Convex Optimization with Nested Evolving Feasible Sets (CONES) under Time-Varying Loss Functions
Updated 1 h ago · first seen 11 Sept 2026
paper_01M294FP3DG6JJ6CWS98XC1XM2
- Published
- 11 Sept 2026
- T1 · 1 h ago
- arXiv
- 2609.11207
- T1 · 1 h ago
- Category
- cs.LG
- T1 · 1 h ago
Abstract
Convex Optimization with Nested Evolving Feasible Sets (CONES)} was introduced in \cite{CONESVaze} 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). In this paper, we extend CONES to allow for loss functions $f_t'$s to also change over time. When all loss functions are convex, we show that the projected proximal algorithm achieves $O(T^{1-\beta}), O(T^\beta)$ simultaneous regret and movement cost, respectively, for any $\beta \in [0,1)$, over a time horizon of $T$. We also show that any {\it weakly adaptive} online algorithm with $O(T^\beta)$ regret has a movement cost of $\Omega\left(T^{\frac{1-\beta}{2}}\right)$ for any $\beta \in [0,1)$. When all loss functions are strongly convex, we show that the projected proximal algorithm simultaneously achieves $O(1)$ regret and a movement cost of $O(\log T)$. To complement this, we show that any online algorithm with sublinear {\it anytime} regret has a movement cost of $\Omega\left(\log T\right)$.
Authors 1
Rahul Vaze
Specification
- Official page
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
- Arxiv announce type
- new
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
- arXiv id
- 2609.11207
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
- Categories
- cs.LG, cs.DS, math.OC
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
- Primary category
- cs.LG
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
- Published
- 11 Sept 2026
Source:arXiv (Atom API + RSS)T1observed 1 h agohigh
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Attributed facts
9
Source tiers
T19
Freshest observation
1 h ago
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None
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- Authors
- Rahul Vaze
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Claims are temporal and append-only: a new observation closes the previous claim (valid_to) instead of overwriting it. Conflicting claims from different sources are kept side by side and flagged — never averaged. Methodology →
- New paperPaperConvex Optimization with Nested Evolving Feasible Sets (CONES) under Time-Varying Loss Functions
New paper: Convex Optimization with Nested Evolving Feasible Sets (CONES) under Time-Varying Loss Functions
arxiv
| Source | Document | Type | Tier | Last observed | Snapshots |
|---|---|---|---|---|---|
| arXiv (Atom API + RSS) | rss.arxiv.org/rss/cs.LG | feed | T1· Official | 1 h ago | 1 |
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