Coordinate descent methods are popular in machine learning and optimization for their simple sparse updates and excellent practical performance. In the context of large-scale sequential game solving, these same properties would be attractive, but until now no such methods were known, because the strategy spaces do not satisfy the typical separable block structure exploited by such methods. We present the first cyclic coordinate-descent-like method for the polytope of sequence-form strategies, which form the strategy spaces for the players in an extensive-form game (EFG). Our method exploits the recursive structure of the proximal update induced by what are known as dilated regularizers, in order to allow for a pseudo block-wise update. We show that our method enjoys a O(1/T)convergence rate to a two-player zero-sum Nash equilibrium, while avoiding the worst-case polynomial scaling with the number of blocks common to cyclic methods. We empirically show that our algorithm usually performs better than other state-of-the-art first-order methods (i.e., mirror prox), and occasionally can even beat CFR+, a state-ofthe-art algorithm for numerical equilibrium computation in zero-sum EFGs. We then introduce a restarting heuristic for EFG solving. We show empirically that restarting can lead to speedups, sometimes huge, both for our cyclic method, as well as for existing methods such as mirror prox and predictive CFR+.

Iterative data generation and model retraining are widely used to align large language models (LLMs). It typically involves a policy model to generate on-policy responses and a reward model to guide training data selection. Direct Preference Optimization (DPO) further enhances this process by constructing preference pairs of chosen and rejected responses. In this work, we aim to \emph{scale up} the number of on-policy samples via repeated random sampling to improve alignment performance. Conventional practice selects the sample with the highest reward as chosen and the lowest as rejected for DPO. However, our experiments reveal that this strategy leads to a \emph{decline} in performance as the sample size increases. To address this, we investigate preference data construction through the lens of underlying normal distribution of sample rewards. We categorize the reward space into seven representative points and systematically explore all 21 ($C_7^2$) pairwise combinations. Through evaluations on four models using AlpacaEval 2, we find that selecting the rejected response at reward position $\mu - 2\sigma$ rather than the minimum reward, is crucial for optimal performance. We finally introduce a scalable preference data construction strategy that consistently enhances model performance as the sample scale increases.

By interpreting a traffic scene as a graph of interacting vehicles, we gain a flexible abstract representation which allows us to apply Graph Neural Network (GNN) models for traffic prediction. These naturally take interaction between traffic participants into account while being computationally efficient and providing large model capacity. We evaluate two state-of-the art GNN architectures and introduce several adaptations for our specific scenario. We show that prediction error in scenarios with much interaction decreases by 30% compared to a model that does not take interactions into account. This suggests a graph interpretation of interacting traffic participants is a worthwhile addition to traffic prediction systems.