The paper presents a quasipolynomial-time algorithm for finding an ε-approximate fixed point of any d-dimensional nonexpansion under the λ∞ norm, running in time −log(1/ε)^{O(log^2 d)}. The method relies on a boosting argument that geometrically shrinks the search region. As a consequence, the algorithm shows that simple stochastic games can be solved in quasipolynomial time.
arXiv:2609. 20701v1 Announce Type: cross Abstract: We study efficient algorithms for realizing the first-order oracle complexity of optimization of $G$-Lipschitz convex functions with respect to the $\ell_{q}$-norm over an $\ell_{p}$-ball of radius $R$, where $1\leq p,q\leq \infty$.
We study efficient algorithms for realizing the first-order oracle complexity of optimization of $G$-Lipschitz convex functions with respect to the $\ell_{q}$-norm over an $\ell_{p}$-ball of radius $R$, where $1\leq p,q\leq \infty$. For $p<q$, we obtain error $\widetilde{O}_{p,q}(GR/T^{1/p-(1/q-1/2)_{+}})$ after $T$ oracle queries, efficiently realizing the nearly optimal rates of (MBG+26), thereby resolving the nonsmooth end of the COLT 2015 open problem (Guz15b).
arXiv:2605.29748v2 Announce Type: replace Abstract: We study the Lipschitz bandit problem, where a learner sequentially maximizes an unknown Lipschitz function $f$ over a domain $\mathcal{X} \subset...
arXiv:2604. 00523v2 Announce Type: replace Abstract: We study for the first time, stochastic dueling bandits over continuous action spaces with Lipschitz structure, where feedback is purely comparative.
arXiv:2608.24731v1 Announce Type: new Abstract: We settle the minimax-optimal alternating regret, a regret notion motivated by alternating learning dynamics in games, for both online linear optimizat...
arXiv:2609.15257v1 Announce Type: cross Abstract: We analyze a stochastic algorithm with Halpern anchoring for constrained convex-concave problems and monotone variational inequalities. This algorith...
arXiv:2609. 23837v1 Announce Type: cross Abstract: We study the complexity of finding $(\delta,\epsilon)$-Goldstein stationary points of nonsmooth nonconvex Lipschitz functions.
arXiv:2608. 12231v2 Announce Type: replace Abstract: We study adversarial combinatorial bandits with $m$-set actions, where at each round the learner selects $m$ out of $d$ items and observes only the aggregate loss of the selected items.
arXiv:2610. 36097v1 Announce Type: cross Abstract: We study full-information online linear optimisation on the unit $\ell_p$ ball in $\mathbb{R}^d$, for fixed $2\le p<\infty$ and losses of dual norm at most one.
arXiv:2607. 10963v1 Announce Type: cross Abstract: We study the problem of efficient online proportional sampling from a high-dimensional domain under a $\sigma$-smoothed adversary, where the sampling distribution is induced by a dynamically evolving weight function defined over a sequence of piecewise-structured partitions.
arXiv:2406. 13668v4 Announce Type: replace Abstract: A set of probabilistic forecasts is calibrated if each prediction of the forecaster closely approximates the empirical distribution of outcomes on the subset of timesteps where that prediction was made.
arXiv:2608. 25182v1 Announce Type: cross Abstract: In this paper, we study alternating regret in online convex optimization (OCO), motivated by the success of alternating learning dynamics in two-player games.