Jiaming Liang

Matthew X. Burns, Jiaming Liang

We propose Log-Averaged Mirror Prox (LAMP), a linear-space primal-dual method for large-scale optimal transport. LAMP implements primal mirror prox updates by tracking an averaged dual sequence, reducing storage complexity from ${O}(nm)$ to $O(n+m)$ while preserving dense, GPU-friendly reductions. Consequently, LAMP preserves the last-iterate $\widetilde{O}( nm\varepsilon^{-1})$ arithmetic complexity of conservatively parameterized primal-dual mirror prox. We further analyze LAMP as a direct optimal transport solver in a more performant parameter regime, providing a last-iterate sub-optimality certificate dependent on infeasibility and an explicit $O(1/t)$ term. Moreover, we give a computable sufficient condition for best-iterate convergence to a saddle-point. Numerical experiments with an optimized CUDA implementation show that LAMP outperforms first-order baselines in several high-accuracy (entropic) optimal transport problems. LAMP is further shown to scale up to problems with $n=m=2^{18}$ marginal supports, which were previously beyond the reach of primal-dual first-order methods.

Dongkun Zhang, Jiaming Liang, Ke Guo et al.

Trajectory planning is vital for autonomous driving, ensuring safe and efficient navigation in complex environments. While recent learning-based methods, particularly reinforcement learning (RL), have shown promise in specific scenarios, RL planners struggle with training inefficiencies and managing large-scale, real-world driving scenarios. In this paper, we introduce \textbf{CarPlanner}, a \textbf{C}onsistent \textbf{a}uto-\textbf{r}egressive \textbf{Planner} that uses RL to generate multi-modal trajectories. The auto-regressive structure enables efficient large-scale RL training, while the incorporation of consistency ensures stable policy learning by maintaining coherent temporal consistency across time steps. Moreover, CarPlanner employs a generation-selection framework with an expert-guided reward function and an invariant-view module, simplifying RL training and enhancing policy performance. Extensive analysis demonstrates that our proposed RL framework effectively addresses the challenges of training efficiency and performance enhancement, positioning CarPlanner as a promising solution for trajectory planning in autonomous driving. To the best of our knowledge, we are the first to demonstrate that the RL-based planner can surpass both IL- and rule-based state-of-the-arts (SOTAs) on the challenging large-scale real-world dataset nuPlan. Our proposed CarPlanner surpasses RL-, IL-, and rule-based SOTA approaches within this demanding dataset.