Scalable Normalizing Flows Enable Boltzmann Generators for Macromolecules

The Boltzmann distribution of a protein provides a roadmap to all of its functional states. Normalizing flows are a promising tool for modeling this distribution, but current methods are intractable for typical pharmacological targets; they become computationally intractable due to the size of the system, heterogeneity of intra-molecular potential energy, and long-range interactions. To remedy these issues, we present a novel flow architecture that utilizes split channels and gated attention to efficiently learn the conformational distribution of proteins defined by internal coordinates. We show that by utilizing a 2-Wasserstein loss, one can smooth the transition from maximum likelihood training to energy-based training, enabling the training of Boltzmann Generators for macromolecules. We evaluate our model and training strategy on villin headpiece HP35(nle-nle), a 35-residue subdomain, and protein G, a 56-residue protein. We demonstrate that standard architectures and training strategies, such as maximum likelihood alone, fail while our novel architecture and multi-stage training strategy are able to model the conformational distributions of protein G and HP35.

Tree Search-Based Evolutionary Bandits for Protein Sequence Optimization

While modern biotechnologies allow synthesizing new proteins and function measurements at scale, efficiently exploring a protein sequence space and engineering it remains a daunting task due to the vast sequence space of any given protein. Protein engineering is typically conducted through an iterative process of adding mutations to the wild-type or lead sequences, recombination of mutations, and running new rounds of screening. To enhance the efficiency of such a process, we propose a tree search-based bandit learning method, which expands a tree starting from the initial sequence with the guidance of a bandit machine learning model. Under simplified assumptions and a Gaussian Process prior, we provide theoretical analysis and a Bayesian regret bound, demonstrating that the combination of local search and bandit learning method can efficiently discover a near-optimal design. The full algorithm is compatible with a suite of randomized tree search heuristics, machine learning models, pre-trained embeddings, and bandit techniques. We test various instances of the algorithm across benchmark protein datasets using simulated screens. Experiment results demonstrate that the algorithm is both sample-efficient and able to find top designs using reasonably small mutation counts.

Is Inverse Reinforcement Learning Harder than Standard Reinforcement Learning?

Inverse Reinforcement Learning (IRL) -- the problem of learning reward functions from demonstrations of an \emph{expert policy} -- plays a critical role in developing intelligent systems, such as those that understand and imitate human behavior. While widely used in applications, theoretical understandings of IRL admit unique challenges and remain less developed compared with standard RL theory. For example, it remains open how to do IRL efficiently in standard \emph{offline} settings with pre-collected data, where states are obtained from a \emph{behavior policy} (which could be the expert policy itself), and actions are sampled from the expert policy. This paper provides the first line of results for efficient IRL in vanilla offline and online settings using polynomial samples and runtime. We first design a new IRL algorithm for the offline setting, Reward Learning with Pessimism (RLP), and show that it achieves polynomial sample complexity in terms of the size of the MDP, a concentrability coefficient between the behavior policy and the expert policy, and the desired accuracy. Building on RLP, we further design an algorithm Reward Learning with Exploration (RLE), which operates in a natural online setting where the learner can both actively explore the environment and query the expert policy, and obtain a stronger notion of IRL guarantee from polynomial samples. We establish sample complexity lower bounds for both settings showing that RLP and RLE are nearly optimal. Finally, as an application, we show that the learned reward functions can \emph{transfer} to another target MDP with suitable guarantees when the target MDP satisfies certain similarity assumptions with the original (source) MDP.

