Clone-Robust AI Alignment

A key challenge in training Large Language Models (LLMs) is properly aligning them with human preferences. Reinforcement Learning with Human Feedback (RLHF) uses pairwise comparisons from human annotators to train reward functions and has emerged as a popular alignment method. However, input datasets in RLHF are not necessarily balanced in the types of questions and answers that are included. Therefore, we want RLHF algorithms to perform well even when the set of alternatives is not uniformly distributed. Drawing on insights from social choice theory, we introduce robustness to approximate clones, a desirable property of RLHF algorithms which requires that adding near-duplicate alternatives does not significantly change the learned reward function. We first demonstrate that the standard RLHF algorithm based on regularized maximum likelihood estimation (MLE) fails to satisfy this property. We then propose the weighted MLE, a new RLHF algorithm that modifies the standard regularized MLE by weighting alternatives based on their similarity to other alternatives. This new algorithm guarantees robustness to approximate clones while preserving desirable theoretical properties.

Improved Regret Bounds for Online Fair Division with Bandit Learning

We study online fair division when there are a finite number of item types and the player values for the items are drawn randomly from distributions with unknown means. In this setting, a sequence of indivisible items arrives according to a random online process, and each item must be allocated to a single player. The goal is to maximize expected social welfare while maintaining that the allocation satisfies proportionality in expectation. When player values are normalized, we show that it is possible to with high probability guarantee proportionality constraint satisfaction and achieve $\tilde{O}(\sqrt{T})$ regret. To achieve this result, we present an upper confidence bound (UCB) algorithm that uses two rounds of linear optimization. This algorithm highlights fundamental aspects of proportionality constraints that allow for a UCB algorithm despite the presence of many (potentially tight) constraints. This result improves upon the previous best regret rate of $\tilde{O}(T^{2/3})$.

Stronger Regret Bounds for Safe Online Reinforcement Learning in the Linear Quadratic Regulator

Many practical applications of online reinforcement learning require the satisfaction of safety constraints while learning about the unknown environment. In this work, we study Linear Quadratic Regulator (LQR) learning with unknown dynamics, but with the additional constraint that the position must stay within a safe region for the entire trajectory with high probability. Unlike in previous works, we allow for both bounded and unbounded noise distributions and study stronger baselines of nonlinear controllers that are better suited for constrained problems than linear controllers. Due to these complications, we focus on 1-dimensional state- and action- spaces, however we also discuss how we expect the high-level takeaways can generalize to higher dimensions. Our primary contribution is the first $\tilde{O}_T(\sqrt{T})$-regret bound for constrained LQR learning, which we show relative to a specific baseline of non-linear controllers. We then prove that, for any non-linear baseline satisfying natural assumptions, $\tilde{O}_T(\sqrt{T})$-regret is possible when the noise distribution has sufficiently large support and $\tilde{O}_T(T^{2/3})$-regret is possible for any subgaussian noise distribution. An overarching theme of our results is that enforcing safety provides "free exploration" that compensates for the added cost of uncertainty in safety constrained control, resulting in the same regret rate as in the unconstrained problem.

Honor Among Bandits: No-Regret Learning for Online Fair Division

We consider the problem of online fair division of indivisible goods to players when there are a finite number of types of goods and player values are drawn from distributions with unknown means. Our goal is to maximize social welfare subject to allocating the goods fairly in expectation. When a player's value for an item is unknown at the time of allocation, we show that this problem reduces to a variant of (stochastic) multi-armed bandits, where there exists an arm for each player's value for each type of good. At each time step, we choose a distribution over arms which determines how the next item is allocated. We consider two sets of fairness constraints for this problem: envy-freeness in expectation and proportionality in expectation. Our main result is the design of an explore-then-commit algorithm that achieves $\tilde{O}(T^{2/3})$ regret while maintaining either fairness constraint. This result relies on unique properties fundamental to fair-division constraints that allow faster rates of learning, despite the restricted action space.