Offline Reinforcement Learning for Fluid Controls: Data-based Multi-observational Policy Extraction

Active flow control involves nonlinear dynamics, partial observations, and computationally expensive simulations, making controller design particularly challenging. Deep reinforcement learning (DRL) has emerged as a powerful framework for such problems, but its success typically relies on large numbers of simulator interactions and produces neural-network policies whose decision process often remains difficult to interpret. In this work, we investigate a different paradigm: instead of optimizing neural-network parameters, we use modern coding agents to search directly for explicit executable feedback laws. We introduce a constrained heuristic-learning protocol in which an agent iteratively proposes, evaluates, and revises controller implementations while interacting exclusively through the public benchmark interface. The proposed framework is evaluated on 13 active flow-control benchmarks spanning one, two, and three-dimensional problems and compared against the strongest available DRL baselines under identical simulation budgets. The discovered heuristic controllers match or outperform the best DRL policy in 10 of the 13 environments while remaining compact, interpretable, and directly inspectable. Beyond aggregate performance, the resulting controllers reveal physically meaningful feedback mechanisms, transfer successfully across more challenging configurations, and remain competitive under varying Reynolds and Rayleigh numbers, actuator counts, and observation sparsity. These results suggest that heuristic learning through coding agents constitutes a credible and complementary alternative to conventional reinforcement learning, combining competitive performance with physically interpretable controller representations. Prompts and source code are available at https://github.com/DonsetPG/fluid-heuristic-learning.

There is growing interest in utilizing flow-based models as decision-making policies in reinforcement learning due to their high expressive capacity. However, effectively leveraging this expressivity for value maximization remains challenging, as naive gradient-based optimization requires backpropagating through numerical solvers and often leads to instability. Existing approaches typically address this issue by restricting the expressive capacity of flow-based policies, resulting in a trade-off between optimization stability and representational flexibility. To resolve this, we introduce Q-Flow, a framework that leverages the deterministic nature of flow dynamics to explicitly propagate terminal trajectory value to intermediate latent states along the policy-induced flow. This formulation enables stable policy optimization using intermediate value gradients without unrolling the numerical solver, effectively bridging the gap between stability and expressivity. We evaluate Q-Flow in the offline learning setting on the challenging OGBench suite, where it consistently outperforms state-of-the-art baselines by an average of 10.6 percentage points, while also enabling stable online adaptation within the same framework.

Recent advances in flow-based offline reinforcement learning (RL) have achieved strong performance by parameterizing policies via flow matching. However, they still face critical trade-offs among expressiveness, optimality, and efficiency. In particular, existing flow policies interpret the $L_2$ regularization as an upper bound of the 2-Wasserstein distance ($W_2$), which can be problematic in offline settings. This issue stems from a fundamental geometric mismatch: the behavioral policy manifold is inherently anisotropic, whereas the $L_2$ (or upper bound of $W_2$) regularization is isotropic and density-insensitive, leading to systematically misaligned optimization directions. To address this, we revisit offline RL from a geometric perspective and show that policy refinement can be formulated as a local transport map: an initial flow policy augmented by a residual displacement. By analyzing the induced density transformation, we derive a local quadratic approximation of the KL-constrained objective governed by the Fisher information matrix, enabling a tractable anisotropic optimization formulation. By leveraging the score function embedded in the flow velocity, we obtain a corresponding quadratic constraint for efficient optimization. Our results reveal that the optimality gap in prior methods arises from their isotropic approximation. In contrast, our framework achieves a controllable approximation error within a provable neighborhood of the optimal solution. Extensive experiments demonstrate state-of-the-art performance across diverse offline RL benchmarks. See project page: https://github.com/ARC0127/Fisher-Decorator.