Optimization Guarantees for Square-Root Natural-Gradient Variational Inference

Variational inference with natural-gradient descent often shows fast convergence in practice, but its theoretical convergence guarantees have been challenging to establish. This is true even for the simplest cases that involve concave log-likelihoods and use a Gaussian approximation. We show that the challenge can be circumvented for such cases using a square-root parameterization for the Gaussian covariance. This approach establishes novel convergence guarantees for natural-gradient variational-Gaussian inference and its continuous-time gradient flow. Our experiments demonstrate the effectiveness of natural gradient methods and highlight their advantages over algorithms that use Euclidean or Wasserstein geometries.

Modelling the performance of delivery vehicles across urban micro-regions to accelerate the transition to cargo-bike logistics

Light goods vehicles (LGV) used extensively in the last mile of delivery are one of the leading polluters in cities. Cargo-bike logistics has been put forward as a high impact candidate for replacing LGVs, with experts estimating over half of urban van deliveries being replaceable by cargo bikes, due to their faster speeds, shorter parking times and more efficient routes across cities. By modelling the relative delivery performance of different vehicle types across urban micro-regions, machine learning can help operators evaluate the business and environmental impact of adding cargo-bikes to their fleets. In this paper, we introduce two datasets, and present initial progress in modelling urban delivery service time (e.g. cruising for parking, unloading, walking). Using Uber's H3 index to divide the cities into hexagonal cells, and aggregating OpenStreetMap tags for each cell, we show that urban context is a critical predictor of delivery performance.