Convex Optimization with Nested Evolving Feasible Sets
\emph{Convex Optimization with Nested Evolving Feasible Sets (CONES)} is considered where the objective function \(f\) remains fixed but the feasible region evolves over time as a nested sequence \(S_1 \supseteq S_2 \supseteq \cdots \supseteq S_T\). The goal of an online algorithm is to simultaneously minimize the regret with respect to hindsight static optimal benchmark and the total movement cost $M_\cA(T)$ while ensuring feasibility at all times. CONES is an optimization-oriented generalization of the well-known \emph{nested convex body chasing} (NCBC). When the loss function is convex, we propose a lazy-algorithm and show that it achieves $O(T^{1-β}), O(T^β)$ simultaneous regret and m...
| Authors | Karthick Krishna M., Haricharan Balasundaram, Rahul Vaze |
|---|---|
| Primary category | cs.LG |
| Published | 8 May 2026 |
| Last updated at source | 16 August 2026 |
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