A.1 Comparison with SOTAModels on 60%/20%/20% Random Splits The main results of the full sets of experiments 17 with statistics of datasets are summarized in Table 2, where we report the mean accuracy (%) and standard deviation. We can see that after applied in ACM or ACMII framework, the performance of baseline models are boosted on almost all tasks and achieve SOTA performance on 9out of 10datasets. Especially, ACMII-GCN+ performs the best in terms of average rank (4.40) across all datasets. Overall, It suggests that ACM or ACMII framework can significantly increase the performance of GNNs on node classification tasks on heterophilic graphs and maintain highly competitive performance on homophilic datasets. The best results are highlighted in grey and the best baseline results (SOTA in Figure 6) are underlined. Results "*" are reported from [8, 26] and results " " are from [36].

Preference learning, or the task of aligning generative models to preference comparison data, has yet to reach the conceptual maturity of classification, density estimation, etc. To close this gap, this work presents a framework to understand preference learning starting from the sampling distribution of pairwise preference data. First, we prove that the only evaluation of a generative model that respects both preferences and prevalences in the data distribution is a form of win rate, justifying win rate as the focal point to understand preference learning. We then analyze preference learning methods as win rate optimization (WRO) or non-WRO. We present novel instances of WRO beyond existing examples (RLHF, NLHF) and identify two key theoretical benefits of all such methods. We prove that common non-WRO methods like DPO and SFT on preferred samples lack these properties and suggest ways to mitigate such theoretical limitations. We also show that WRO underperforms in practice due optimization difficulties and that optimization success predicts performance better than choices which affect the objective's solution. Our analysis highlights best practices for existing methods and provides recommendations for future research, guided by the principle that one should either align non-WRO methods more closely with WRO or improve the optimization of WRO objectives.

Interactive decision-making is essential in applications such as autonomous driving, where the agent must infer the behavior of nearby human drivers while planning in real-time. Traditional predict-then-act frameworks are often insufficient or inefficient because accurate inference of human behavior requires a continuous interaction rather than isolated prediction. To address this, we propose an active learning framework in which we rigorously derive predicted belief distributions. Additionally, we introduce a novel model-based diffusion solver tailored for online receding horizon control problems, demonstrated through a complex, non-convex highway merging scenario. Our approach extends previous high-fidelity dual control simulations to hardware experiments, which may be viewed at https://youtu.be/Q_JdZuopGL4, and verifies behavior inference in human-driven traffic scenarios, moving beyond idealized models. The results show improvements in adaptive planning under uncertainty, advancing the field of interactive decision-making for real-world applications.

Decentralized stochastic control problems are intrinsically difficult to study because of the inapplicability of standard tools from centralized control such as dynamic programming and the resulting computational complexity. In this paper, we address some of these challenges for decentralized stochastic control with Borel spaces under three different but tightly related information structures under a unified theme: the one-step delayed information sharing pattern, the K-step periodic information sharing pattern, and the completely decentralized information structure where no sharing of information occurs. We will show that the one-step delayed and K-step periodic problems can be reduced to a centralized MDP, generalizing prior results which considered finite, linear, or static models, by addressing several measurability questions. The separated nature of policies under both information structures is then established. We then provide sufficient conditions for the transition kernels of both centralized reductions to be weak-Feller, which facilitates rigorous approximation and learning theoretic results. We will then show that for the completely decentralized control problem finite memory local policies are near optimal under a joint conditional mixing condition. This is achieved by obtaining a bound for finite memory policies which goes to zero as memory size increases. We will also provide a performance bound for the K-periodic problem, which results from replacing the full common information by a finite sliding window of information. The latter will depend on the condition of predictor stability in expected total variation, which we will establish. We finally show that under the periodic information sharing pattern, a quantized Q-learning algorithm converges asymptotically towards a near optimal solution. Each of the above, to our knowledge, is a new contribution to the literature.

Diffusion models have gained huge popularity in recent years in machine learning, as a method to learn and generate new samples from a data distribution. Score-based generative modeling (SGM), as a particular kind of diffusion model, uses learned score functions (gradients of the log-pdf) to transform white noise to the data distribution through following a stochatic differential equation. While SGM has achieved state-of-theart performance for artificial image and audio generation [SE19; Dat+19; Gra+19; SE20; Son+20; Men+21; Son+21b; Son+21a; Jin+22], including being a key component of text-to-image systems [Ram+22], our theoretical understanding of these models is still nascent. In particular, basic questions on the convergence of the generated distribution to the data distribution remain unanswered. Recent theoretical work on SGM has attempted to answer these questions [De +21; LLT22; De 22], but they either suffer from exponential dependence on parameters or rely on strong assumptions on the data distribution such as functional inequalities or smoothness, which are rarely satisfied in practical situations. For example, considering the hallmark application of generating images from text, we expect the distribution of images to be (a) multimodal, and hence not satisfying functional inequalities with reasonable constants, and (b) supported on lower-dimensional manifolds, and hence not smooth. However, SGM still performs remarkably well in these settings. Indeed, this is one relative advantage to other approaches to generative modeling such as generative adversarial networks, which can struggle to learn multimodal distributions [ARZ18]. In this work, we aim to develop theoretical convergence guarantees with polynomial complexity for SGM under minimal data assumptions.