Tian Lan

Zuyuan Zhang, Zeyu Fang, Tian Lan

Geometric properties can be leveraged to stabilize and speed reinforcement learning. Existing examples include encoding symmetry structure, geometry-aware data augmentation, and enforcing structural restrictions. In this paper, we take a novel view of RL through the lens of order theory and recast value function estimates into learning a desired poset (partially ordered set). We propose \emph{GCR-RL} (Geometric Coherence Regularized Reinforcement Learning) that computes a sequence of super-poset refinements -- by refining posets in previous steps and learning additional order relationships from temporal difference signals -- thus ensuring geometric coherence across the sequence of posets underpinning the learned value functions. Two novel algorithms by Q-learning and by actor--critic are developed to efficiently realize these super-poset refinements. Their theoretical properties and convergence rates are analyzed. We empirically evaluate GCR-RL in a range of tasks and demonstrate significant improvements in sample efficiency and stable performance over strong baselines.

Sizhe Tang, Rongqian Chen, Tian Lan

While scaling test-time compute through trajectory-level sampling has significantly improved Graphical User Interface (GUI) agents, the lack of regressive ability prevents the reuse of partial successes and the recovery from early missteps. In this paper, we introduce Agent Alpha, a unified framework that synergizes generation, exploration, and evaluation through step-level Monte Carlo Tree Search (MCTS). It enables active modeling or exploiting structures of the planning space. By integrating alpha-UCT guided search into the interaction loop, Agent Alpha enables deliberate planning, facilitating early pruning of suboptimal branches and efficient prefix reuse. We also employ comparison-driven evaluation to mitigate absolute scoring biases and diversity-constrained expansion to maintain a compact, informative search space. Regret bound of alpha-UCT is analyzed. On the OSWorld benchmark, Agent Alpha achieves a state-of-the-art success rate of $\sim 77\%$, significantly outperforming trajectory-level baselines under equivalent compute.

Zeyu Fang, Zuyuan Zhang, Mahdi Imani et al.

Model-based offline reinforcement learning is brittle under distribution shift: policy improvement drives rollouts into state--action regions weakly supported by the dataset, where compounding model error yields severe value overestimation. We propose Manifold-Constrained Energy-based Transition Models (MC-ETM), which train conditional energy-based transition models using a manifold projection--diffusion negative sampler. MC-ETM learns a latent manifold of next states and generates near-manifold hard negatives by perturbing latent codes and running Langevin dynamics in latent space with the learned conditional energy, sharpening the energy landscape around the dataset support and improving sensitivity to subtle out-of-distribution deviations. For policy optimization, the learned energy provides a single reliability signal: rollouts are truncated when the minimum energy over sampled next states exceeds a threshold, and Bellman backups are stabilized via pessimistic penalties based on Q-value-level dispersion across energy-guided samples. We formalize MC-ETM through a hybrid pessimistic MDP formulation and derive a conservative performance bound separating in-support evaluation error from truncation risk. Empirically, MC-ETM improves multi-step dynamics fidelity and yields higher normalized returns on standard offline control benchmarks, particularly under irregular dynamics and sparse data coverage.