We then propose a novel algorithm based on minimum-distance functionals in the setting where the transition model is given and the expert is deterministic.Thealgorithmissuboptimalby .|S|H3/2/N,matchingourlower

However, in terms of making the gradients small, the original SGD does not give an optimal rate, even when f(x) is convex. If f(x) is convex, to find a point with gradient norm ε, we design an algorithm SGD3withanear-optimalrate eO(ε 2),improvingthebestknownrateO(ε 8/3) of [17].

In the multi-armed bandit problem, an agent has several possible decisions, usually referred to as "arms", and chooses or "pulls" sequentially one of them at each time step. This generates a sequence of rewards and the objective is to maximize their cumulative sum.

Inthis paper, to overcome these limitations, we propose a new algorithm based on the principle ofoptimism inthefaceofuncertainty.

Inthis paper, to overcome these limitations, we propose a new algorithm based on the principle ofoptimism inthefaceofuncertainty.

The fair-ranking problem, which asks to rank a given set of items to maximize utility subject togroup fairness constraints, has received attention inthe fairness, information retrieval, and machine learning literature.

See also, e.g., [1] fora Bayesianinferenceperspective.

Various results suggest that achieving optimal regret in the fully adversarial sleeping experts problem is computationally hard.

Let D be an unknown distribution on a spaceZ, and let H be a set of classifiers. Consider a (randomized) learning algorithmA = (An)n 1 that selects an elementˆh in H, based onn i.i.d.

However, to obtain the desired effect, the step-size should be chosen sufficiently large, a task which is problem dependent andcanbedifficultinpractice.