Dynamical Models and Tracking Regret in Online Convex Programming
This work addresses the challenge of handling highly variable comparator sequences in nonstationary settings for applications like dynamic scene analysis and social network tracking, representing an incremental improvement over existing methods.
The paper tackles the problem of online convex optimization in nonstationary environments by proposing a Dynamic Mirror Descent method that incorporates candidate dynamical models, achieving tracking regret bounds that scale with the comparator's deviation from the best model, as demonstrated empirically in dynamic scene observation and social network tracking.
This paper describes a new online convex optimization method which incorporates a family of candidate dynamical models and establishes novel tracking regret bounds that scale with the comparator's deviation from the best dynamical model in this family. Previous online optimization methods are designed to have a total accumulated loss comparable to that of the best comparator sequence, and existing tracking or shifting regret bounds scale with the overall variation of the comparator sequence. In many practical scenarios, however, the environment is nonstationary and comparator sequences with small variation are quite weak, resulting in large losses. The proposed Dynamic Mirror Descent method, in contrast, can yield low regret relative to highly variable comparator sequences by both tracking the best dynamical model and forming predictions based on that model. This concept is demonstrated empirically in the context of sequential compressive observations of a dynamic scene and tracking a dynamic social network.