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.

Actions Speak What You Want: Provably Sample-Efficient Reinforcement Learning of the Quantal Stackelberg Equilibrium from Strategic Feedbacks

We study reinforcement learning (RL) for learning a Quantal Stackelberg Equilibrium (QSE) in an episodic Markov game with a leader-follower structure. In specific, at the outset of the game, the leader announces her policy to the follower and commits to it. The follower observes the leader's policy and, in turn, adopts a quantal response policy by solving an entropy-regularized policy optimization problem induced by leader's policy. The goal of the leader is to find her optimal policy, which yields the optimal expected total return, by interacting with the follower and learning from data. A key challenge of this problem is that the leader cannot observe the follower's reward, and needs to infer the follower's quantal response model from his actions against leader's policies. We propose sample-efficient algorithms for both the online and offline settings, in the context of function approximation. Our algorithms are based on (i) learning the quantal response model via maximum likelihood estimation and (ii) model-free or model-based RL for solving the leader's decision making problem, and we show that they achieve sublinear regret upper bounds. Moreover, we quantify the uncertainty of these estimators and leverage the uncertainty to implement optimistic and pessimistic algorithms for online and offline settings. Besides, when specialized to the linear and myopic setting, our algorithms are also computationally efficient. Our theoretical analysis features a novel performance-difference lemma which incorporates the error of quantal response model, which might be of independent interest.

Provable Benefits of Policy Learning from Human Preferences in Contextual Bandit Problems

A crucial task in decision-making problems is reward engineering. It is common in practice that no obvious choice of reward function exists. Thus, a popular approach is to introduce human feedback during training and leverage such feedback to learn a reward function. Among all policy learning methods that use human feedback, preference-based methods have demonstrated substantial success in recent empirical applications such as InstructGPT. In this work, we develop a theory that provably shows the benefits of preference-based methods in offline contextual bandits. In particular, we improve the modeling and suboptimality analysis for running policy learning methods on human-scored samples directly. Then, we compare it with the suboptimality guarantees of preference-based methods and show that preference-based methods enjoy lower suboptimality.

Reward-Directed Conditional Diffusion: Provable Distribution Estimation and Reward Improvement

We explore the methodology and theory of reward-directed generation via conditional diffusion models. Directed generation aims to generate samples with desired properties as measured by a reward function, which has broad applications in generative AI, reinforcement learning, and computational biology. We consider the common learning scenario where the data set consists of unlabeled data along with a smaller set of data with noisy reward labels. Our approach leverages a learned reward function on the smaller data set as a pseudolabeler. From a theoretical standpoint, we show that this directed generator can effectively learn and sample from the reward-conditioned data distribution. Additionally, our model is capable of recovering the latent subspace representation of data. Moreover, we establish that the model generates a new population that moves closer to a user-specified target reward value, where the optimality gap aligns with the off-policy bandit regret in the feature subspace. The improvement in rewards obtained is influenced by the interplay between the strength of the reward signal, the distribution shift, and the cost of off-support extrapolation. We provide empirical results to validate our theory and highlight the relationship between the strength of extrapolation and the quality of generated samples.

Sample-Efficient Learning of POMDPs with Multiple Observations In Hindsight

This paper studies the sample-efficiency of learning in Partially Observable Markov Decision Processes (POMDPs), a challenging problem in reinforcement learning that is known to be exponentially hard in the worst-case. Motivated by real-world settings such as loading in game playing, we propose an enhanced feedback model called ``multiple observations in hindsight'', where after each episode of interaction with the POMDP, the learner may collect multiple additional observations emitted from the encountered latent states, but may not observe the latent states themselves. We show that sample-efficient learning under this feedback model is possible for two new subclasses of POMDPs: \emph{multi-observation revealing POMDPs} and \emph{distinguishable POMDPs}. Both subclasses generalize and substantially relax \emph{revealing POMDPs} -- a widely studied subclass for which sample-efficient learning is possible under standard trajectory feedback. Notably, distinguishable POMDPs only require the emission distributions from different latent states to be \emph{different} instead of \emph{linearly independent} as required in revealing POMDPs.

