Research map / Reinforcement learning / Policy gradient and actor-critic

A Differential and Pointwise Control Approach to Reinforcement Learning

NeurIPS 2025 · Reinforcement learning › Policy gradient and actor-critic · approach: Model-based RL with guarantees · 0 citations (OpenAlex)

Read the paperCheck your idea against 108,967 papers

AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.

Proposes Differential RL, reformulating RL via a differential dual (Pontryagin/Hamiltonian) view, and dfPO, a stage-wise pointwise policy optimization algorithm with claimed convergence and O(K^{5/6}) regret, evaluated on surface modeling, grid control, and molecular dynamics against 12 RL baselines.

Problem

RL in continuous state-action scientific computing suffers from poor sample efficiency, lack of pathwise physical consistency, and weak theoretical guarantees, especially when rewards are only available along explored trajectories and no re-planning is allowed.

Approach

Reformulate RL as a continuous-time optimal control problem with a Hamiltonian (symplectic) differential dual, learn a discrete dynamics operator G = Id + Δt S∇g via a learned score function g over the extended state-adjoint space, and train it stage-wise with pointwise error guarantees.

Key results

• dfPO achieves final cost 6.32 on surface modeling, vs 6.42 for best baseline CrossQ and 6.48 for TRPO (lower is better).
• dfPO achieves 6.06 on grid control vs 6.58 for DDPG (best baseline).
• dfPO achieves 53.34 on molecular dynamics vs 68.20 for DDPG reward-shaped variant and 76.87 for TQC variant.

Measured effects reported in the paper

Surprising findings

• Standard PPO and TRPO with negative-energy rewards are stuck near 1842 on molecular dynamics, while several baselines reach far lower costs.
• Plain TRPO (6.48) is nearly tied with CrossQ on surface modeling, so the margin over the strongest baseline is small there (6.32 vs 6.42).

Limitations

• Theoretical guarantees rely on strong assumptions (Lipschitz dynamics, weakly convex and linearly bounded hypothesis classes) and the Ω(K) constants are not fully explicit.
• Experiments are limited to three tasks with single runs and small margins over some baselines (e.g. surface 6.32 vs 6.42), with no variance or significance reported.
• Regret analysis assumes a fixed small horizon H and the paper itself notes trajectories on surface and molecular tasks are not always smooth.

Experimental setup

Datasets: simulated surface modeling environment (random polygon initial shapes) grid-based PDE control environment (uniform initial coarse grids) octa-alanine molecular dynamics with PyRosetta energy

Benchmarks: surface modeling cost grid control cost octa-alanine molecular dynamics energy

Metrics: final mean evaluation cost F(s) at terminal step

Baselines: TRPO PPO DDPG SAC CrossQ TQC

Builds on: Pontryagin's Maximum Principle TRPO PPO SAC

Closest papers by meaning

• Sample-efficient and Scalable Exploration in Continuous-Time RL (ICLR 2026 · similarity 0.88)
• Diffusion Policy Policy Optimization (ICLR 2025 · similarity 0.87)
• Geometric Active Exploration in Markov Decision Processes: the Benefit of Abstraction (ICML 2024 · similarity 0.87)
• Parameter Exploration for RLVR via Variational Learning (NeurIPS 2026 · similarity 0.87)
• Stabilizing Reinforcement Learning in Differentiable Multiphysics Simulation (ICLR 2025 · similarity 0.86)
• OCEAN-MBRL: Offline Conservative Exploration for Model-Based Offline Reinforcement Learning (AAAI 2024 · similarity 0.86)