Rethinking Learnability in Offline Data-driven Optimization

Black-Box Optimization (BBO) has found broad applications, but evolutionary algorithms and Bayesian optimization face efficiency challenges as real-world BBO problems grow increasingly complex. Data-driven optimization improves the efficiency of BBO algorithms by learning from data. Offline data-driven optimization seeks high-quality solutions using only a fixed set of previous evaluations, attracting substantial attention because it requires no additional online evaluations. Many offline optimization methods have been proposed, but a fundamental question remains unanswered: what learnability is sufficient for offline optimization? Prior theoretical studies show that Probably Approximately Correct (PAC) learnability is insufficient, as the optimal region may remain poorly learned even when most regions are well learned. In this paper, we propose algorithm-dependent learnability, which requires accuracy only on the optimizer's trajectory. We prove that its value-query form is sufficient for representative discrete settings, including greedy and local search for submodular maximization, while its first-order analogue is sufficient for projected gradient descent on convex minimization. Motivated by this notion, we formalize a trajectory-learning framework comprising trajectory construction, trajectory modeling, and candidate generation, and analyze existing trajectory-based methods under it. We further propose Uncertainty-aware Gradient-guided Trajectory Learning (UGTL), which constructs locally coherent improvement trajectories reflecting plausible search paths, models them with conditional diffusion, and selects a diverse candidate set. On five Design-Bench tasks, UGTL achieves the best aggregate mean rank, $3.1/25$, among 25 methods. Controlled trajectory analyses and cross-architecture replacements confirm that our trajectory construction plays a significant role in the improvement.

From Final Artifacts to Trajectories: Retrospective Process Supervision for Evidence-Grounded Long-Form Generation

Trajectory data is getting more vital for training large language models for boosting the agentic abilities. Unlike the verifiable domains such as coding or mathematics, scaling trajectory data for open-ended tasks is much more difficult because these tasks lack singular ground truth and are costly to annotate or verify. In this paper, we propose RetroGen, a self-improving framework of retrospective process supervision. Our key observation is that although expert trajectories are scarce, high-quality final artifacts such as literature reviews, analyst reports and legal judgments, are abundant in pre-training data and can be viewed as compressed traces of the evidence-seeking processes that produced them. RetroGen reconstructs candidate latent trajectories from expert artifacts, verifies them against both the artifact and supporting evidence, and trains models on their own successful reconstruction data, without requiring trajectory data from stronger models. Experiments show that RetroGen improves grounding, faithful synthesis, and long-form evidence-seeking agent tasks.

MeanSR: Restoration Trajectory Learning for One-Step Perceptual Super-Resolution

Diffusion-based super-resolution (SR) achieves strong perceptual quality but requires costly iterative denoising. Existing one-step distillation methods reduce inference time but depend on expensive pretrained teachers, whereas CTMSR avoids distillation through PF-ODE consistency training yet does not explicitly model the restoration dynamics from low-resolution (LR) inputs to high-resolution (HR) images. We propose MeanSR, a one-step perceptual SR method that learns an LR-conditioned average velocity field to directly capture the finite-time transition from degraded or noisy inputs to plausible HR outputs. We further reformulate distribution trajectory matching for average-velocity generation and introduce a Stage-Aware Temporal Sampling strategy to improve trajectory learning. Experiments on synthetic and real-world benchmarks show that MeanSR outperforms CTMSR on CLIPIQA, MUSIQ, and MANIQA while substantially reducing FLOPs and inference latency. MeanSR also reconstructs sharper structures and more realistic textures with fewer perceptual artifacts.

Robot Learning from Human Demonstrations: Handwritten Alphabet Trajectories and Human-Likeness Evaluation

Learning from demonstration (LfD) provides a developmental framework through which robots can develop motor skills by observing and imitating human dynamics, reducing reliance on explicit programming to teach a skill to a robot. The resulting human-like robot motion is recognised as a key factor in building trust and enabling natural collaboration in human-robot interaction. This paper presents a framework for learning human-like robot motion from demonstration, including data collection, probabilistic trajectory learning, and perceptual user evaluation. A dataset of 3,142 handwriting demonstrations was collected from 22 participants across all 52 Latin alphabet character-case combinations via a touchscreen teleoperation interface, capturing planar position, contact force, and timing. Building on the widely used Gaussian Mixture Model and Gaussian Mixture Regression approach for learning from demonstration, the framework is extended in this work by incorporating force and normalised time dimensions to enable richer representation of human dynamics, and adapting it to handle non-continuous, multi-segment trajectories, enabling generalisation across demonstrations. A user study with 21 participants evaluated the perceived human-likeness of the generated trajectories using a continuous scale anchored between robotic and human-like motion, normalised to 0-100 where 50 represents the neutral midpoint. The generated trajectories achieved an overall human-likeness score of 71.50 (SD=22.56), indicating that the majority of trajectories were perceived as more human-like. Participants identified geometric positioning and trajectory sequence as the most influential perceptual factors, and reported positive attitudes toward human-like robot behaviour. The datasets are released as open-source, providing a reproducible benchmark for developing and evaluating human-like robot motion methods.