arXiv AI

Learning When to Refine: Long-Horizon Reinforcement Learning for Budgeted Neural-Operator PDE Solvers

The paper introduces a budgeted adaptive neural‑operator framework for solving time‑dependent PDEs, combining a global Fourier neural operator with a local patch‑wise residual corrector and a set‑aware selector that decides where to refine. A macro policy governs the timing and amount of refinement, and the authors propose rollout‑verified policy improvement (RV‑PI) to evaluate feasible refinement counts via actual rollouts, converting long‑horizon advantages into conservative policy targets and accepting updates only when held‑out trajectory error improves. Experiments on shallow‑water and Brusselator benchmarks show that RV‑PI outperforms immediate‑only and random macro policies, demonstrating that the value of a local correction depends on its downstream effect rather than just its immediate error reduction.

arXiv Machine Learning
3d ago

Transferability of Learned States in Neural PDE Solvers

The paper introduces a framework for evaluating how well learned states from neural PDE solvers can be reused in new contexts. By separating solution accuracy, learning contribution, and numerical utility through paired state comparisons and cost accounting, the authors audit 12 papers and conduct experiments on linear PDE families, Fourier neural operators, and convolutional networks. Their results show that matched state comparisons and downstream computational evidence can lead to significant savings in conjugate‑gradient iterations and demonstrate finite‑budget pretraining value.

By Shunye Wang, Haochen Wen, Shuo Li Liu, Xuanyi Wang, Lihao Liu, Zhongying Deng
arXiv AI
Jun 26

Error-Conditioned Neural Solvers

arXiv:2606. 27354v1 Announce Type: cross Abstract: Neural surrogate models offer fast approximate mappings from PDE parameters to solutions, but they typically treat solving as a purely statistical task: once trained, they struggle to correct their own constraint violations and extrapolate beyond the training distribution.

By Haina Jiang, Liam Wang, Peng-Chen Chen, Min Seop Kwak, Seungryong Kim, Brian Bell, Jeong Joon Park
arXiv Machine Learning
Sep 14

MInTRL: Off-policy Intervention can boost On-policy RL

MInTRL (Minimal Intervention Reinforcement Learning) expands exploration in on-policy reinforcement learning by inserting sparse, local corrections into rollouts via a judge-intervention policy. These interventions replace erroneous suffixes and immediately return control to the main policy, allowing the agent to explore beyond its natural trajectory while maintaining on-policy data. The method uses a sequence-level advantage-regression objective, avoiding importance sampling, and demonstrates superior performance on math and code benchmarks compared to standard on-policy and off-policy baselines.

By Mingyu Chen, Yefan Tao, Gerald Friedland, Xuezhou Zhang, Chris Kong
arXiv Machine Learning
4d ago

An Informational Curse of Horizon in Goal-Conditioned Policy Learning

The paper identifies an informational curse of horizon in goal-conditioned policy learning, showing that longer goal relabeling horizons during training can hurt policy generalization and performance. Controlled experiments with oracle planners separate training horizons from test horizons, revealing that behavioral cloning policies degrade with longer horizons while reinforcement learning mitigates this effect. The authors attribute this to reduced conditional mutual information between actions and hindsight-relabeled goals, and demonstrate that distilling short-horizon policy Jacobians into long-horizon policies improves performance, especially in combinatorial manipulation tasks.

By John L. Zhou, Yuxuan Dong, Jonathan C. Kao
arXiv Machine Learning
Jul 16

Where Should RL Post-Training Compute Go? Model Size, Search, Learning, and Feedback

arXiv:2607. 13389v1 Announce Type: new Abstract: Reinforcement Learning (RL) post-training is increasingly used to adapt foundation models for reasoning, planning, and feedback-driven robot-learning pipelines, but constrained post-training resources are often summarized by a single total FLOP budget.

By Patrick Wilhelm, Odej Kao
arXiv AI
Oct 5

When a Correct Reward Is Not Enough: Diagnosing and Guiding PPO in an Analytically Solved Broker-Trader Game

The paper investigates whether a proximal policy optimisation (PPO) agent can learn to act as a broker in a continuous‑time broker‑trader game that has an analytically solved optimal strategy. By discretising the continuous‑time reward and validating the implementation, the authors show that a PPO agent with a feed‑forward neural network can approximate the reference action when there is no uninformed order flow, but struggles under stochastic uninformed flow, with critics failing to rank actions reliably. The study further demonstrates that a causal certainty‑equivalent controller based on observable history outperforms PPO under partial information, and that freezing the analytical policy and fine‑tuning PPO after a change in execution cost yields a measurable improvement. whyItMatters:"The analytical solution serves both as a diagnostic benchmark for RL performance and as a practical starting policy that can be adapted to changing market conditions, illustrating how theoretical finance models can guide and improve reinforcement learning in complex financial control tasks."

By Siu Tung Wong (Institute of Finance and Technology, University College London), Carlo Campajola (Institute of Finance and Technology, University College London, UZH Blockchain Center)