arXiv research

New algorithm achieves both static and dynamic regret optimally against an oblivious adversary for deterministic losses.

Reduces dynamic regret to static problem in RKHS.

Recursive least-squares algorithms often use forgetting factors as a heuristic to adapt to non-stationary data streams. The first contribution of this paper rigorously characterizes the effect of forgetting factors for a class of online Newton algorithms. For exp-concave and strongly convex objectives, the algorithms a…

Optimizes nonconvex optimization by converting it to static regret minimization.

In online learning, the dynamic regret metric chooses the reference (optimal) solution that may change over time, while the typical (static) regret metric assumes the reference solution to be constant over the whole time horizon. The dynamic regret metric is particularly interesting for applications such as online reco…

Dynamic regret minimization is shown equivalent to static regret minimization for linear losses.

We propose algorithms for online principal component analysis (PCA) and variance minimization for adaptive settings. Previous literature has focused on upper bounding the static adversarial regret, whose comparator is the optimal fixed action in hindsight. However, static regret is not an appropriate metric when the un…

Optimal switching regret for all segmentations in online convex optimisation.

The paper tackles minimax optimality in continuum contextual bandits with Hölder continuity.

Dynamic pricing improves DeFi lending efficiency by reducing regret to logarithmic levels.

New algorithms reduce dynamic regret in non-stationary RL environments.

New algorithm reduces constraint violation to $O(T^{1/3})$ while maintaining $O(\sqrt{T})$ regret.

Online learning is a powerful tool for analyzing iterative algorithms. However, the classic adversarial setup sometimes fails to capture certain regularity in online problems in practice. Motivated by this, we establish a new setup, called Continuous Online Learning (COL), where the gradient of online loss function cha…

Study of 3D vacuum static spaces with specific curvature properties.

We construct infinite-dimensional families of non-singular static space times, solutions of the vacuum Einstein-Maxwell equations with a negative cosmological constant. The families include an infinite-dimensional family of solutions with the usual AdS conformal structure at conformal infinity.

We construct a large class of new singularity-free static Lorentzian four-dimensional solutions of the vacuum Einstein equations with a negative cosmological constant. The new families of metrics contain space-times with, or without, black hole regions. Two uniqueness results are also established.

The paper proves conjectures and classifies metrics on 3D manifolds.

To deal with changing environments, a new performance measure -- adaptive regret, defined as the maximum static regret over any interval, was proposed in online learning. Under the setting of online convex optimization, several algorithms have been successfully developed to minimize the adaptive regret. However, existi…

We show that the recent work of Lee [23] implies existence of a large class of new singularity-free strictly static Lorentzian vacuum solutions of the Einstein equations with a negative cosmological constant. This holds in all space-time dimensions greater than or equal to four, and leads both to strictly static soluti…

In this paper, we study short-time existence of static flow on complete noncompact asymptotically static manifolds from the point of view that the stationary points of the evolution equations can be interpreted as static solutions of the Einstein vacuum equations with negative cosmological constant. For a static vacuum…

A new metric, Weighted Regret, unifies FDR and power evaluation in online multiple testing.

Near-logarithmic regret per switch achieved for mixable/exp-concave losses.

New black hole solutions with positive and negative masses in 4 and 5 dimensions.

New approach reduces unconstrained linear bandits to simpler optimization problems.

We consider a multi-armed bandit problem in a setting where each arm produces a noisy reward realization which depends on an observable random covariate. As opposed to the traditional static multi-armed bandit problem, this setting allows for dynamically changing rewards that better describe applications where side inf…

Alternative proof for static black hole uniqueness with nonpositive mass.

Paper proposes algorithms to minimize both dynamic and adaptive regret simultaneously.

In this paper we propose and discuss a notion of mass for compact static metrics with positive cosmological constant. As a consequence, we characterise the de Sitter solution as the only static vacuum metric with zero mass. Finally, we show how to adapt our analysis to the case of negative cosmological constant, leadin…

Paper derives formulas for static Einstein spaces, linking Neumann data to stability.

We study stochastic multi-armed bandits with many players. The players do not know the number of players, cannot communicate with each other and if multiple players select a common arm they collide and none of them receive any reward. We consider the static scenario, where the number of players remains fixed, and the d…

We prove existence of large families of solutions of Einstein-complex scalar field equations with a negative cosmological constant, with a stationary or static metric and a time-periodic complex scalar field.

New static black hole uniqueness theorems for negative cosmological constant.

We prove that an $(n+1)$-dimensional spin static vacuum with negative cosmological constant whose null infinity has a boundary admitting a non-trivial Killing spinor field is the AdS spacetime. As a consequence, we generalize previous uniqueness results by X. Wang \cite{Wa2} and by Chru{ś}ciel-Herzlich \cite{CH} and in…

We show that Wang's proof of uniqueness of Anti-de Sitter spacetime can be adapted to provide uniqueness results for strictly static asymptotically locally hyperbolic vacuum metrics with toroidal infinity, and to prove negativity of the free energy $E-TS$ of asymptotically AdS black holes with higher-genus horizons.

We provide a general Böchner type formula which enables us to prove some rigidity results for $V$-static spaces. In particular, we show that an $n$-dimensional positive static triple with connected boundary and positive scalar curvature must be isometric to the standard hemisphere, provided that the metric has zero rad…

This paper considers distributed online optimization with time-varying coupled inequality constraints. The global objective function is composed of local convex cost and regularization functions and the coupled constraint function is the sum of local convex functions. A distributed online primal-dual dynamic mirror des…

New findings on static near horizon geometries and quasi-Einstein manifolds, including rigidity results for negative cosmological constant.

Improved regret bounds for online convex optimization under stochastic and adversarial settings.

We prove two theorems, announced in hep-th/0108170, for static spacetimes that solve Einstein's equation with negative cosmological constant. The first is a general structure theorem for spacetimes obeying a certain convexity condition near infinity, analogous to the structure theorems of Cheeger and Gromoll for manifo…

In this paper, we consider the problem of prediction with expert advice in dynamic environments. We choose tracking regret as the performance metric and develop two adaptive and efficient algorithms with data-dependent tracking regret bounds. The first algorithm achieves a second-order tracking regret bound, which impr…

New analysis shows how temporal variability affects online learning performance.

New algorithm learns and unlearns from streaming data efficiently.

New method tackles online DR-submodular maximization with improved regret guarantees.

Two algorithms for linear contextual bandits with rare updates achieve optimal regret and efficiency.

In this paper, we introduce a new parabolic equation on Kähler manifolds. The static point of this flow is related to the existence of a lower bound of the Mabuchi energy. In this paper, we prove the flow always exists for all times for any initial smooth data. Further more, if the initial metric has non-negative bisec…

This paper tackles near-optimal adversarial RL with switching costs, providing algorithms and matching lower bounds.

New algorithms reduce dynamic regret in online MDPs with changing losses.

New approach for distributed online optimization of non-convex losses with sublinear regret.