Posterior Sampling with Delayed Feedback for Reinforcement Learning with Linear Function Approximation

Recent studies in reinforcement learning (RL) have made significant progress by leveraging function approximation to alleviate the sample complexity hurdle for better performance. Despite the success, existing provably efficient algorithms typically rely on the accessibility of immediate feedback upon taking actions. The failure to account for the impact of delay in observations can significantly degrade the performance of real-world systems due to the regret blow-up. In this work, we tackle the challenge of delayed feedback in RL with linear function approximation by employing posterior sampling, which has been shown to empirically outperform the popular UCB algorithms in a wide range of regimes. We first introduce Delayed-PSVI, an optimistic value-based algorithm that effectively explores the value function space via noise perturbation with posterior sampling. We provide the first analysis for posterior sampling algorithms with delayed feedback in RL and show our algorithm achieves $\widetilde{O}(\sqrt{d^3H^3 T} + d^2H^2 E[\tau])$ worst-case regret in the presence of unknown stochastic delays. Here $E[\tau]$ is the expected delay. To further improve its computational efficiency and to expand its applicability in high-dimensional RL problems, we incorporate a gradient-based approximate sampling scheme via Langevin dynamics for Delayed-LPSVI, which maintains the same order-optimal regret guarantee with $\widetilde{O}(dHK)$ computational cost. Empirical evaluations are performed to demonstrate the statistical and computational efficacy of our algorithms.

Sample Complexity of Preference-Based Nonparametric Off-Policy Evaluation with Deep Networks

A recently popular approach to solving reinforcement learning is with data from human preferences. In fact, human preference data are now used with classic reinforcement learning algorithms such as actor-critic methods, which involve evaluating an intermediate policy over a reward learned from human preference data with distribution shift, known as off-policy evaluation (OPE). Such algorithm includes (i) learning reward function from human preference dataset, and (ii) learning expected cumulative reward of a target policy. Despite the huge empirical success, existing OPE methods with preference data often lack theoretical understanding and rely heavily on heuristics. In this paper, we study the sample efficiency of OPE with human preference and establish a statistical guarantee for it. Specifically, we approach OPE by learning the value function by fitted-Q-evaluation with a deep neural network. By appropriately selecting the size of a ReLU network, we show that one can leverage any low-dimensional manifold structure in the Markov decision process and obtain a sample-efficient estimator without suffering from the curse of high data ambient dimensionality. Under the assumption of high reward smoothness, our results \textit{almost align with the classical OPE results with observable reward data}. To the best of our knowledge, this is the first result that establishes a \textit{provably efficient} guarantee for off-policy evaluation with RLHF.

Federated Multi-Level Optimization over Decentralized Networks

Multi-level optimization has gained increasing attention in recent years, as it provides a powerful framework for solving complex optimization problems that arise in many fields, such as meta-learning, multi-player games, reinforcement learning, and nested composition optimization. In this paper, we study the problem of distributed multi-level optimization over a network, where agents can only communicate with their immediate neighbors. This setting is motivated by the need for distributed optimization in large-scale systems, where centralized optimization may not be practical or feasible. To address this problem, we propose a novel gossip-based distributed multi-level optimization algorithm that enables networked agents to solve optimization problems at different levels in a single timescale and share information through network propagation. Our algorithm achieves optimal sample complexity, scaling linearly with the network size, and demonstrates state-of-the-art performance on various applications, including hyper-parameter tuning, decentralized reinforcement learning, and risk-averse optimization.

A 5' UTR Language Model for Decoding Untranslated Regions of mRNA and Function Predictions

The 5' UTR, a regulatory region at the beginning of an mRNA molecule, plays a crucial role in regulating the translation process and impacts the protein expression level. Language models have showcased their effectiveness in decoding the functions of protein and genome sequences. Here, we introduced a language model for 5' UTR, which we refer to as the UTR-LM. The UTR-LM is pre-trained on endogenous 5' UTRs from multiple species and is further augmented with supervised information including secondary structure and minimum free energy. We fine-tuned the UTR-LM in a variety of downstream tasks. The model outperformed the best-known benchmark by up to 42% for predicting the Mean Ribosome Loading, and by up to 60% for predicting the Translation Efficiency and the mRNA Expression Level. The model also applies to identifying unannotated Internal Ribosome Entry Sites within the untranslated region and improves the AUPR from 0.37 to 0.52 compared to the best baseline. Further, we designed a library of 211 novel 5' UTRs with high predicted values of translation efficiency and evaluated them via a wet-lab assay. Experiment results confirmed that our top designs achieved a 32.5% increase in protein production level relative to well-established 5' UTR optimized for therapeutics.

