SDE approximation for TD learning with linear features under Markovian noise
A new arXiv preprint replaces the classical ODE description of linear TD(0) learning with a stochastic differential equation (SDE) approximation that accounts for Markovian sampling noise. The model separates contraction dynamics governed by the projected Bellman operator from the influence of Markovian long-run covariance, providing a theoretical explanation for the constant-stepsize error floor. The work is a theoretical contribution to the foundations of reinforcement learning policy evaluation.
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Kolmogorov Regression lifts diffusion policies to Cameron-Martin space for robust long-horizon control
Researchers introduce a backward Kolmogorov equation framework that reformulates diffusion policy training as a deterministic boundary-value PDE problem in Cameron-Martin space, replacing stochastic score matching. The approach uses a precision-weighted Cameron-Martin loss and a Kolmogorov residual as an inference-time failure detector, yielding convergence guarantees tied to kernel effective rank rather than action dimension. Validation on the PushT manipulation benchmark shows 17% improvement in episode reward and 67.6% reduction in inter-step drift; a 6-station manufacturing scheduling task shows 28.4% lower RMSE than LSTM baselines and 96% reduction in deadlock events via Hamilton-Jacobi reachability certification.
RL without TD Learning: Divide-and-Conquer Value Learning for Long-Horizon Off-Policy RL
A BAIR blog post introduces a divide-and-conquer paradigm for off-policy reinforcement learning that avoids temporal difference (TD) learning's error accumulation problem by reducing Bellman recursions logarithmically rather than linearly. The approach leverages the triangle inequality structure of goal-conditioned RL to define a transitive Bellman update rule, enabling value learning that scales to long-horizon tasks. The authors claim this is the first practical realization of divide-and-conquer value learning at scale in goal-conditioned RL settings, building on an idea traceable to Kaelbling (1993). The post frames this as a third paradigm alongside TD and Monte Carlo methods, addressing a key gap in scalable off-policy RL.
Finetune Stable Diffusion Models with DDPO via TRL
Hugging Face's TRL library adds support for DDPO (Denoising Diffusion Policy Optimization), enabling reinforcement learning-based finetuning of Stable Diffusion models. This extends TRL's RLHF tooling beyond language models to image generation, allowing reward-driven optimization of diffusion models. The post demonstrates practical usage of the new DDPO trainer within the TRL ecosystem.
PTL-Diffusion: Diffusion framework with periodic terminal laws for manifold-aware generation
PTL-Diffusion is a new diffusion modeling framework that replaces the standard single Gaussian terminal distribution with a periodic family of Gaussian terminal laws, embedding phase structure directly into the forward noising dynamics rather than only in the denoising network. The authors derive closed-form forward marginals and reverse posteriors for a periodically forced Ornstein-Uhlenbeck process, enabling standard noise-prediction training. Experiments on torus, cylinder, and face datasets show improvements in manifold-level distributional matching over DDPM baselines. The work is a proof-of-concept motivating structured terminal reference laws as a direction for geometry-aware generative modeling.
Analysis of on-policy distillation reveals sparse, geometrically structured parameter updates
A new arXiv paper analyzes on-policy distillation (OPD) — a post-training method combining on-policy student trajectories with dense teacher supervision — across language and vision-language model pairs. The authors find that OPD updates are coordinate-sparse and distributed across layers (FFN-heavy), and that training only the discovered sparse subnetwork recovers near-full performance. Geometrically, updates are numerically full-rank but spectrally concentrated, falling disproportionately on near-zero weight coordinates, suggesting OPD retains distinct geometric signatures rather than behaving like ordinary dense parameter rewriting.
Second-order path kernel interpolation formulas extend Domingos' gradient-descent characterization
This paper extends Pedro Domingos' 2020 first-order path-kernel interpolation formula for gradient-descent-trained models to second-order forms. The authors derive curvature-weighted correction terms for standard SGD, an additional sampling-induced component coupling prediction curvature with mini-batch gradient noise covariance, and an extension to SGD with momentum. A concentration estimate for the terminal prediction is also established, quantifying fluctuation around the expected second-order representation.
Perturbation Theory for Spherical Hellinger-Kantorovich Flows with Differential Privacy Guarantees
This paper develops a perturbation theory for Spherical Hellinger-Kantorovich (SHK) gradient flows, which couple transport and reaction dynamics and coincide with birth-death Langevin dynamics. The authors derive dimension-free bounds on log-likelihood ratios and Rényi/KL divergences when two potentials differ, quantifying how perturbations propagate over time. These results are applied to differential privacy: the likelihood-ratio control yields explicit Pure-DP guarantees for SHK-based samplers implementing the exponential mechanism, while KL bounds provide Approximate-DP certificates. A utility bound is also derived that separates intrinsic exponential-mechanism suboptimality from finite-time sampling error.
d-OPSD: First on-policy self-distillation framework tailored for diffusion LLMs
Researchers introduce d-OPSD, the first on-policy self-distillation (OPSD) framework designed specifically for diffusion large language models (dLLMs). The method addresses a fundamental mismatch between existing autoregressive OPSD approaches and dLLMs' arbitrary-order generation by using suffix conditioning on self-generated answers and step-level rather than token-level divergence supervision. Across four reasoning benchmarks, d-OPSD outperforms RLVR and SFT baselines while requiring only ~10% of the optimization steps of RLVR, suggesting strong sample efficiency gains for dLLM post-training.