We study online convex optimization with dueling (pairwise comparison) feedback, where the learner observes only a binary preference between two queried points. While dueling feedback is well understood in discrete or stochastic settings, the adversarial convex setting has remained unexplored. We propose a simple reduction that converts dueling feedback into approximate gradients, enabling the use of standard first-order methods. We show that regret guarantees transfer under this reduction, yielding the first results for this setting, including $\mathcal{O}(T^{3/4})$ static, adaptive, and dynamic regret. Under additional structure, we obtain improved rates of $\mathcal{O}(T^{2/3})$ for smooth objectives and $\mathcal{O}(\sqrt{T \log T})$ for strongly convex functions.
Yiyang Lu, Hareshkumar Jadav, M. Pedramfar et al.· 0 citations
The main result is an adversarial resilience theorem for the Spiteful Greedy Swap Poisson Process (SGS-Poisson): without modifying its Poisson intensity, single-element exchange rule, or spiteful drop step, the algorithm retains limiting approximation factors for non-monotone objectives and $1-1/e for monotone objectives.
HT-PAder is proposed, a parameter-free algorithm combining restarted AdaGrad experts over a geometric pool of block lengths with a pathwise meta-algorithm, which requires no moment conditions on meta-losses and provides the first parameter-free minimax universal dynamic regret guarantee.