Sample Complexity of Neural Policy Mirror Descent for Policy Optimization on Low-Dimensional Manifolds

Policy-based algorithms equipped with deep neural networks have achieved great success in solving high-dimensional policy optimization problems in reinforcement learning. However, current analyses cannot explain why they are resistant to the curse of dimensionality. In this work, we study the sample complexity of the neural policy mirror descent (NPMD) algorithm with convolutional neural networks (CNN) as function approximators. Motivated by the empirical observation that many high-dimensional environments have state spaces possessing low-dimensional structures, such as those taking images as states, we consider the state space to be a $d$-dimensional manifold embedded in the $D$-dimensional Euclidean space with intrinsic dimension $d\ll D$. We show that in each iteration of NPMD, both the value function and the policy can be well approximated by CNNs. The approximation errors are controlled by the size of the networks, and the smoothness of the previous networks can be inherited. As a result, by properly choosing the network size and hyperparameters, NPMD can find an $\epsilon$-optimal policy with $\widetilde{O}(\epsilon^{-\frac{d}{\alpha}-2})$ samples in expectation, where $\alpha\in(0,1]$ indicates the smoothness of environment. Compared to previous work, our result exhibits that NPMD can leverage the low-dimensional structure of state space to escape from the curse of dimensionality, providing an explanation for the efficacy of deep policy-based algorithms.

Deep Reinforcement Learning for Efficient and Fair Allocation of Health Care Resources

Scarcity of health care resources could result in the unavoidable consequence of rationing. For example, ventilators are often limited in supply, especially during public health emergencies or in resource-constrained health care settings, such as amid the pandemic of COVID-19. Currently, there is no universally accepted standard for health care resource allocation protocols, resulting in different governments prioritizing patients based on various criteria and heuristic-based protocols. In this study, we investigate the use of reinforcement learning for critical care resource allocation policy optimization to fairly and effectively ration resources. We propose a transformer-based deep Q-network to integrate the disease progression of individual patients and the interaction effects among patients during the critical care resource allocation. We aim to improve both fairness of allocation and overall patient outcomes. Our experiments demonstrate that our method significantly reduces excess deaths and achieves a more equitable distribution under different levels of ventilator shortage, when compared to existing severity-based and comorbidity-based methods in use by different governments. Our source code is included in the supplement and will be released on Github upon publication.

Aligning Agent Policy with Externalities: Reward Design via Bilevel RL

In reinforcement learning (RL), a reward function is often assumed at the outset of a policy optimization procedure. Learning in such a fixed reward paradigm in RL can neglect important policy optimization considerations, such as state space coverage and safety. Moreover, it can fail to encompass broader impacts in terms of social welfare, sustainability, or market stability, potentially leading to undesirable emergent behavior and potentially misaligned policy. To mathematically encapsulate the problem of aligning RL policy optimization with such externalities, we consider a bilevel optimization problem and connect it to a principal-agent framework, where the principal specifies the broader goals and constraints of the system at the upper level and the agent solves a Markov Decision Process (MDP) at the lower level. The upper-level deals with learning a suitable reward parametrization corresponding to the broader goals and the lower-level deals with learning the policy for the agent. We propose Principal driven Policy Alignment via Bilevel RL (PPA-BRL), which efficiently aligns the policy of the agent with the principal's goals. We explicitly analyzed the dependence of the principal's trajectory on the lower-level policy, prove the convergence of PPA-BRL to the stationary point of the problem. We illuminate the merits of this framework in view of alignment with several examples spanning energy-efficient manipulation tasks, social welfare-based tax design, and cost-effective robotic navigation.