNs), such as Hamiltonian or Lagrangian NNs, dramatically outperform other learned dynamics models by leveraging strong inductive biases. These models, however, are challenging to apply to many real world systems, such as those that don't conserve energy or contain contacts, a common setting for robotics and reinforcement learning. In this paper, we examine the inductive biases that make physics-inspired models successful in practice. We show that, contrary to conventional wisdom, the improved generalization of HNNs is the result of modeling acceleration directly and avoiding artificial complexity from the coordinate system, rather than symplectic structure or energy conservation. We show that by relaxing the inductive biases of these models, we can match or exceed performance on energy-conserving systems while dramatically improving performance on practical, non-conservative systems. We extend this approach to constructing transition models for common Mujoco environments, showing that our model can appropriately balance inductive biases with the flexibility required for model-based control., Comment: ICLR 2022. Code available at https://github.com/ngruver/decon-hnn

With a principled representation of uncertainty and closed form posterior updates, Gaussian processes (GPs) are a natural choice for online decision making. However, Gaussian processes typically require at least $\mathcal{O}(n^2)$ computations for $n$ training points, limiting their general applicability. Stochastic variational Gaussian processes (SVGPs) can provide scalable inference for a dataset of fixed size, but are difficult to efficiently condition on new data. We propose online variational conditioning (OVC), a procedure for efficiently conditioning SVGPs in an online setting that does not require re-training through the evidence lower bound with the addition of new data. OVC enables the pairing of SVGPs with advanced look-ahead acquisition functions for black-box optimization, even with non-Gaussian likelihoods. We show OVC provides compelling performance in a range of applications including active learning of malaria incidence, and reinforcement learning on MuJoCo simulated robotic control tasks., Comment: NeurIPS 2021

Knowledge distillation is a popular technique for training a small student network to emulate a larger teacher model, such as an ensemble of networks. We show that while knowledge distillation can improve student generalization, it does not typically work as it is commonly understood: there often remains a surprisingly large discrepancy between the predictive distributions of the teacher and the student, even in cases when the student has the capacity to perfectly match the teacher. We identify difficulties in optimization as a key reason for why the student is unable to match the teacher. We also show how the details of the dataset used for distillation play a role in how closely the student matches the teacher -- and that more closely matching the teacher paradoxically does not always lead to better student generalization., Comment: NeurIPS 2021. Code available at https://github.com/samuelstanton/gnosis

Gaussian processes (GPs) provide a gold standard for performance in online settings, such as sample-efficient control and black box optimization, where we need to update a posterior distribution as we acquire data in a sequential fashion. However, updating a GP posterior to accommodate even a single new observation after having observed $n$ points incurs at least $O(n)$ computations in the exact setting. We show how to use structured kernel interpolation to efficiently recycle computations for constant-time $O(1)$ online updates with respect to the number of points $n$, while retaining exact inference. We demonstrate the promise of our approach in a range of online regression and classification settings, Bayesian optimization, and active sampling to reduce error in malaria incidence forecasting. Code is available at https://github.com/wjmaddox/online_gp., Comment: AISTATS 2021

For over a decade, model-based reinforcement learning has been seen as a way to leverage control-based domain knowledge to improve the sample-efficiency of reinforcement learning agents. While model-based agents are conceptually appealing, their policies tend to lag behind those of model-free agents in terms of final reward, especially in non-trivial environments. In response, researchers have proposed model-based agents with increasingly complex components, from ensembles of probabilistic dynamics models, to heuristics for mitigating model error. In a reversal of this trend, we show that simple model-based agents can be derived from existing ideas that not only match, but outperform state-of-the-art model-free agents in terms of both sample-efficiency and final reward. We find that a model-free soft value estimate for policy evaluation and a model-based stochastic value gradient for policy improvement is an effective combination, achieving state-of-the-art results on a high-dimensional humanoid control task, which most model-based agents are unable to solve. Our findings suggest that model-based policy evaluation deserves closer attention., Comment: L4DC 2021

The translation equivariance of convolutional layers enables convolutional neural networks to generalize well on image problems. While translation equivariance provides a powerful inductive bias for images, we often additionally desire equivariance to other transformations, such as rotations, especially for non-image data. We propose a general method to construct a convolutional layer that is equivariant to transformations from any specified Lie group with a surjective exponential map. Incorporating equivariance to a new group requires implementing only the group exponential and logarithm maps, enabling rapid prototyping. Showcasing the simplicity and generality of our method, we apply the same model architecture to images, ball-and-stick molecular data, and Hamiltonian dynamical systems. For Hamiltonian systems, the equivariance of our models is especially impactful, leading to exact conservation of linear and angular momentum., Comment: ICML 2020. Code available at https://github.com/mfinzi/LieConv