Reconstructing population dynamics is a central problem in the physical and data sciences. Often, the dynamics are modeled as a Wasserstein gradient flow (WGF): a curve of distributions driven by an energy functional. Though there are multiple mathematical characterizations of a WGF, the dominant algorithmic approach relies on the Jordan--Kinderlehrer--Otto (JKO) scheme. JKO-based methods are inflexible to time discretisation and require solving costly optimal transport problems. We take a residual approach, enforcing the continuity equations via a non-negative loss function whose minimum is the WGF. Combined with a data-fitting divergence, this gives a single global objective. This perspective unifies several existing methods and leads to a new particle-based method, stitching, that is simulation-free and robust to large gaps between observations. We demonstrate that the stitching method achieves state-of-the-art performance across trajectory inference benchmarks. For code see github.com/BasisResearch/wasserstein-residuals.
We study stochastic multi-armed bandits on dynamic graphs, where arms correspond to the vertices of a network with time-varying edges. In this setting, the learner is restricted to local movement, selecting only its current node or an immediate neighbor at each round. This constr…
Sepsis is a leading cause of mortality, yet optimal treatment policies remain contested. Existing reinforcement learning (RL) approaches learn fixed strategies for sepsis treatment, limiting adaptability to changing clinical objectives during inference. We propose EHRMPC, a frame…
As AI-driven Decision Makers (ADMs) influence our socioeconomic reality, their roles in both enhancing efficiency and amplifying the social biases have drawn attention. In this paper, we revisit the nuances of long-term `fairness' achievable by an ADM, specifically in the context…
The Continual Learning (CL) literature has long been driven by the goal of mitigating catastrophic forgetting. This objective rests on a pervasive, often unstated assumption: that a lifelong learner should approximate the Joint-Task Learning (JTL) solution and retain all previous…
Outlier detection (OD) aims to identify anomalous instances by learning the underlying structure of normal data (inliers), and is particularly challenging in fully unsupervised settings where no information about anomalies is available during training. Recent advances have levera…
Active Inference (AIF) frames adaptive behavior as the minimization of expected free energy (EFE), combining epistemic and pragmatic objectives within a single variational principle. We frame AIF as policy optimization and show that, for closed-loop control policies, EFE minimiza…