Scaling In-Context Demonstrations with Structured Attention

The recent surge of large language models (LLMs) highlights their ability to perform in-context learning, i.e., "learning" to perform a task from a few demonstrations in the context without any parameter updates. However, their capabilities of in-context learning are limited by the model architecture: 1) the use of demonstrations is constrained by a maximum sentence length due to positional embeddings; 2) the quadratic complexity of attention hinders users from using more demonstrations efficiently; 3) LLMs are shown to be sensitive to the order of the demonstrations. In this work, we tackle these challenges by proposing a better architectural design for in-context learning. We propose SAICL (Structured Attention for In-Context Learning), which replaces the full-attention by a structured attention mechanism designed for in-context learning, and removes unnecessary dependencies between individual demonstrations, while making the model invariant to the permutation of demonstrations. We evaluate SAICL in a meta-training framework and show that SAICL achieves comparable or better performance than full attention while obtaining up to 3.4x inference speed-up. SAICL also consistently outperforms a strong Fusion-in-Decoder (FiD) baseline which processes each demonstration independently. Finally, thanks to its linear nature, we demonstrate that SAICL can easily scale to hundreds of demonstrations with continuous performance gains with scaling.

Nonparametric Classification on Low Dimensional Manifolds using Overparameterized Convolutional Residual Networks

Convolutional residual neural networks (ConvResNets), though overparameterized, can achieve remarkable prediction performance in practice, which cannot be well explained by conventional wisdom. To bridge this gap, we study the performance of ConvResNeXts, which cover ConvResNets as a special case, trained with weight decay from the perspective of nonparametric classification. Our analysis allows for infinitely many building blocks in ConvResNeXts, and shows that weight decay implicitly enforces sparsity on these blocks. Specifically, we consider a smooth target function supported on a low-dimensional manifold, then prove that ConvResNeXts can adapt to the function smoothness and low-dimensional structures and efficiently learn the function without suffering from the curse of dimensionality. Our findings partially justify the advantage of overparameterized ConvResNeXts over conventional machine learning models.

Effective Minkowski Dimension of Deep Nonparametric Regression: Function Approximation and Statistical Theories

Existing theories on deep nonparametric regression have shown that when the input data lie on a low-dimensional manifold, deep neural networks can adapt to the intrinsic data structures. In real world applications, such an assumption of data lying exactly on a low dimensional manifold is stringent. This paper introduces a relaxed assumption that the input data are concentrated around a subset of $\mathbb{R}^d$ denoted by $\mathcal{S}$, and the intrinsic dimension of $\mathcal{S}$ can be characterized by a new complexity notation -- effective Minkowski dimension. We prove that, the sample complexity of deep nonparametric regression only depends on the effective Minkowski dimension of $\mathcal{S}$ denoted by $p$. We further illustrate our theoretical findings by considering nonparametric regression with an anisotropic Gaussian random design $N(0,\Sigma)$, where $\Sigma$ is full rank. When the eigenvalues of $\Sigma$ have an exponential or polynomial decay, the effective Minkowski dimension of such an Gaussian random design is $p=\mathcal{O}(\sqrt{\log n})$ or $p=\mathcal{O}(n^\gamma)$, respectively, where $n$ is the sample size and $\gamma\in(0,1)$ is a small constant depending on the polynomial decay rate. Our theory shows that, when the manifold assumption does not hold, deep neural networks can still adapt to the effective Minkowski dimension of the data, and circumvent the curse of the ambient dimensionality for moderate sample sizes.

Visual Adversarial Examples Jailbreak Large Language Models

Recently, there has been a surge of interest in introducing vision into Large Language Models (LLMs). The proliferation of large Visual Language Models (VLMs), such as Flamingo, BLIP-2, and GPT-4, signifies an exciting convergence of advancements in both visual and language foundation models. Yet, the risks associated with this integrative approach are largely unexamined. In this paper, we shed light on the security and safety implications of this trend. First, we underscore that the continuous and high-dimensional nature of the additional visual input space intrinsically makes it a fertile ground for adversarial attacks. This unavoidably expands the attack surfaces of LLMs. Second, we highlight that the broad functionality of LLMs also presents visual attackers with a wider array of achievable adversarial objectives, extending the implications of security failures beyond mere misclassification. To elucidate these risks, we study adversarial examples in the visual input space of a VLM. Specifically, against MiniGPT-4, which incorporates safety mechanisms that can refuse harmful instructions, we present visual adversarial examples that can circumvent the safety mechanisms and provoke harmful behaviors of the model. Remarkably, we discover that adversarial examples, even if optimized on a narrow, manually curated derogatory corpus against specific social groups, can universally jailbreak the model's safety mechanisms. A single such adversarial example can generally undermine MiniGPT-4's safety, enabling it to heed a wide range of harmful instructions and produce harmful content far beyond simply imitating the derogatory corpus used in optimization. Unveiling these risks, we accentuate the urgent need for comprehensive risk assessments, robust defense strategies, and the implementation of responsible practices for the secure and safe utilization of VLMs.