Despite the remarkable success of Large Language Models (LLMs), evaluating their outputs' quality regarding *preference* remains a critical challenge. Existing works usually leverage a powerful LLM (e.g., GPT4) as the judge for comparing LLMs' output pairwisely, yet such model-based evaluator is vulnerable to *conflicting preference*, i.e., output A is better than B, B than C, but C than A, causing contradictory evaluation results. To improve model-based preference evaluation, we introduce GED (Preference Graph Ensemble and Denoise), a novel approach that leverages multiple model-based evaluators to construct preference graphs, and then ensemble and denoise these graphs for better, non-contradictory evaluation results. In particular, our method consists of two primary stages: aggregating evaluations into a unified graph and applying a denoising process to eliminate cyclic inconsistencies, ensuring a directed acyclic graph (DAG) structure. We provide theoretical guarantees for our framework, demonstrating its efficacy in recovering the ground truth preference structure. Extensive experiments across ten benchmark datasets show that GED outperforms baseline methods in model ranking, response selection, and model alignment tasks. Notably, GED combines weaker evaluators like Llama3-8B, Mistral-7B, and Qwen2-7B to surpass the performance of stronger evaluators like Qwen2-72B, highlighting its ability to enhance evaluation reliability and improve model performance.

Reinforcement Learning from Human Feedback (RLHF) stands out as the primary method for aligning large language models with human preferences (Bai et al., 2022; Christiano et al., 2017; Ouyang et al., 2022). Instead of starting from scratch with unsupervised training on extensive datasets, RLHF aligns pre-trained models using labeled human preferences on pairs of responses, offering a statistically lightweight approach to making language models more human-like. While labeling response pairs is easier than generating new responses, the volume of these pairs is critical for effective alignment. A large dataset is needed to ensure broad coverage of linguistic nuances, reduce the impact of noisy human feedback, and provide enough statistical power for the model to generalize well. Although labeling individual pairs is simpler, scaling this process can still become resource-intensive, making the volume of response pairs a key factor in successful model alignment. In the light of this, recently a theoretical question of interest has arisen: How can algorithms be designed to be sample-efficient during this alignment phase? Two main approaches have emerged in addressing this question: online RLHF and offline RLHF. Online methods (Cen et al., 2024; Xie et al., 2024; Zhang et al., 2024) have interactive access to human feedback or leverage a more powerful language model to explore diverse and novel responses beyond what the pre-trained model can provide.

We propose Dual Approximation Policy Optimization (DAPO), a framework that incorporates general function approximation into policy mirror descent methods. In contrast to the popular approach of using the $L_2$-norm to measure function approximation errors, DAPO uses the dual Bregman divergence induced by the mirror map for policy projection. This duality framework has both theoretical and practical implications: not only does it achieve fast linear convergence with general function approximation, but it also includes several well-known practical methods as special cases, immediately providing strong convergence guarantees.

We investigate the fixed-budget best-arm identification (BAI) problem for linear bandits in a potentially non-stationary environment. Given a finite arm set $\mathcal{X}\subset\mathbb{R}^d$, a fixed budget $T$, and an unpredictable sequence of parameters $\left\lbrace\theta_t\right\rbrace_{t=1}^{T}$, an algorithm will aim to correctly identify the best arm $x^* := \arg\max_{x\in\mathcal{X}}x^\top\sum_{t=1}^{T}\theta_t$ with probability as high as possible. Prior work has addressed the stationary setting where $\theta_t = \theta_1$ for all $t$ and demonstrated that the error probability decreases as $\exp(-T /\rho^*)$ for a problem-dependent constant $\rho^*$. But in many real-world $A/B/n$ multivariate testing scenarios that motivate our work, the environment is non-stationary and an algorithm expecting a stationary setting can easily fail. For robust identification, it is well-known that if arms are chosen randomly and non-adaptively from a G-optimal design over $\mathcal{X}$ at each time then the error probability decreases as $\exp(-T\Delta^2_{(1)}/d)$, where $\Delta_{(1)} = \min_{x \neq x^*} (x^* - x)^\top \frac{1}{T}\sum_{t=1}^T \theta_t$. As there exist environments where $\Delta_{(1)}^2/ d \ll 1/ \rho^*$, we are motivated to propose a novel algorithm $\mathsf{P1}$-$\mathsf{RAGE}$ that aims to obtain the best of both worlds: robustness to non-stationarity and fast rates of identification in benign settings. We characterize the error probability of $\mathsf{P1}$-$\mathsf{RAGE}$ and demonstrate empirically that the algorithm indeed never performs worse than G-optimal design but compares favorably to the best algorithms in the stationary setting.

We investigate learning the equilibria in non-stationary multi-agent systems and address the challenges that differentiate multi-agent learning from single-agent learning. Specifically, we focus on games with bandit feedback, where testing an equilibrium can result in substantial regret even when the gap to be tested is small, and the existence of multiple optimal solutions (equilibria) in stationary games poses extra challenges. To overcome these obstacles, we propose a versatile black-box approach applicable to a broad spectrum of problems, such as general-sum games, potential games, and Markov games, when equipped with appropriate learning and testing oracles for stationary environments. Our algorithms can achieve $\widetilde{O}\left(\Delta^{1/4}T^{3/4}\right)$ regret when the degree of nonstationarity, as measured by total variation $\Delta$, is known, and $\widetilde{O}\left(\Delta^{1/5}T^{4/5}\right)$ regret when $\Delta$ is unknown, where $T$ is the number of rounds. Meanwhile, our algorithm inherits the favorable dependence on number of agents from the oracles. As a side contribution that may be independent of interest, we show how to test for various types of equilibria by a black-box reduction to single-agent learning, which includes Nash equilibria, correlated equilibria, and coarse correlated equilibria.

In this paper, we investigate Nash-regret minimization in congestion games, a class of games with benign theoretical structure and broad real-world applications. We first propose a centralized algorithm based on the optimism in the face of uncertainty principle for congestion games with (semi-)bandit feedback, and obtain finite-sample guarantees. Then we propose a decentralized algorithm via a novel combination of the Frank-Wolfe method and G-optimal design. By exploiting the structure of the congestion game, we show the sample complexity of both algorithms depends only polynomially on the number of players and the number of facilities, but not the size of the action set, which can be exponentially large in terms of the number of facilities. We further define a new problem class, Markov congestion games, which allows us to model the non-stationarity in congestion games. We propose a centralized algorithm for Markov congestion games, whose sample complexity again has only polynomial dependence on all relevant problem parameters, but not the size of the action set.