Multi-User Dueling Bandits: A Fair Approach using Nash Social Welfare

Learning from human preference data is becoming a useful tool, from fine-tuning large language models to training reinforcement learning agents. However, in most scenarios, the model is trained on the average preference of all human evaluators, which, under large variations of preferences, can be unfair to minority groups. In this work, we consider fairness in dueling bandits, a standard framework for online learning from preference data. We assume that each user has a (potentially distinct) Condorcet winner, which is an arm preferred to every other arm. Using these user-specific Condorcet winners as reference points, we evaluate and score arms according to their performance relative to the corresponding winner. To promote fairness across heterogeneous users, we adopt the well-established Nash Social Welfare objective, which maximizes the product of user utilities, thereby inherently penalizing inequality and preventing the marginalization of any single user. Within this framework, we construct a hard instance to establish a regret lower bound of $Ω(T^{2/3}\min(K,D)^\frac{1}{3})$ for a time horizon $T$, $K$ arms, and $D$ users, which, to the best of our knowledge, is the first result quantifying the cost of fairness in dueling bandits with heterogeneous preferences. We then present the Fair-Explore-Then-Commit and Fair-$ε$-Greedy algorithms with a Condorcet winner identification phase. We further derive their regret upper bounds that match the lower-bound dependence on $T$ up to logarithmic factors.

Reinforcement Learning from Multi-level and Episodic Human Feedback

Designing an effective reward function has long been a challenge in reinforcement learning, particularly for complex tasks in unstructured environments. To address this, various learning paradigms have emerged that leverage different forms of human input to specify or refine the reward function. Reinforcement learning from human feedback is a prominent approach that utilizes human comparative feedback, expressed as a preference for one behavior over another, to tackle this problem. In contrast to comparative feedback, we explore multi-level human feedback, which is provided in the form of a score at the end of each episode. This type of feedback offers more coarse but informative signals about the underlying reward function than binary feedback. Additionally, it can handle non-Markovian rewards, as it is based on the evaluation of an entire episode. We propose an algorithm to efficiently learn both the reward function and the optimal policy from this form of feedback. Moreover, we show that the proposed algorithm achieves sublinear regret and demonstrate its empirical effectiveness through extensive simulations.