Active Timepoint Selection for Learning Measure-Valued Trajectories

The effectiveness of active learning hinges on the choice of the acquisition criterion by which a learning algorithm selects potentially informative data points whose label is subsequently queried. This paper proposes a novel gradient-based acquisition criterion, derived from a generalization bound introduced by Luo et al. (2022). This criterion can be applied in lieu of uncertainty measures in uncertainty sampling, or incorporated into diversity-based methods that consider the spread of sampled points in addition to the uncertainty of their labels. We provide a theoretical justification of the proposed acquisition criterion, and demonstrate its effectiveness in an empirical evaluation.

Active feature acquisition (AFA) considers prediction problems in which features are costly to obtain and the learner adaptively decides which feature values to acquire for each instance and when to stop and predict. AFA can be formulated as a partially observable Markov decision process (POMDP), which naturally admits a sequential decision-making perspective. In this paper, we present non-myopic pathwise policy gradients (NM-PPG), a new AFA method built around this formulation. We introduce a continuous relaxation of the acquisition process that enables pathwise gradients through the full acquisition trajectory, avoiding the high variance of standard score-function policy gradients while allowing end-to-end optimization of a non-myopic acquisition policy. To better align training with deployment, we further develop a straight-through rollout scheme that follows hard feature acquisitions in the forward pass while backpropagating through the corresponding soft relaxation in the backward pass. We stabilize optimization with entropy regularization and staged temperature sharpening. Experiments on both synthetic and real-world datasets demonstrate that NM-PPG yields superior performance relative to state-of-the-art AFA baselines.

Online residual learning can reduce model mismatch in predictive control, but passive data collection may fail to adequately cover states that become important later in the task. Task-agnostic active learning targets uncertain or informative regions, but information acquired in such regions does not necessarily improve task performance. This paper introduces Task-Oriented Information Acquisition (ToIA), an active-learning criterion for model predictive path integral control (MPPI) with online Gaussian process (GP) residual learning. For each sampled control sequence, ToIA estimates how much an observation obtained early in the rollout would reduce predictive uncertainty at later states on the same rollout, and weights this reduction by the rollout's relevance to the task. The score is evaluated over the existing MPPI rollout batch without sampling future observations or re-optimizing control under hypothetical posterior updates. In simulated off-road navigation across held-out maps with heterogeneous terrain, ToIA improved the goal-reaching success rate over passive GP learning by 19.3 and 27.4 percentage points and outperformed task-agnostic active-learning baselines across dense and sparse online-learning intervals. An ablation study indicates that task relevance is particularly important under sparse model updates. The implementation supports online control at 20 Hz on an NVIDIA RTX 2080 Ti.